Xenharmonic Wiki - User contributions [en]

7afdo

2024-12-28T21:17:18Z

Xenwolf: (improve link)

{{Infobox AFDO|steps=7}}
'''7afdo''' ([[AFDO|arithmetic frequency division of the octave]]), or '''7odo''' ([[otonal division]] of the octave), divides the octave into seven parts of 1/7 each. As a scale it may be known as [[Harmonic mode|mode 7 of the harmonic series]] or the [[Overtone scale#Over-7 scales|Over-7]] scale. As 7 is a small odd number, this AFDO does not contain a perfect fifth or any reasonable approximation to it, and it is relatively poor for its size at creating traditional tonal music.

== Intervals ==
{| class="wikitable center-all"
! #
! Cents
! Ratio
! Decimal
! Interval name
! Audio
|-
| 0
| 0
| [[1/1]]
| 1.0000
| perfect unison
|
|-
| 1
| 231.2
| [[8/7]]
| 1.1429
| supermajor second
| [[File:Jid_8_7_pluck_adu_dr220.mp3]]
|-
| 2
| 435.1
| [[9/7]]
| 1.2857
| supermajor third
| [[File:Jid_9_7_pluck_adu_dr220.mp3]]
|-
| 3
| 617.5
| [[10/7]]
| 1.4286
| high tritone
| [[File:Jid_10_7_pluck_adu_dr220.mp3]]
|-
| 4
| 782.4
| [[11/7]]
| 1.5714
| undecimal minor sixth
| [[File:Jid_11_7_pluck_adu_dr220.mp3]]
|-
| 5
| 933.1
| [[12/7]]
| 1.7143
| supermajor sixth
| [[File:Jid_12_7_pluck_adu_dr220.mp3]]
|-
| 6
| 1071.7
| [[13/7]]
| 1.8571
| tridecimal submajor seventh
| [[File:Jid_13_7_pluck_adu_dr220.mp3]]
|-
| 7
| 1200.0
| [[2/1]]
| 2.0000
| perfect octave
| [[File:Jid_2_1_pluck_adu_dr220.mp3]]
|}

== Scala files ==
* [[Harmd-mix]]
* [[Oheptad]] – same, but starts with 8/7

Now and Xen

2023-02-16T22:53:24Z

Xenwolf: fix typo

[[File:Nowandxen.webp|frame|Logo for the Now and Xen podcast since August 17th, 2022.]]
'''Now and Xen''' (formerly '''Now&Xen''') is a podcast about xenharmonic and microtonal music and discussion created by [[Stephen Weigel]] and [[Sevish]] in 2018.

== Episodes ==
Notes:
* Episode number 12 was skipped on purpose.
* Bonus episodes are only available to patrons of the podcast on Patreon.
{| class="wikitable sortable center-1"
|-
! No. !! Title !! style="width:8em;" | Host(s) !! Guest(s) !! Music artists !! Release date
|-
| 0 || [https://nowandxen.libsyn.com/0edo-pilot Pilot] || rowspan="4" | [[Stephen Weigel]] [[Sevish]] || None || [[Stephen Weigel]] [[Sevish]] || November 25, 2018
|-
| 1 || [https://nowandxen.libsyn.com/episode-11 Software] || None || [[Tony Dubshot]] [[Randy Winchester]] || November 30, 2018
|-
| 2 || [https://nowandxen.libsyn.com/episode-21 Elaine Walker] || [[Elaine Walker]] || [[ZIA]] || December 20, 2018
|-
| 3 || [https://nowandxen.libsyn.com/32-john-chalmers John Chalmers] || [[John Chalmers]] || [[Ivor Darreg]] [[Warren Burt]] || January 24, 2019
|-
| 4 || [https://nowandxen.libsyn.com/400c-jacob-barton-and-chris-bailey Chris Bailey and Jacob Barton] || [[Stephen Weigel]] || [[Christopher Bailey]] [[Jacob Barton]] || [[Christopher Bailey]] [[Jacob Barton]] [[Stephen Weigel]] [[Aaron Krister Johnson]] [[Andrew Heathwaite]] || January 31, 2019
|-
| 5 || [https://nowandxen.libsyn.com/episode-54-jack-tickner Jack Tickner] || rowspan="2" | [[Stephen Weigel]] [[Sevish]] || [[Jack Tickner]] || [[Jack Tickner]] [[Stephen Weigel]] [[Sevish]] [[Stephen James Taylor]] || February 12, 2019
|-
| 6 || [https://nowandxen.libsyn.com/666-cents-neil-haverstick Neil Haverstick] || [[Neil Haverstick]] || [[Neil Haverstick]] || March 11, 2019
|-
| 7 || [https://nowandxen.libsyn.com/74-bruce-hamilton Bruce Hamilton] || [[Stephen Weigel]] || [[Bruce Hamilton]] || [[Bruce Hamilton]] [[Easley Blackwood]] [[Stephen Weigel]] [[Jonathon McCullough]] || March 24, 2019
|-
| 8 || [https://nowandxen.libsyn.com/8910-tolgahan-oulu Tolgahan Çoğulu] || [[Stephen Weigel]] [[Sevish]] || [[Tolgahan Çoğulu]] || [[Tolgahan Çoğulu]] [[Sinan Cem Eroğlu]] [[W. A. Mathieu|William Allaudin Mathieu]] || April 12, 2019
|-
| 9 || [https://nowandxen.libsyn.com/9688-cents-ben-fuhrman Ben Fuhrman] || rowspan="2" | [[Stephen Weigel]] || [[Ben Fuhrman]] || [[Ben Fuhrman]] || April 16, 2019
|-
| 10 || [https://nowandxen.libsyn.com/easley-blackwood10 Easley Blackwood[10]] || [[Easley Blackwood]] || [[Easley Blackwood]] [[Wikipedia:Alexander Scriabin|Alexander Scriabin]] [[Wikipedia:Giles Farnaby|Giles Farnaby]] [[Wikipedia:Nicola Vicentino|Nicola Vicentino]] [[Stephen Weigel]] || May 11, 2019
|-
| 11 || [https://nowandxen.libsyn.com/118-brendan-byrnes Brendan Byrnes] || rowspan="3" | [[Stephen Weigel]], [[Sevish]] || [[Brendan Byrnes]] || [[Brendan Byrnes]] [[Sevish]] || May 11, 2019
|-
| 13 || [https://nowandxen.libsyn.com/1317-the-mercury-tree-0 The Mercury Tree] || [[Ben Spees]] [[Oliver Campbell]] [[Connor Reilly]] [[Jason Yerger]] || [[The Mercury Tree]] [[Brendan Byrnes]] [[Wendy Carlos]] [[ZIA]] [[Sevish]] [[Wikipedia:Jacob Collier|Jacob Collier]] [[Wikipedia:John Stafford Smith|John Stafford Smith]] [[Wikipedia:Eagles (band)|The Eagles]] [[City of the Asleep]] [[Randy Winchester]] || May 31, 2019
|-
| 14 || [https://nowandxen.libsyn.com/149-partch-ensemble PARTCH ensemble] || [[John Schneider]] || [[Harry Partch]] [[Lou Harrison]] [[Ben Johnston]] [[Robert Johnston]] [[Neil Haverstick]] [[John Schneider]] [[Bill Alves]] || June 12, 2019
|-
| 15 || [https://nowandxen.libsyn.com/158-brian-riordan Brian Riordan] || [[Stephen Weigel]] || [[Brian Riordan]] || [[Brian Riordan]] [[Matthew Rosenblum]] [[Aaron Myers-Brooks]] [[Devon Tipp]] [[Per Bloland]] [[Harry Partch]] [[Sam Pluta]] [[Peter Evans]] [[Jim Altieri]] [[Stephen Weigel]] [[Dangdut Cowboys]] [[Rhoma Irama]] || June 25, 2019
|-
| 16 || [https://nowandxen.libsyn.com/quadruple-octave-jude-thomas Jude Thomas] || rowspan="3" | [[Stephen Weigel]], [[Sevish]] || [[Jude Thomas]] || [[Jude Thomas]] [[Wikipedia:Voices of Gotham|Voices of Gotham]] (arr.) [[Löis Lancaster]] [[Wikipedia:Instant Classic|Instant Classic]] (arr.) [[Stephen Weigel]] [[Mileece]] || July 11, 2019
|-
| 17 || [https://nowandxen.libsyn.com/172-dolores-catherino Dolores Catherino] || [[Dolores Catherino]] || [[Dolores Catherino]] [[10cc]] [[Wikipedia:György Ligeti|György Ligeti]] [[Sevish]] || July 31, 2019
|-
| 18 || [https://nowandxen.libsyn.com/18edo-bill-sethares Bill Sethares] || [[Bill Sethares]] [[Kevin Hobby]] (not heard) || [[Carlos Devizia]] [[Giovanni Dettori]] || August 12, 2019
|-
| 19 || [https://nowandxen.libsyn.com/untwelve-19-0 UnTwelve '19] || rowspan="3" | [[Stephen Weigel]] || [[Thomas Scheurich]] [[Christopher Bailey]] [[Jacob Barton]] [[Clem Fortuna]] [[Hans Gunter-Lock]] [[John Jansen]] [[Ashkan Tabatabaie]] [[Nick Osborn]] [[Ari Fiekowsky]] [[Gareth Hearne]] [[Vincenzo Sicurella]] [[Douglas Blumeyer]] || [[Jacob Barton]] [[Nick Osborn]] [[Daniel Lessler]] [[Michael Levy]] [[Christopher Bailey]] [[Gareth Hearne]] [[Douglas Blumeyer]] [[Ashkan Tabatabaie]] [[Wikipedia:Carl Orff|Carl Orff]] [[Stephen Weigel]] [[Hans Gunter-Lock]] [[Andrew Heathwaite]] || August 27, 2019
|-
| 20 || [https://nowandxen.libsyn.com/one-20-eight-tuning-johnny-reinhard Johnny Reinhard] || [[Johnny Reinhard]] || [[Johnny Reinhard]] [[Kite Giedraitis]] [[John C. L. Jansen]] [[Charles Ives]] [[Harry Partch]] [[Michael Hafftka]] [[Jeroen Thesseling]] [[Georg Friedrich Haas]] [[Peter Thoegersen]] [[Anton Rovner]] || September 10, 2019
|-
| 21 || [https://nowandxen.libsyn.com/21-tuning-forks-warren-burt Warren Burt] || [[Warren Burt]] || [[Warren Burt]] [[Wikipedia:John Cage|John Cage]] [[Wikipedia:Lejaren Hiller|Lejaren Hiller]] [[Wikipedia:Charlemagne Palestine|Charlemagne Palestine]] [[Wikipedia:Kenneth Gaburo|Kenneth Gaburo]] || September 30, 2019
|-
| 22 || [https://nowandxen.libsyn.com/22edo-room-talks 22edo Room Talks] || rowspan="2" | [[Stephen Weigel]] [[Jacob Barton]] || [[Brendan Byrnes]] [[Gareth Hearne]] [[Sevish]] [[Thomas Scheurich]] || [[Paul Erlich]] [[Brendan Byrnes]] [[William Lynch]] [[Jacob Barton]] [[Xotla]] [[Sevish]] [[Benyamind]] [[Ivor Darreg]] [[Gareth Hearne]] [[Juhani Nuorvala]] [[Cody Hallenbeck]] [[Hans Straub]] [[Christopher Bailey]] [[Cam Taylor]] [[Thomas Scheurich]] [[Stephen Weigel]] [[Kit Hagerstrom]] [[Vito Sicurella]] [[Redrick Sultan]] [[Cryptic Ruse]] || October 31, 2019
|-
| 23 || [https://nowandxen.libsyn.com/23571113-ji-kyle-gann-0 Kyle Gann] || [[Kyle Gann]] || [[Kyle Gann]] [[Tom Flaherty]] [[Wikipedia:Steve Reich|Steve Reich]] [[John Eaton]] || October 31, 2019
|-
| 24 || [https://nowandxen.libsyn.com/14-tone-reilly-spitzfaden Reilly Spitzfaden] || rowspan="3" | [[Stephen Weigel]] || [[Reilly Spitzfaden]] || [[Reilly Spitzfaden]] || November 12, 2019
|-
| 25 || [https://nowandxen.libsyn.com/25-hz-amanda-cole Amanda Cole] || [[Amanda Cole]] || [[Amanda Cole]] [[Alvin Lucier]] || November 12, 2019
|-
| 26 || [https://nowandxen.libsyn.com/glacier-20-6-venues Christian Klinkenberg] || [[Christian Klinkenberg]] || [[Christian Klinkenberg]] [[Nick Rushton-Givens]] [[Wikipedia:György Ligeti|György Ligeti]] || December 30, 2019
|-
| 27 || [https://nowandxen.libsyn.com/1027-toby-twining-ft-thomas-schuerich-bill-alves Toby Twining (feat. Thomas Scheurich & Bill Alves)] || [[Stephen Weigel]] [[Jacob Barton]] || [[Toby Twining]] [[Thomas Scheurich]] [[Bill Alves]] || [[Toby Twining]] [[Andrew Heathwaite]] || December 31, 2019
|-
| 27B || [https://www.patreon.com/posts/027b-bonus-toby-32885743 BONUS Toby Twining ft. Bill Alves] || rowspan="18" | [[Stephen Weigel]] || [[Toby Twining]] [[Bill Alves]] || [[Toby Twining]] || January 5, 2020
|-
| 28 || [https://nowandxen.libsyn.com/no-2s-or-8s-lis-lancaster Löis Lancaster] || [[Löis Lancaster]] || [[Löis Lancaster]] [[Wikipedia:Caetano Veloso|Caetano Veloso]] [[Wikipedia:Pink Floyd|Pink Floyd]] [[Wikipedia:M.I.A. (rapper)|M.I.A.]] [[Wikipedia:Mr. Bungle|Mr. Bungle]] [[Wikipedia:The Cure|The Cure]] [[Wikipedia:Gentle Giant|Gentle Giant]] [[Wikipedia:Screaming Headless Torsos|Screaming Headless Torsos]] [[Wikipedia:Patife Band|Patife Band]] [[Wikipedia:Fantômas (band)|Fantômas]] [[Wikipedia:Vampire Weekend|Vampire Weekend]] [[Stephen Weigel]] [[Wikipedia:Kassin|Kassin]] [[Wikipedia:David Bowie|David Bowie]] || January 17, 2020
|-
| 28B || [https://www.patreon.com/posts/no-2s-or-8s-lois-33573341 BONUS - Elaine Walker, Löis Lancaster, BP and chill!] || [[Elaine Walker]] [[Löis Lancaster]] || [[Elaine Walker]] [[Stephen Weigel]] [[Löis Lancaster]] || January 30, 2020
|-
| 29 || [https://nowandxen.libsyn.com/29268-cents-kite-giedraitis-aaron-wolf-spencer-hargraves-jacob-collier Kite Giedraitis, Aaron Wolf, Spencer Hargraves] || [[Kite Giedraitis]] [[Aaron Wolf]] [[Spencer Hargraves]] [[Jacob Collier]] (cameo) || [[Aaron Wolf]] [[Jason Yerger]] || January 29, 2020
|-
| 30 || [https://nowandxen.libsyn.com/3030-or-2020-sevish-benyamind-xotla Sevish, benyamind, Xotla] || [[Sevish]] [[benyamind]] [[Xotla]] || [[benyamind]] [[Xotla]] [[Göksel Baktagir]] [[Randy Winchester]] [[Sevish]] [[Stephen Weigel]] [[Aphex Twin]] [[Elaine Walker]] [[Brendan Byrnes]] [[Wikipedia:Adam Neely|Adam Neely]] [[Andrew Heathwaite]] [[Colin McPhee]] || February 11, 2020
|-
| 31 || [https://nowandxen.libsyn.com/miracle31-paul-erlich Paul Erlich] || [[Paul Erlich]] || [[Paul Erlich]] [[Ari Sarkissian]] [[Joseph Pehrson]] [[Herman Miller]] || February 26, 2020
|-
| 31B || [https://www.patreon.com/posts/031b-bonus-paul-34387388 BONUS Paul Erlich #1] || [[Paul Erlich]] || [[Paul Erlich]] || February 27, 2020
|-
| 32 || [https://nowandxen.libsyn.com/32-a-12th-tone-robert-lopez-hanshaw Robert Lopez-Hanshaw] || [[Robert Lopez-Hanshaw]] || [[Robert Lopez-Hanshaw]] [[Aaron Krister Johnson]] || February 27, 2020
|-
| 33 || [https://nowandxen.libsyn.com/033-aaron-krister-johnson Aaron Krister Johnson] || [[Aaron Krister Johnson]] || [[Aaron Krister Johnson]] [[Wikipedia:Jacob Obrecht|Jacob Obrecht]] [[Wikipedia:John Dowland|John Dowland]] [[Stephen Weigel]] [[Wikipedia:Josquin des Prés|Josquin des Prés]] [[Wikipedia:David Cope|David Cope]] [[filtercreed]] || March 22, 2020
|-
| 34 || [https://nowandxen.libsyn.com/034-hunter-ewen Hunter Ewen] || [[Hunter Ewen]] || [[Hunter Ewen]] [[Wikipedia:John Cage|John Cage]] || March 27, 2020
|-
| 34B || [https://www.patreon.com/posts/034b-bonus-synth-35474052 BONUS Synth Time (ft. Vito Sicurella)] || [[Vito Sicurella]] || None? || March 31, 2020
|-
| 35 || [https://nowandxen.libsyn.com/035-kraig-grady Kraig Grady] || [[Kraig Grady]] || [[Clocks and Clouds]] [[Harry Partch]] [[Anaphoria]] || April 12, 2020
|-
| 36 || [https://nowandxen.libsyn.com/036-james-mulvale James Mulvale] || [[James Mulvale]] || [[James Mulvale]] [[Wikipedia:Sufjan Stevens|Sufjan Stevens]] [[Wikipedia:Boards of Canada|Boards of Canada]] [[Elaine Walker]] [[The Rasa]] [[Wikipedia:Jerry Goldsmith|Jerry Goldsmith]] [[Microwave 64]] [[Zhea Erose]] [[Stephen Weigel]] Unknown (from the [[Sagittal Songbook]]){{todo|clarify}} || April 20, 2020
|-
| 37 || [https://nowandxen.libsyn.com/037-isaac-schankler Isaac Schankler] || [[Isaac Schankler]] || [[Isaac Schankler]] [[Wikipedia:Enno Poppe|Enno Poppe]] [[Wikipedia:Gérard Grisey|Gérard Grisey]] [[Kyle Gann]] [[Wikipedia:Ted Hearne|Ted Hearne]] [[Herman Miller]] [[Stephen Weigel]] [[An Exciting Event]] || April 29, 2020
|-
| 37B || [https://www.patreon.com/posts/037b-bonus-36560680 BONUS Brendan Byrnes & Sevish] || [[Brendan Byrnes]] [[Sevish]] || [[Sevish]] [[Brendan Byrnes]] [[Wikipedia:Westminster Chorus|Westminster Chorus]] || April 30, 2020
|-
| 38 || [https://nowandxen.libsyn.com/038-joe-monzo Joe Monzo] || [[Joe Monzo]] || [[Joe Monzo]] [[Wikipedia:The Beatles|The Beatles]] [[Stephen Weigel]] [[Wikipedia:Giovanni Battista Benedetti|Giovanni Battista Benedetti]] || May 29, 2020
|-
| 38B || [https://www.patreon.com/posts/038b-bonus-37660784 BONUS Brendan Byrnes & Elaine Walker] || [[Brendan Byrnes]] [[Elaine Walker]] || [[Elaine Walker]] || May 29, 2020
|-
| 39 || [https://nowandxen.libsyn.com/039-hitomi-shimizu-syzygys Hitomi Shimizu (Syzygys)] || [[Hitomi Shimizu]] || [[Syzygys]] [[Harry Partch]] [http://www.vietnam-guide.com/hanoi/water-puppet-theatre.htm Thang Long Water Puppet Theatre Ensemble] [[Wikipedia:Âşık Veysel|Âşık Veysel]] [[Dolores Catherino]] || May 30, 2020
|-
| 40 || [https://nowandxen.libsyn.com/40edo 🎧👂🔜🖤💗📛🎲🎰🎮🥇🚴🌫👂👂💘] || [[Sevish]] [[Jacob Barton]] || [[Stephen Weigel]] || [[Stephen Weigel]] [[Diamond Doll]] [[Bazil Müzik]] [[Wikipedia:György Ligeti|György Ligeti]] || June 15, 2020
|-
| 41 || [https://nowandxen.libsyn.com/hidekazu-wakabayashi Hidekazu Wakabayashi (微分音チャンネル)] || rowspan="35" | [[Stephen Weigel]] || [[Hidekazu Wakabayashi]] || [[Hidekazu Wakabayashi]] [[Horii Kojiro]] [[Wikipedia:Inti-Illimani|Inti-Illimani]] [[Wikipedia:The Beatles|The Beatles]] [[Wikipedia:Jevetta Steele|Jevetta Steele]] || June 30, 2020
|-
| 41B || [https://www.patreon.com/posts/041b-bonus-what-38813675 BONUS Sevish (What is a microtonalist?)] || [[Sevish]] || [[Stephen Weigel]] [[Sevish]] [[Tony Dubshot]] || June 30, 2020
|-
| 42 || [https://nowandxen.libsyn.com/042-sintel-0 Sintel] || [[Sintel]] || [[Sintel]] [[Wikipedia:Erik Satie|Erik Satie]] [[Wikipedia:Scott Joplin|Scott Joplin]] || July 12, 2020
|-
| 43 || [https://nowandxen.libsyn.com/043-amelia-huff-zhea-erose Amelia Huff (Zhea Erose)] || [[Amelia Huff]] || [[Zhea Erose]] || July 31, 2020
|-
| 43B || [https://www.patreon.com/posts/043b-bonus-huff-39889504 BONUS Amelia Huff (Zhea Erose)] || [[Amelia Huff]] || [[Zhea Erose]] || July 30, 2020
|-
| 44 || [https://nowandxen.libsyn.com/044-paul-dolden Paul Dolden] || [[Paul Dolden]] || [[Paul Dolden]] || August 19, 2020
|-
| 45 || [https://nowandxen.libsyn.com/045-vivian-tylinska Vivian Tylinska] || [[Vivian Tylinska]] || [[Victory Over the Sun]] [[Sevish]] [[Stephen Weigel]] [[Vivian Tylinska]] [[Brendan Byrnes]] [[The Mercury Tree]] [[Jock Tears]] [[Xotla]] || August 25, 2020
|-
| 45B || [https://www.patreon.com/posts/045b-bonus-margo-40877930 BONUS Margo Schulter] [https://www.patreon.com/posts/045b-bonus-margo-40877566 (video)] || [[Margo Schulter]] || [[Margo Schulter]] || August 26, 2020
|-
| 46 || [https://nowandxen.libsyn.com/046-msico-nerd-gustavo-silveira Músico Nerd (Gustavo Silveira)] || [[Gustavo Silveira]] || [[Gustavo Silveira]] || September 12, 2020
|-
| 46B || [https://www.patreon.com/posts/046b-bonus-nerd-41536053 BONUS Músico Nerd microtonal controller!] || [[Gustavo Silveira]] || None || September 12, 2020
|-
| 47 || [https://nowandxen.libsyn.com/047-michael-harrison Michael Harrison] || [[Michael Harrison]] || [[Michael Harrison]] [[LaMonte Young]] Traditional [[Indian]] [[Sharanu Siddhi Vinayaka]] [[Wikipedia:Caroline Shaw|Caroline Shaw]] [[Terry Riley]] || data-sort-value="October 12, 2020" | October 11, 2020 (patrons only) October 12, 2020
|-
| 48 || [https://nowandxen.libsyn.com/048-erica-dal-bassa-soprano-sfogato https://nowandxen.libsyn.com/048-erica-dal-bassa-soprano-sfogato] || [[Erica dal Bassa]] || [[Erica dal Bassa]] || data-sort-value="October 31, 2020" | October 29, 2020 (patrons only) October 31, 2020
|-
| 48B || [https://www.patreon.com/posts/048b-bonus-paul-43352183 BONUS Paul Erlich #2] || [[Paul Erlich]] || [[knowsur]] || October 30, 2020
|-
| 49 || [https://nowandxen.libsyn.com/049-taylor-brook Taylor Brook] || [[Taylor Brook]] || [[Taylor Brook]] [[Wikipedia:James Tenney|James Tenney]] [[Thomas Nicholson]] [[Wikipedia:Georg Friedrich Haas|Georg Friedrich Haas]] || November 12, 2020
|-
| 49B || [https://www.patreon.com/posts/049b-bonus-xotla-44391227 BONUS Sevish, benyamind, Xotla] || [[Sevish]] [[benyamind]] [[Xotla]] || [[Stephen Weigel]] [[Xotla]] [[Elaine Walker]] [[kalleaho]] [[Sevish]] [[Wikipedia:A-ha|A-ha]] || November 27, 2020
|-
| 50 || [https://nowandxen.libsyn.com/050-robin-meiksins Robin Meiksins] || [[Robin Meiksins]] || [[Robin Meiksins]] [[Wikipedia:Brian Ferneyhough|Brian Ferneyhough]] [[Justin Houser]] [[Jacob Barton]] [[Luis Gelgado]] [[Christopher Bailey]] || data-sort-value="November 30, 2020" |November 27, 2020 (patrons only) November 30, 2020
|-
| 51 || [https://nowandxen.libsyn.com/051-dsilton-georg-vogel Dsilton (Georg Vogel)] || [[Georg Vogel]] || [[Dsilton]] [[Georg Vogel]] || December 12, 2020
|-
| 52 || [https://nowandxen.libsyn.com/052-eric-ederer Eric Ederer] || [[Eric Ederer]] || [[Eric Ederer]] || December 29, 2020
|-
| 52B || [https://www.patreon.com/posts/052b-bonus-singh-45589773 BONUS Subhraag Singh] || [[Subhraag Singh]] || [[Subhraag Singh]] || December 30, 2020
|-
| 53 || [https://nowandxen.libsyn.com/053-automatic-microtonal-guitar-tolgahan-oulu Automatic Microtonal Guitar (Tolgahan Çoğulu)] || [[Tolgahan Çoğulu]] || [[Benjamin Barbarič]] [[Âşık Veysel]] [[Tolgahan Çoğulu]] || May 24, 2021
|-
| 53B || [https://www.patreon.com/posts/053b-bonus-do-re-51718514 BONUS arranging Blowin', Do-Re-Mi] || None || [[Stephen Weigel]] [[Wikipedia:Bob Dylan|Bob Dylan]] || May 26, 2021
|-
| 54 || [https://nowandxen.libsyn.com/054-browsers-and-inharmonic-sleep-therapy-sevish browsers and inharmonic sleep therapy (Sevish)] || [[Sevish]] || [[Sevish]] || June 30, 2021
|-
| 54B || [https://www.patreon.com/posts/054b-bonus-peg-53146548 BONUS arranging Bridge, Peg] || None || [[Stephen Weigel]] [[Wikipedia:Simon and Garfunkel|Simon and Garfunkel]] [[Wikipedia:Steely Dan|Steely Dan]] || June 30, 2021
|-
| 55 || [https://nowandxen.libsyn.com/055-hear-between-the-lines Hear Between the Lines] || [[Rami Olsen]] [[Freddi Sturm]] || [[Hear Between the Lines]] [[Wikipedia:John Coltrane|John Coltrane]] [[Stephen Weigel]] [[Wikipedia:Gustav Holst|Gustav Holst]] [[Jacob Collier]] [[The Rasa]] [[Wikipedia:Simon and Garfunkel|Simon and Garfunkel]] [[King Gizzard and the Lizard Wizard]] || data-sort-value="July 30, 2021" |July 15, 2021 (patrons only) July 30, 2021
|-
| 56 || [https://nowandxen.libsyn.com/056-ben-hjertmann-emmalee-hunnicutt Ben Hjertmann & Emmalee Hunnicutt] || [[Ben Hjertmann]] [[Emmalee Hunnicutt]] || [[Ben Hjertmann]] [[Emmalee Hunnicutt]] [[Stephen Weigel]] || November 1, 2021
|-
| 57 || [https://nowandxen.libsyn.com/057-ventifacts Ventifacts] || [[Ben Spees]] [[Damon Waitkus]] || [[Ventifacts]] [[Damon Waitkus]] [[Wikipedia:David Bowie|David Bowie]] Traditional [[Georgian]] || November 12, 2021
|-
| 58 || [https://nowandxen.libsyn.com/058-anna-maria-hefele Anna-Maria Hefele] || [[Anna-Maria Hefele]] || [[Anna-Maria Hefele]] || March 12, 2022
|-
| 58B || [https://www.patreon.com/posts/058b-bonus-63529215 BONUS Lambdoma tuning] || None || None || March 12, 2022
|-
| 59 || [https://nowandxen.libsyn.com/059-stephen-james-taylor Stephen James Taylor] || [[Stephen James Taylor]] || [[Stephen James Taylor]] [[Wikipedia:Béla Bartók|Béla Bartók]] || March 31, 2022
|-
| 60 || [https://nowandxen.libsyn.com/060-aaron-breeze Aaron Breeze] || [[Aaron Breeze]] || [[Aaron Breeze]] Sarah Brand [[Stephen Weigel]] QW4RTZ Tim Robinson || April 12, 2022
|-
| 61 || [https://nowandxen.libsyn.com/061-nicholas-denton-protsack Nicholas Denton Protsack] || [[Nicholas Denton Protsack]] || [[Nicholas Denton Protsack]] Sounds Like Things [[Stephen Weigel]] || April 30, 2022
|-
| 62 || [https://nowandxen.libsyn.com/062-skueue Skueue] || [[Skueue]] || [[Skueue]] [[Wikipedia:Geinoh Yamashirogumi|Geinoh Yamashirogumi]] [[Aphex Twin]] [[Wikipedia:John Coltrane|John Coltrane]] || August 22, 2022
|-
| 63 || [https://nowandxen.libsyn.com/063-acreil acreil] || [[acreil]] || [[acreil]] [[Stephen Weigel]] [[Wikipedia:Bernard Parmegiani|Bernard Parmegiani]] [[Wikipedia:Denis Smalley|Denis Smalley]] || August 29, 2022
|-
| 64 || [https://nowandxen.libsyn.com/064-the-one-footed-bride The One Footed Bride] || [[Taylor Brook]] [[John Schneider]] || [[Taylor Brook]] [[Harry Partch]] [[Ben Johnston]] [[Wikipedia:Bob Dylan|Bob Dylan]] || November 15, 2022
|-
| 65 || [https://nowandxen.libsyn.com/065-aaron-myers-brooks Aaron Myers-Brooks] || [[Aaron Myers-Brooks]] || [[Aaron Myers-Brooks]] || November 28, 2022
|}

== External links ==
* [https://nowandxen.libsyn.com/ Now and Xen on Libsyn]
* [https://www.patreon.com/nowandxen Now and Xen on Patreon]
* [https://www.youtube.com/channel/UCnmYNMpemAIq8DnK5HJ9gsA Now and Xen on YouTube]

[[Category:Podcasts]]

User:Xenwolf/common.css

2023-01-04T06:53:37Z

Xenwolf: remove HEJI font test as it is now added to MediaWiki:Common.css

.sequence-audio-button {
background: #777777;
}
.sequence-audio-button:hover,.sequence-audio-button:active {
cursor: not-allowed;
}

.sequence-audio-button.sequence-audio-valid {
background: #ffffaa;
}
.sequence-audio-button.sequence-audio-valid:hover,.sequence-audio-button.sequence-audio-valid:active {
background: #eeee66;
cursor: pointer;
}

.sequence-audio-button.sequence-audio-playing {
background: #aaffaa;
}
.sequence-audio-button.sequence-audio-playing:hover,.sequence-audio-button.sequence-audio-playing:active {
background: #66ee66;
cursor: progress;
}

.sequence-audio-button.sequence-audio-paused {
background: #ffcc88;
}
.sequence-audio-button.sequence-audio-paused:hover,.sequence-audio-button.sequence-audio-paused:active {
background: #ee9944;
}

.sequence-audio-button.sequence-audio-valid.white-key {
background: #ffffff;
}
.sequence-audio-button.sequence-audio-valid.white-key:hover,.sequence-audio-button.sequence-audio-valid.white-key:active {
background: #ffffaa;
}

.sequence-audio-button.sequence-audio-valid.black-key {
background: #000000;
}
.sequence-audio-button.sequence-audio-valid.black-key:hover,.sequence-audio-button.sequence-audio-valid.black-key:active {
background: #005555;
}

.sequence-audio-button.sequence-audio-invalid {
background: #ffaaaa;
}
.sequence-audio-button.sequence-audio-invalid:hover,.sequence-audio-button.sequence-audio-invalid:active {
background: #ee6666;
cursor: not-allowed;
}

User talk:Xenwolf

2023-01-04T06:52:32Z

Xenwolf: /* Add HEJI font to CSS */ done

{{User:Xenwolf/New-topic reminder}}
== MonoBook issue ==

When in the MonoBook skin, the Search bar is down, so it requires scrolling. [[User:PiotrGrochowski|PiotrGrochowski]] ([[User talk:PiotrGrochowski|talk]]) 11:47, 17 September 2018 (UTC)
: I suggest not to use a user-defined skin. After Wikipedia switched to Vector, MonoBook seems to be no longer maintained by the MediaWiki team. Maybe you can still use MonoBook and change the search bar position via user-defined CSS and/or user-defined JavaScript, but I'm currently not able to help you with this issue. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:27, 17 September 2018 (UTC)
:: That's in [[Special:Preferences]] by the way. [[User:PiotrGrochowski|PiotrGrochowski]] ([[User talk:PiotrGrochowski|talk]]) 14:01, 17 September 2018 (UTC)

A nice advantage of MediaWiki is that broken links are immediately visible, which is helpful in pages like [[EDO#100...199]]. [[User:PiotrGrochowski|PiotrGrochowski]] ([[User talk:PiotrGrochowski|talk]]) 14:01, 17 September 2018 (UTC)
: Absolutely. I even more like the MediaWiki tables, look here for a [[SandBox#Table_Syntax|little table demo]] :) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:09, 17 September 2018 (UTC)

Why is there a site named dev.xen.wiki that copies the xenharmonic articles and uses Timeless as the default skin? What's the point of that site? [[User:PiotrGrochowski|PiotrGrochowski]] ([[User talk:PiotrGrochowski|talk]]) 13:10, 18 September 2018 (UTC)
: It's a test page as it seems, there was a [https://www.facebook.com/groups/xenwiki/permalink/2119836524949007/ poll on Facebook which skin to prefer], it's still open, but a majority for Default (=Vector) is on the horizon. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:28, 18 September 2018 (UTC)

== Why did you ban me?! ==

Allowing any [[list model]] is the exact opposite of a personal opinion! You are so ironic! [[User:PiotrGrochowski|PiotrGrochowski]] ([[User talk:PiotrGrochowski|talk]]) 07:04, 15 October 2018 (UTC)
: Nobody disallows your opinion. But it's extremely disturbing that you tell people working on this wikis for years that they are childish if they use the simplest thing possible to write lists. Maybe it's a misconception to think that MediaWiki is about coding, it's about writing and communication. ''Did you read'' the help pages in [[wikipedia:Help:List|Wikipedia]] or [[mediawikiwiki:Help:List|MediaWiki]]? What do you think about their expertise? They start with simple lists, later they explain HTML-like features, but they try to keep the wiki text as readable as possible and usable in diffs. Most (if not all lists we used in this wiki were simple enough for ''basic lists''). Show me the actual problem that can be solved via [[template:list]] that cannot be solved via * and #. I mean: ''find'' an existing one, not ''construct'' one. I see a problem in very long lines containing a lot of <code><nowiki></li><li></nowiki></code> markup: they are not easy to change and they have a lower signal-to-noise ratio. And this can be solved by basic lists. And as to answer your initial question: You try to invent Conventions for the wiki with a lot of effort and when I tried to correct you about this, you show how fast you can revert my justified changes and tell me that I'm vandalizing the wiki? I have not enough time to play this ''I'm better than you'' game. I have the feeling that you don't read carefully what other people write. Best regards --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:19, 15 October 2018 (UTC)
:: It's true that you are worse than me. You are the one trying to push a personal opinion. All [[list model]]s are equally acceptable and a specific one should not be taught in [[:en:Help:Wiki help]], no matter what advantages it might have. [[User:PiotrGrochowski|PiotrGrochowski]] ([[User talk:PiotrGrochowski|talk]]) 14:42, 15 October 2018 (UTC)
::: I suggest to set up an own page "Help:Links" or "Help:Link" to contain the options <code><nowiki><ul><li></li></ul></nowiki></code> and <code><nowiki><ol><li></li></ol></nowiki></code> as well as your list template(s), provided that they are introduced with realistic use cases not as "just another opinion". Pages with style A ("my pages") and pages with style B ("your pages") without good reason will cause endless future wars, won't it? As for your claim that preferring * and # would show a "personal opinion": you remember your "unofficial poll"? I hope this helps you understand why a help page should start to teach the simplest way first. And when you claim ''"All [[list model]]s are equally acceptable"'', this is wrong. A list template will have limits, and <code><nowiki> </nowiki></code> doesn't build a valid list, right? The HTML list tags are acceptable if they are well structured even in the source code since basically ''everyone'' should be able to edit the wiki not only those who are coding in HTML. Best regards --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 15:37, 15 October 2018 (UTC)
:::: Realistic use cases don't matter. Every single list model is subjectively best, so it's very wrong to include only one in [[:en:Help:Wiki help]]. And all [[list model]]s really are equally acceptable; it's racist to say that a plaintext or defined list model results in an invalid list. And the convention that an edit consisting only of a list model change should not be done is supposed to prevent the edit war bug. [[User:PiotrGrochowski|PiotrGrochowski]] ([[User talk:PiotrGrochowski|talk]]) 16:11, 15 October 2018 (UTC)
::::Maybe [[:en:Help:Wiki help#Lists]] should soft redirect to [[:en:List model]], like [[:dev:Help:Wiki help#Lists]] does? Whatever the final solution may be, it definitely must show all [[list model]]s as possibilities that users may use, with no subjective recommendation or anything. The objective advantages and disadvantages are too specific to be shown in [[:en:Help:Wiki help|the xen.wiki school]], and they can always be found out by users later on, so it's best to state all [[list model]]s neutrally. Can't believe you are complaining while doing worse in [[:en:Help:Wiki help]]. [[User:PiotrGrochowski|PiotrGrochowski]] ([[User talk:PiotrGrochowski|talk]]) 05:17, 16 October 2018 (UTC)

== 11-limit Intervals ==

Hello there, I see that the intervals 55/32 and 64/55 are not present in the chart on the Gallery of Just Intervals page, and I have no idea how to add them as I don't know how to add cells to the chart. As I told Mike Battaglia in a recent email, I've found both 55/32 and 64/55 extremely useful in 11-limit music as they help harmonically bridge the 16/11 fifth. They are made even more useful by the fact that they differ from septimal intervals such as 12/7 and 7/6 by only a Keenanisma. Accordingly, I use them in a 44:55:64 overtonal triads built on the octave-reduced eleventh harmonic of the tonic as a predominant chord, and this is one of the two best 11-limit chords to use for such a purpose as it is clearly distinct from a diminished chord. While this chord is strange-sounding, it can help to evoke a sense of both the strange and wonderful, particularly if followed up by a traditional dominant seventh built on the third harmonic of the tonic. Possible set-ups I've found so far include a 4:5:6 major triad built on the octave-reduced third harmonic, a 10:12:15 minor triad built on the octave-reduced fifth harmonic, a 27:32:40 minor third built on the octave-reduced twenty-seventh harmonic, and of course, the tonic triad itself. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:15, 2 September 2020 (UTC)

Excuse me for the second message, and sorry if your user talk page isn't the right place for having this discussion, but I just found 64/55 on the list on the Gallery of Just Intervals page. However, 55/32 is still missing though, and I still don't know how to add it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:40, 2 September 2020 (UTC)

: I tried to add some of the information (to [[55/32]], [[64/55]], [[Gallery of just intervals]]).
: BTW: Welcome on board, Aura 🙂
: --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:48, 2 September 2020 (UTC)

:: Thanks! I took the time to complete the first sentence of information on [[55/32]], and I added information to [[64/55]] about the triad formed with a 5/4 major third and a 64/55 keenanismic subminor third. I hope you can test this triad out for yourself. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:01, 2 September 2020 (UTC)

== Links on my User Page ==

Hey, I just created an EDO impressions page- with the link at the bottom of my user page. However, the links on my user page need work in general, and I'm not sure how to go about fixing them, let alone getting my work seen on the Table of EDO impressions... Could you spare a moment and help me out? Thanks! --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:56, 4 September 2020 (UTC)
: I [https://en.xen.wiki/index.php?title=User%3AAura&type=revision&diff=48488&oldid=48471 tried my best]. The links are relatively easy to understand. First remember square brackets (double for internal, single for external links). Internal links are automatically built from page titles (the case of the very first character is ignored). External links always start with http(s), the URL part stops at the first space, what follows (before the closing bracket) is taken as display text. Read the whole story under [[Help:Links]]. Have a nice day 🙂 --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:36, 4 September 2020 (UTC)

:: Thanks a ton! Hopefully all I have to do now is study what you did this... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:48, 4 September 2020 (UTC)

== Diatonic Functions of Xenharmonic Intervals ==

Okay, so one thing I'm interested in is covering the diatonic functions of notes at various intervals' distance away from the tonic- you know, for microtonal composers who still want to work with tonality- I honestly think pages like 3/2 and 4/3 could benefit from having information on things like this. On another note, do we have information on the thirty-five 12edo proper modes? Pages documenting these modes would serve to gather variations and alternative tunings for these scales and modes into one place. For the record, I know that in my own microtonal composing, I tend not to go very far from my 12edo roots for reasons detaild in [[A recovering microtonalist's critical reaction to Why Microtonality]], yet, I also can't help but agree with Mike S in his comments in [[Microtonalists critical reaction to a recovering microtonalists critical reaction to Why Microtonaltiy?]] on 7-limit and 11-limit being important- in fact, I would add the 13-limit to his list. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:11, 5 September 2020 (UTC)

: First, I guess that I'm not the right person to ask about ''diatonic functions of notes''. Second, as far as I know there are no pages about the 35 [[12edo]] modes, but it could as well be that I only missed it/them. Third, I didn't compose anything yet. Currently I mostly help others to put information into the wiki ... I really like listening xen music of any kind, I also like "meditating" on intervals, that's why I uploaded several sound examples, especially those in prime limits above 5. But I also know that timbre is very important. BTW: today I discovered that [[11/7]] has a very convincing sound. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:33, 5 September 2020 (UTC)

:: Well, to be fair, you are one of the people who runs this wiki- at least to my knowledge- so you're one of the first people I can think of to ask about even the possibility of adding information to the wiki about the diatonic functions of notes at various intervals away from the tonic- just as a guide to help microtonal composers. Truth be told, I think Mike Battaglia could also be of help in deciding and working on the matter as he's got experience with jazz, but still, it's just as well that I approached you about this because I don't want to put stuff on this wiki if it doesn't belong here. As to whether or not there are pages on the 35 modes of 12edo that are "proper" in the sense mentioned on the [[Periodic scale]] page, I did find a page about what a [[Mode]] is. The reason I brought all this up in the first place is because I've found that in tunings closer to JI, the conventional Ionian, Dorian, Phrygian, Lydian, Mixolydian and Aeolian scales are not simply modes of the same diatonic scale, but rather, differing diatonic scales in their own right on account of using different tunings of their notes relative to one another for the purposes of establishing tonality. Locrian however proves to be an exception to this as according to my calculations, it is still a mode of the Lydian scale if you don't use 77/64 as the minor third above the tonic- I know I myself prefer to use 77/64 as the minor third above the tonic for Locrian as well as for minor scales in general so there's that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:40, 6 September 2020 (UTC)

::: If you wish to add information - including new pages - to the wiki, you are welcome. I'm very interested in learning about your perspective on modes. And should it still happen that you add duplicate information, others will point it out to us.--[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:06, 6 September 2020 (UTC)

:::: Okay, so I've added the page on my diatonic scales, however, it needs a table of contents due to its size... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:12, 6 September 2020 (UTC)

::::: Continuation to the latter on [[User talk:Aura/Aura's Diatonic Scales]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:51, 7 September 2020 (UTC)

== Unnoticeable Comma ==

Okay, so I've recently found an unnoticeable comma- 117440512/117406179- that is only slightly more than half a cent in size. It is the difference between five 33/32 quartertones and a 7/6 subminor third, as well as the difference between six 33/32 quartertones and a 77/64 minor third... I've only seen it mentioned once on this wiki aside from on talk pages- specifically on the page for [[3125edo]]- and I've also been told that it doesn't have a name... Since this unnoticeable comma involves 11-limit quartertones, can we call it the "Quartisma"? If so, then when this comma is tempered out, then can we can call the resulting temperaments "Quartismatic"? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:12, 6 September 2020 (UTC)

I have to ask about the name for the temperaments that temper out this comma because as I mentioned to Inthar on Sam's talk page, the comma's proposed name "Quartisma" comes from "Quarter" and "Schisma" on account of the comma both involving stacks of quartertones and being extremely small itself, and, the name for temperaments that temper out the Schisma is "Schismatic". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:08, 6 September 2020 (UTC)

Never mind about the name for the temperaments now... I think we've settled on the name "Quartismic" for the temperament name. However, now I'm curious... I know that 159edo is the first EDO divisible by 53 to temper out the "Quartisma", however, I also see that 24edo tempers out this interval as well... So that leaves me with questions as to which EDOs temper out the "Quartisma" and which ones don't... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:50, 7 September 2020 (UTC)

: Since you're tempering out a comma in a rank-4 JI subgroup (2.3.7.11), you'll have to find 3 linearly independent (non-contorted) edos (not necessarily using their patent vals) that temper out the comma. None of the other relatively simple edos I can think of (17edo, 26edo, 34edo) do it, though. [[User:IlL|IlL]] ([[User talk:IlL|talk]]) 03:00, 7 September 2020 (UTC)

: Apparently 46edo (using the patent val) does! So the edos that are quartismic are all edos of the form 24A + 46B + 159C, where A, B, C are integers (but the resulting edo might not be a patent val). [[User:IlL|IlL]] ([[User talk:IlL|talk]]) 03:04, 7 September 2020 (UTC)

:: I do know that the page for [[3125edo]] makes mention of the Quartisma by way of it's ratio- 117440512/117406179. However, it's not totally clear from the text on that page whether 3125 actually tempers out the Quartisma or not. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:18, 7 September 2020 (UTC)

::: I believe it does. (It's saying that all the 11 limit commas tempered out by 3125 can be found by taking linear combinations of the commas given.) [[User:IlL|IlL]] ([[User talk:IlL|talk]]) 03:39, 7 September 2020 (UTC)

:::: So that's four different EDOs that temper out the quartisma, and none of these EDOs seem to have the exact same prime factorizations- though 46edo and 24edo do share a prime factor in 2... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:49, 7 September 2020 (UTC)

:::: I have to admit that I don't know all the necessary math for this, it is the patent vals for the intervals 33/32, 7/6 and 77/64 in 24edo and 159edo that make me suspect that these EDOs temper out the quartisma in the first place. It would be nice to confirm these findings with the more rigorous math- however, I'm not in a position to do this as I don't know the right equations and stuff, and chances are that I wouldn't even know the meanings of some of the symbols involved... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:01, 7 September 2020 (UTC)
::::: 3125 = 17*159 + 5*46 + 8*24 so we're ok unless it's a non-patent val of 3125 or something. [It's not about the prime factorization of the edo number, it's about whether the edo is a sum of some number of the edos 24, 46 and 159 or not.] [[User:IlL|IlL]] ([[User talk:IlL|talk]]) 04:17, 7 September 2020 (UTC)
:::::: Okay then... With this knowledge in hand, let's see if we can find other quartismic EDOs... Chances are high that any additional EDOs we find are bound to have ridiculously small step sizes though... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:27, 7 September 2020 (UTC)
:::::: Oh and before we continue, let's take this to your own talk page, shall we, Inthar?

Sorry about blowing up your talk page Xenwolf... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 04:34, 7 September 2020 (UTC)

Have you been following the ongoing discussion on how I've dubbed 117440512/117406179 the "quartisma" and on what EDOs temper it out? I bring this up because when we gather enough data, I'm thinking we should add pages about both the quartisma and the temperaments that result from it being tempered out. That and I hope other people in the microtonal community like the name I've picked... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:19, 8 September 2020 (UTC)

: I, personally, am not a big friend of the name "'''Quartisma'''". Is it really obvious that it comes from "'''Quart'''er tone" and "Sch'''isma'''"? But I do not want to stop you here in any way. Good luck! 🙂 --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:53, 8 September 2020 (UTC)

:: Well, to be frank, even if it isn't obvious, the term "quart" itself often means "quarter"- even if "quart" is dated or even obsolete, see [https://en.wiktionary.org/wiki/quart| this Wiktionary entry]. Besides, "quartertonisma" strikes me as being a bit too long and awkward... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:32, 8 September 2020 (UTC)

Hey Xenwolf, I see you're doing work on microtemperaments right about now. For the record the quartisma is about 0.50619 cents in size, and so tempering it out results in a microtemperament. I figured I'd bring this up while you're at it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:10, 11 September 2020 (UTC)

: Hi Aura, I'm only formally working on redirects and categories (gardening/housekeeping stuff). if you feel that something should be linked or categorized, don't hesitate to do it yourself! (to be honest I'm not an expert in (micro)temperament terminology).
: Best regards --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 17:22, 11 September 2020 (UTC)

== Tridecimal Neutral Intervals ==

I don't know about you, but something tells me we need additional names for 39/32 and 64/39 that reference how they are tridecimal neutral intervals. I know that I personally would prefer to call 39/32 the "Tridecimal Narrow Neutral Third" while calling 16/13 the "Tridecimal Wide Neutral Third". Similarly, I would call 13/8 the "Tridecimal Narrow Neutral Sixth" while calling 64/39 the "Tridecimal Wide Neutral Sixth". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:19, 8 September 2020 (UTC)

: I have nothing against the names you suggest. In the opposite: I'm a bit lost with finding the right name. Please change the pages at your own free discretion. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:43, 8 September 2020 (UTC)

: I suggest small tridecimal neutral third and (large/greater) tridecimal neutral third. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 07:45, 8 September 2020 (UTC)

:: Okay then. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:20, 8 September 2020 (UTC)

== Linking Info on Articles to Relevant Comments on Talk Pages ==

Hello Xenwolf, I just recently modified the page on [[3125edo]] to reflect how it is so far the only EDO known to have been confirmed as tempering out the quartisma prior to me finding out that comma's significance. I can see from the page's history at its current site address that the info on 3125edo tempering out the quartisma has been known at least since 2015 when it was imported here by Gene Ward Smith- or by someone else with the username "genewardsmith" on Wikispaces. However, I certainly can't forget the day I discovered the quartisma's significance, and thus, since the earliest comments about the quartisma's significance on this Wiki are dated September 6th, 2020, I'd like to see this confirmed by means of a link to the relevant discussions on Sam's talkpage and your talkpage. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:54, 9 September 2020 (UTC)

: If you link to talks, it could help to add the permanent link as well (see [https://en.xen.wiki/index.php?title=User_talk:Xenwolf&oldid=49001#Unnoticeable_Comma this example]). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 05:45, 9 September 2020 (UTC)

:: Okay, here's a link to the [https://en.xen.wiki/index.php?title=User_talk:CritDeathX&oldid=48622#Unnoticeable_Commas other relevant comment]... I hope this helps...

== Cantonisma ==

Hey, I just checked the calculations with wolfram alpha, and it turns out that 159edo tempers out the cantonisma- the unnoticeable comma which is the difference between three 14/13 trienthirds and one 5/4 major third. I'm wondering if there should be a page on the cantonisma and those temperaments that temper it out... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:18, 10 September 2020 (UTC)

: Why not? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:16, 10 September 2020 (UTC)

== Classifying Prime Limits by Diatonic Function ==

I have an idea as to how to classify primes based on their functions relative to the tonic, but I don't know if I should modify the [[harmonic limit]] page for this or not. I know I would classify the 2-limit as being the "Pitch Class Prime" in light of how pitches related to the tonic by powers of two naturally seem to our hearing to be the same as the tonic in ways that other primes don't. I would classify the 3-limit and the 5-limit as the "Diatonic Primes" for their key functions in just diatonic and just chromatic music. I would classify the 7-limit, 11-limit and 13-limit as the "Paradiatonic Primes because of their relative ease of use as accidentals in otherwise diatonic keys, and, due to the fact that these relatively low primes can create intervals that can be readily used as alongside diatonic intervals or even as substitutions for them. I'd go on to classify the 17-limit and 19-limit as "Quasidiatonic Primes" owing to the most basic intervals in these families having striking similarities to diatonic intervals, but with greater complexity. I'd then go on to label the 23-limit, the 29-limit, and 31-limit the "Pseudodiatonic Primes" because even though these primes are not diatonic by any stretch, they can still serve as substitutes for the paradiatonic primes in a pinch. Does all this sound like a good idea to you? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:17, 11 September 2020 (UTC)

: I think the [[harmonic limit]] page is a good place for your classification concept (maybe as a section?), but I must say that the classifications (especially the distinction between Quasi and Pseudo) after Paradiatonic look a bit strange (or artificial/sophisticated) to me. In general, I don't believe in such a high precision of the human ear. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:31, 11 September 2020 (UTC)

:: The distincton between "Quasidiatonic Primes" and "Pseudodiatonic Primes" boils down to the fact that the base 17-limit and 19-limit intervals closely resemble diatonic intervals, whereas this is not the case for the 23-limit, 29-limit, and 31-limit. This has the effect of determining how well the related ratios tend to blend in with diatonic harmonies. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:42, 11 September 2020 (UTC)

::: Well, I'm not the one who will draw red lines here. Please add you ideas freely! --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:46, 11 September 2020 (UTC)

:::: Okay Xenwolf, I've posted [[User:Aura/Aura's Ideas of Consonance|my ideas of consonance]], feel free to check this stuff out. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 05:15, 12 September 2020 (UTC)

== Spitting "Quartimic Temperaments" into multiple pages ==

Hey! Given what you are doing, I think it would be best if we split the page "Quartimic Temperaments" into "Quartisma" and "Quartismic Family". The page "Quartisma" would be the page containing the information on the quartisma itself, while the page "Quartismic Family" could contain the information on the various quartismic temperaments. With this in mind, the page "Quartisma" would read as follows:

The '''quartisma''' or '''Saquinlu-azo comma''' is a comma with a ratio of '''117440512/117406179''' and a [[monzo]] of {{monzo|24 -6 0 1 -5}}. It is an [[unnoticeable comma]] of the [[11-limit]]- specifically one of the the 2.9.7.11 subgroup- with a value of approximately 0.50619 cents. The quartisma is significant on account of it being the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third in Just Intonation. The '''quartismic temperament''' or '''Saquinlu-azo temperament''' is the temperament that tempers out this comma, for the list of such temperaments, see [[Quartismic family]].

Of course, while we're in the process of splitting things up, we need to keep the old "Quartimic Temperaments". Once all the data has been retrieved- including the data from the talk pages- then we can delete the old "Quartimic Temperaments" page.

I'd appreciate some help with this. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 13:39, 13 September 2020 (UTC)

: Looks good so far. Would it be okay to just rename the [[Quartismic temperaments]] article into [[Quartismic family]]? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:48, 13 September 2020 (UTC)

:: Actually, yes, but I don't know how to do that... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 13:55, 13 September 2020 (UTC)

::: Done. (Renaming requires organizer rights which you haven't.) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:57, 13 September 2020 (UTC)

:::: [[Quartismic family]] seems to have a good start now. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:22, 13 September 2020 (UTC) PS: I'll be a bit AFK for now.

== Neapolitan Augmented Sixth ==
Hey, Xenwolf, I know I gave [[225/128]] the name "Neapolitan Augmented Sixth" on this wiki on the assumption that there were other people who have also referred to this interval by that same name- even if there's only a handful, as the two [https://en.wikipedia.org/wiki/Neapolitan_scale Neapolitan scales] don't seem to be all that well known by musicians at large. However, I can't help but wonder if I inadvertently coined my own name for 225/128, because I don't personally know of any other people besides me who refer to it by the name "Neapolitan Augmented Sixth". All I know for sure is that the Just Semitone has a ratio of 16/15, and that in any Neapolitan scale, there's an area where two semitones occur consecutively, adding up to a diminished third- the octave complement of this is an augmented sixth. So it stands to reason- at least from what I know- that in any 5-limit just Neapolitan scale, there's an area where two 16/15 semitones occur consecutively, adding up to a 256/225 diminished third, and the octave complement of this is a 225/128 augmented sixth... I just want to know for sure that I'm doing this right and not spreading misinformation... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:35, 16 September 2020 (UTC)

: I don't know if you are right. Let's see if another one knows better ... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:45, 16 September 2020 (UTC)

:: I should point out that if my assumption about the "Neapolitan Augmented Sixth" is correct, however, it might help explain why people say 7/4 is also an augmented sixth, as 7/4 is smaller than 225/128, and the two are equated in marvel temperaments- even though this sort of thing seems to bother Flora. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:46, 16 September 2020 (UTC)

::: I see no problem with intervals serving two (or more) different functions. This is common in [[12edo]], the intervals (on interval pages) are not bound to any temperament or ET. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:51, 16 September 2020 (UTC)

:::: Right then. I guess the secondary name "Neapolitan Augmented Sixth" for 225/128 stays. However, I should also point out that it seems that notes in the region roughly between 256/255 and 7/6 and in the region roughly between 12/7 and 225/128 are the most susceptible to having multiple functions even within the same system. If so, then I guess it's a good thing I labeled the paradiatonic functions of these regions "Varicant" and "Contravaricant", as "Varicant" means "straddling". For the record, if you want to know which region I've labeled what, well, all you have to do is look at the scale's direction of construction, as when you start from the Tonic and travel in this direction, the "Contravaricant" region is the one that's encountered first, with the "Varicant" region being its counterpart. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:59, 16 September 2020 (UTC)

::::: The ''(contra)varicant'' naming seems helpful. Have you maybe an image at hand for it, so your "all you have to do is look" would fit better. I'm really not great at finding/building scales. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:06, 16 September 2020 (UTC)

:::::: I'll be able to do this better once my theory on treble-down tonality and my terminology on [[User:Aura/Aura's Diatonic Scales|these]] [[User:Aura/Aura's Ideas of Consonance|two]] pages become more firmly established, as this sort of theory is largely unique to me at this point. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:16, 16 September 2020 (UTC)

:::::: Do also bear in mind that I'm having to make sure to pick the optimal boundaries for some of the different diatonic and paradiatonic regions at the moment. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:26, 16 September 2020 (UTC)

== Diatonic and Paradiatonic Function Map ==
Hey Xenwolf, remember when you asked for an image for the locations of different diatonic and paradiatonic regions? Well, here it is...

[[File:Diatonic_Function_Map.png]]

I hope you find this helpful... Do bear in mind that this is a preliminary version... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:04, 17 September 2020 (UTC)
: Thanks so much for the image. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:18, 18 September 2020 (UTC)
:: What do you plan on doing with the image? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:02, 18 September 2020 (UTC)
:: Oh, and you're welcome... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:03, 18 September 2020 (UTC)
::: It's interesting to see the regions (zones) and their names and the borders. Concerning the relation to known concepts, it could as well include the positions of some just intervals such as 5/4 or 7/4 (even if they don't ''represent'' zones or zone borders). And, well, the legend is a bit confusing (Where is up and down?). Wouldn't it be less confusing to use ratios below 1.0 for undertones (such as <code>1/2 .. 2/3 .. 3/4 .. 1/1 .. 4/3 .. 3/2 .. 2/1</code>)? And, sorry for so much criticism, could you increase the resolution a bit? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:03, 18 September 2020 (UTC)
:::: I could definitely make a larger chart and show the positions of some of the more well-known intervals. However, I need a good way to really show how Bass-Up contrasts with Treble-Down in terms of structure. The starting point is in the center of the chart as 1/1 is guaranteed to be your initial Tonic- as is 2/1- though I suppose it wouldn't hurt to make that clearer. The reason I used ratios above 1/1 for all intervals regardless of direction is to show distance from the Tonic in the center- I mean, the Dominant really is characterized by being situated at 3/2 away from the Tonic in the direction of construction. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:22, 18 September 2020 (UTC)

Okay, I didn't know that the site wouldn't let me replace the older file with a new version... Let me try and post the newest version for real this time... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 01:12, 19 September 2020 (UTC)

[[File:New_Diatonic_Function_Map.png]]

Very interesting graph. Thanks for sharing. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:50, 20 September 2020 (UTC)

: Thanks, can you make more sense of this graph than you could the earlier version? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:55, 20 September 2020 (UTC)

== Names and functions of 45/44, 55/54 and 33/32==
Hey Xenwolf, I see in your recent creation of the 242/225 article that you said that 45/44 felt like an undecimal chroma to you. You're not the first to say something to that effect, as I myself have called 45/44 the "greater undecimal parachroma" and 55/54 the "lesser undecimal parachroma". That said, since we've also decided that 33/32 is somewhat similar in the sense of having chroma-like properties, and since a "parachroma" is an interval with properties akin to a chroma, only involving primes 7, 11, and thirteen, I think we need to give 33/32 a name that both reflects its parachromatic nature and sets it apart from both 45/44 and 55/54. Do you have any ideas? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:44, 20 September 2020 (UTC)

Just for the record, the only name I can currently think of for 33/32 is the "undecimal parachromatic quartertone". This name contrasts with other more complicated undecimal intervals in the area such as 512/495, which could perhaps be called the "undecimal paradiatonic quartertone"... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:50, 20 September 2020 (UTC)

: I have to admit that this observation is very new to me. I'm not even sure if I didn't mix things up. I need more time for this. BTW: I like the varicant/contravarivant regions of your graph. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:56, 20 September 2020 (UTC)

:: Trust me, you're right about 45/44. I know because I've attempted to use it before in my own compositions. Oh, and thanks for your comments on the graph! --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:58, 20 September 2020 (UTC)

:: If you're worried about whether or not you can use 45/44 in melodies, well, I can assure you from experience that you can use even 64/63 in melodies, and that's even smaller than 45/44. I'd only really be concerned on this front if the interval was smaller than 25 cents. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:03, 20 September 2020 (UTC)

== Names for New Third and Sixth ==
Xenwolf, there's already both a tridecimal minor third in 13/11 and a tridecimal major sixth in 22/13... We need to come up with some better names... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:13, 21 September 2020 (UTC)

I see that this new minor third and new major sixth differ from the old ones by 693/676... Perhaps the new minor third and new major sixth should be named for this comma... That is, once we give it a name... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:15, 21 September 2020 (UTC)

: As to solve this issue, ''any'' suggestion is welcome. I already looked into the [[gallery of just intervals]] and saw the name clashes I caused. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:19, 21 September 2020 (UTC)

: BTW: it can also be that these pages seem useless to you. I must honestly admit that sometimes I simply let myself be driven by curiosity for unusual sounds. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:21, 21 September 2020 (UTC)

:: No problem...

:: Hmm... I have to admit we need a good name for the 693/676 comma... Wait- this is no comma... it has a value of about 42.9985270 cents! --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:36, 21 September 2020 (UTC)

:: Yeah, calling 693/676 a "comma" is a bad idea... I mean, the idea of 33/32 being called a "comma" already bugs me considering it's a very useful quartertone, not something we want to try and temper out- unless of course we're talking about EDOs like 12edo or something... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:41, 21 September 2020 (UTC)

::: Being a comma is not a death sentence for an interval ;) As I learned, we have these ranges: 0 .. 3.5 cents for [[:Category:Unnoticeable comma|unnoticeable]], 3.5 .. 30 cents for "[[:Category:Comma|comma]]", 30 .. 100 cents for [[:Category:Medium comma|medium comma]], and 100 cents and above for [[:Category:Large comma|large commas]]. Especially the "commacity" is another dimension. I'd say even the Tone [[9/8]] is some kind of comma. I think that the higher the limit the more intervals fight for being ''the representative'' of that limit, the classic diatonic nomenclature (minor/major) helps a bit but this is also limited. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:02, 21 September 2020 (UTC)

:::: At the same time, however, only intervals above 25 cents can be reasonably used as melodic intervals, and, the way I see it, commas in the purest sense can't really do that well. Yes, I'm aware that there are limitations to the classic diatonic nomenclature, however, said nomenclature is still needed, even if we must incorporate it into a larger system. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:17, 22 September 2020 (UTC)

: For now, what about "submajor" and "supraminor" for 26/21 and 63/52? Since there is septendecimal submajor third [[21/17]] and septendecimal supraminor third [[17/14]]. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 02:34, 22 September 2020 (UTC)

:: Hmm... I think that might work, but I can't speak for Xenwolf on this... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:58, 22 September 2020 (UTC)

::: Thanks for the help, I changed the names of [[26/21]], [[63/52]], [[104/63]], and [[21/13]] accordingly. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 05:19, 22 September 2020 (UTC)

== MOS scales of various EDOs ==
Hey, Xenwolf, since 159edo now has its own category, should we add [[79MOS 159edo]] to said category? To be fair, I'm also proposing that we link [[31edo MOS scales]] under [[:Category:31edo]] in the same way, and that we do the same for other edos and their MOS scales. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:18, 2 October 2020 (UTC)

: This absolutely makes sense. Just don't be afraid to categorize pages! Categorizing is by no means reserved for organizers only, on the contrary: if you discover that a category is missing or too much, think about how it could be changed and express suggestions for improvement actively (by making appropriate changes). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:26, 2 October 2020 (UTC)

:: PS: (already changed in your comment): Linking categories is of course possible. It's done by placing a colon just after the opening bracket pair, like this <code><nowiki>[[</nowiki>''':'''Category:31edo]]</code>. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:33, 2 October 2020 (UTC)

== Notation for 159edo ==
Excuse me, Xenwolf, I've been waiting for a response from Mike Battaglia on this, but he seems to be busy or something... I'd like to hear what y'all think of this proposed system for notation in 159edo- admittedly the drawing is a bit crude, but all the same, I'd like to know if this combination of mainstream quartertone accidentals, Helmholz notation, and Ups and Downs notation is any good...

[[File:159edo_Notation.png]]

You should notice right away that I'm combining simple accidentals to create composite accidentals- at least this way there aren't so many simple accidentals to memorize, and you won't loose track of all the iterations of the Ups and Downs accidentals... Any thoughts? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:58, 2 October 2020 (UTC)

: It's hard for me to value this: I have little experiences with high-order EDOs (well, I already know that [[53edo]] (=[[159edo|159]]/3) has good approximations of 5-limit ratios). In the image, it's unclear to me where I am at a given tick. However, The idea of combining accidentals seems good to me, provided the (de)composition rules are simple and unambiguous. What about the "grammar" of this system: what kind of music (scales etc.) is this notation supposed to support? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:42, 2 October 2020 (UTC)

:: Well, how should I make it easier for you to keep track of where you are at any given tick?

:: As for what this is supposed to support, I'm looking to support things like different varieties of near-just diatonic scales, as well as near-just harmonic major scales, near-just harmonic minor scales, near-just melodic minor scales, and near-just neapolitan scales. I'm also thinking of supporting of at least two proper 7-limit heptatonic scales with modes and derivatives using supermajor and subminor triads, and I'm also looking to support basic 11-limit music. Basically, I'm trying to make high-order edos like 159edo more accessible to composers with a background in 12edo and 24edo. Still, it's clear that this system needs some work. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:03, 2 October 2020 (UTC)

::: It seems to me that you are searching for a basis (or superset) of actual tonal systems. Do you know [[205edo]], which builds the basis of the [[Hunt System]]? Maybe the theory webpages of the author could be of help for you. About the ticks: you maybe show only the set of accidentals - I searched for the 159 relation in that graph. So the tick distance seem to be <code>1\159</code>, right? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:52, 3 October 2020 (UTC)

:::: The tick distance on that chart is indeed 1\159, and the distance between the larger ticks is one whole tone of 9/8. I feel it's necessary to show the ticks on some level to show how the accidentals relate to one another. That said, I wouldn't mind removing the composite accidentals and only showing the simple accidentals on the chart. That said, the Helmholz arrows indicating the raising or lowering by a syntonic comma seem to need a host accidental in order to even appear to begin with, and the only thing new about their appearance in this chart is that they can now be bound to mainstream quartertone accidentals. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:04, 3 October 2020 (UTC)

::::: There is another issue with the graphics that I should have pointed out a long time ago, I'm sorry it's only now: it's the resolution again: the symbols are to small. I'm trying to make a [[SVG]] image myself of it (right now installing font [http://doc.rhavin.de/MuML/ QMuML9.ttf] that should contain quarter tone accidentals...) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:29, 3 October 2020 (UTC)

:::::: Well, the thing is that I'm not exactly the best one to ask for high-resolution images without large image size seeing as I'm stuck with MS paint for creating images in the first place... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:33, 3 October 2020 (UTC)

:::::: Did I mention that chances are high that one might have difficulty combining the Helmholz syntonic comma arrows with the quartertone accidentals using existing fonts? I mean, the idea of combining these two things together seems fairly new, as Helmholz notation itself has a different symbols for 11-limit demisharps and seems to lack symbols for both 11-limit sesquisharps and sesquiflats... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:38, 3 October 2020 (UTC)

::::::: [MS paint] I guessed that, and that's why I decided to try a version myself (SVG images, supported by the wiki software, can be created with Inkscape, but it's not as easy for beginners, I have some experiences with it). [Did I mention] The font mentioned above was a miss, as was the [https://www.fileformat.info/info/unicode/block/musical_symbols/images.htm Unicode "Musical Symbols Block"], the latter only contains one flavor for quarter-tone accidentals, so I have to pick the ones you use from [https://commons.wikimedia.org/wiki/Category:Quarter_tone_accidentals Wikipedia Commons]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:50, 3 October 2020 (UTC)

:::::::: For the record, MuseScore 3 seems to support both Helmholz notation and the quartertone accidentals I use. However, I'm again confronted with the problem of combining the Helmholtz syntonic comma arrows with the mainstream quartertone accidentals... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:15, 3 October 2020 (UTC)

::::::: PS: please be a bit less agile on your questions/comments. Changing questions afterwards creates edit conflicts to the one who want's to answer (this is the 5th time I try to save my answer). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:50, 3 October 2020 (UTC)

:::::::: Sorry about that... I must confess I feel the need to get the comments and questions down as quickly as possible before I forget about them... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 11:06, 3 October 2020 (UTC)

:::::: I can't believe I forgot about this, but I honestly think that there are other 11-limit chromas that need to be addressed besides just 33/32, as 45/44 and 55/54 seem to also be worth taking account of. Even though I'm in favor of not only making a new version of Helmholtz/Ellis notation in which the current symbol for raising by 33/32 is replaced by the mainstream demi-sharp accidental but also putting the current Helmholtz/Ellis symbol for raising by 33/32 to use in representing one of the other 11-limit chromas instead, the fact is that I don't have the capabilities nor the permissions to do such a thing myself... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:47, 3 October 2020 (UTC)

:[...unindenting...]
I finally got the picture done, as said with Inkscape (originally in SVG format), here is a PNG preview:

[[File:159edo-accidentals.png|640px]]

It's not perfect, but hopefully better to read now. Well, a bit of legend is still missing. Are the accidentals reproduced correctly? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:28, 3 October 2020 (UTC)

: I think that the sharps, flats, naturals, demisharps, demiflats, sesquisharps and sesquiflats are indeed reproduced correctly, as are the Ups-and-Downs-derived accidentals- which I'll simply call up-darts and down-darts. However, when it come to both the Helmholtz syntonic comma arrows, as wells as the Helmholtz septimal accidentals, you might find help in reproducing them by looking at the [[Helmholtz-Ellis_notation|Helmholtz-Ellis notation page]]. On another note, I realized in looking this over that ''I myself'' botched some of the composite accidentals. Specifically, for the composite accidentals comprised of the sesquisharp and the different varieties of down-darts, as the two elements in these composite accidentals should be arranged in the same order as in the combinations of the sesquisharp and the up-darts... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:58, 3 October 2020 (UTC)

:: I reworked the file (same filename, if you don't see changes, force a browser reload). The symbols are now based on the [[HEJI]] SVG we already have. I'd upload the combinations you used for your notation that are not part of HEJI (of quartertone accidentals with syntonic commas). I also started the page [[159edo notation]] with a table that contains inline combinations of some symbols, I hope I counted correctly. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:23, 4 October 2020 (UTC)

::: After I made a few corrections in the table, I checked things over, and I'd definitely say you've counted correctly. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:10, 4 October 2020 (UTC)

:[...unindenting...]
Okay, so, I'm considering the idea of extending the current 159edo notation system to the 13-limit, with this being the highest prime extension due to the 13-limit being the last paradiatonic prime, and the last one that offers something new other than modulation possibilities. However, this would involve further modifying Helmholtz-Ellis notation to better accommodate trientones (one third tones) and stuff such, and I'm also considering other alterations along the same lines- for instance, reviving the original Helmholtz-Ellis 11-limit quartertone glyph and putting it to a different use relative to the 11-limit to represent a raising by [[45/44]], and pairing it with a new symbol to represent a lowering by [[45/44]]. However, I need more feedback on our current 159edo system first, and so far, all I know is that I need to build on the familiar in order to create this notation system, which, if all goes well, can be integrated with an improved version of the SHEFKHED interval naming system that has been extended to 171edo... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:36, 6 October 2020 (UTC)

: I think it is good to have a basis for discussion at all, it does not have to be perfect. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:57, 6 October 2020 (UTC)

:: What do you mean by that? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:00, 6 October 2020 (UTC)

::: I picked out your ''more feedback on our current 159edo system'' because I find that it would be helpful to wait for responses from people who did not participate in the development, like Kite. I'm still not experienced with high-order EDOs. I think all these additional characters reduce the legibility of the notation in a considerable way. When I compare this with the conventional system, say for baroque music, where I casually pick up the accidentals and do not really have to decipher them, also because there is usually only one variant that makes musical sense, I get almost dizzy in our "battle of symbols". In the classic notation, accidentals are not just modifiers for single notes, but signs that indicate the change of the tonal base. I'm still searching for a parallel in alternative tonal systems. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:36, 6 October 2020 (UTC)

:::: You are right in saying that in the classic notation, accidentals are not just modifiers for single notes, but signs that indicate the change of the tonal base. The classical and quartertone accidentals as found in this system actually have the same function, believe it or not- yes, this is even true of the combinations of these accidentals and the syntonic comma arrows. I mean, if Jacob Collier can seamlessly modulate from E-Natrual Major to G-Demisharp Major, I want to know the specifics of the notes he uses, and if changing keys seamlessly like that involves using different tunings for notes, I want to see the tuning changes in action- hence the need for so many accidentals. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:50, 6 October 2020 (UTC)

:::: Nevertheless, we do need feedback from others who did not participate in the development, and I'm hoping that my reasoning for the sheer number of accidentals- namely my need to see tuning changes in action- makes sense to these other people as well. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:08, 6 October 2020 (UTC)

:[...unindenting...]
Hey, Xenwolf, I just realized- the rastma, 243/242, is something akin to an 11-limit version of the syntonic comma... What's more striking is that a stack of three rastmas differs from a syntonic comma by 1771561/1771470, which has a value of only about 0.08893 cents... So, perhaps 243/242 is the interval that we need to consider as a JI basis for the single step of 159edo... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:21, 7 October 2020 (UTC)

So, based on Kite's feedback, I have several proposals for modifying the current Helmholtz-Ellis-based system- see [[Talk:159edo_notation#Dart_symbol(s)|our discussion on dart symbols]]. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:01, 7 October 2020 (UTC)

Xenwolf, do you have time to help me rework our Helmholtz-Ellis-based notations system? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:10, 8 October 2020 (UTC)

: Hardly this time, but it depends on whether there are concrete questions to answer (easy), to discuss topics in their full breadth (hard), or to make glyphs (impossible). For me it's still unclear how your approach relates to [[205edo]] one of Hunt. Did you have a look on it (41x5 leads to a system with a perfect 3-limit approximation and very good to fair approximations of other limits)? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:28, 8 October 2020 (UTC)

:: Okay, firstly, the steps of [[205edo]] are a bit too small, and are likely to blend into one another, whereas 159edo doesn't have that problem as the step size is greater than 7 cents. In comparing the patent vals up to the 17-limit, I can see that the approximations of the 3-limit, 7-limit and 11-limit in [[159edo]] are superior to those of 205edo in terms of absolute error, though the reverse is true when it comes to the 5-limit, the 13-limit and the 17-limit. Considering that the 3-limit is the major diatonic navigational prime for the main key signatures, while the 11-limit is the major paradiatonic navigational prime for things like quartertone key signatures, and that both of these prime limits are significant for the many microtonalists who end up starting with [[24edo]] on account of 24edo being perhaps one the best known microtonal systems, I'd say that 159edo's better performance in these limits is a major factor to be considered, as are the issues with 205edo's smaller stepsize. Are there any other facets of the relationship between my approach to 159edo and Hunt's approach to 205edo that you wish to know about? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:02, 8 October 2020 (UTC)

::: Thanks for having a look into it.
::: You wrote: ''the approximations of the 3-limit, 7-limit and 11-limit in [[159edo]] are superior'' - I guess you mean p-limit intervals here? How do you measure approximation quality (I mean 9/7 is also a 7-limit interval)? I tried this [http://musictheory.zentral.zone/huntsystemcalc.html calculator] but was not satisfied with the idea of averaging. For me it is also still unclear which set of musical intervals can be regarded as sufficiently representative, if such an idea makes sense at all... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:59, 8 October 2020 (UTC)

:::: For the record, that whole phrase reads: ''the approximations of the 3-limit, 7-limit and 11-limit in 159edo are superior to those of 205edo in terms of absolute error''. Long story short, I measure the absolute errors in cents as they accumulate when tempered p-limit intervals are stacked, and the number of such intervals I can stack without the absolute error exceeding an unnoticeable comma's distance of 3.5 cents determines the quality of representation, and thus the portions of the harmonic lattice that can be sufficiently represented by any given EDO. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:44, 8 October 2020 (UTC)

:::: For prime limits that form the backbone of key signature navigation such as the 3-limit and the 11-limit, having a high number of tempered intervals that can be stacked without exceeding an unnoticeable comma's distance of 3.5 cents is actually pretty important. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:52, 8 October 2020 (UTC)

:::: In the case of [[9/7]], we have two prime factors to consider- the 3-limit, and the 7-limit. Now, I can already assure you that you can only use one tempered 7-limit interval max before the absolute error exceeds 3.5 cents, as after [[7/4]], the next interval in the 7-limit chain is [[49/32]], and the difference between the JI version and the 159edo-tempered version exceeds 3.5 cents, and this is also true for the 205edo-tempered version of 49/32. However, when two different EDOs have the same number of intervals of a given p-limit that can be stacked before the absolute error exceeds 3.5 cents, it is the absolute error in cents of the tempered stack relative to the JI equvalent that determines which EDO is superior for representing that p-limit, with the better EDO for representation having the smaller absolute error in cents. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:05, 8 October 2020 (UTC)

:::: Using [http://musictheory.zentral.zone/huntsystemcalc.html the same calculator] that you linked, I tested how 159edo and 205edo each represent this set of intervals- [[3/2]], [[9/8]], [[27/16]], [[81/64]], [[243/128]], [[729/512]], [[5/4]], [[25/16]], [[125/64]], [[625/512]], [[7/4]], [[49/32]], [[343/256]], [[11/8]], [[121/64]], [[13/8]], [[169/128]], [[17/16]] and [[289/256]]- and as I'm forced to limit the interval set somehow, I've decided that the odd-limit of any interval in the set has to be less than 1024. I looked for the number of "P" ratings given by both 205edo and 159edo, as "P" ratings are the only ratings I'm really interested in at this point, and I also looked at their distribution. Both 205edo and 159edo give 7 "P" ratings total out of this set, and are surpassed in this respect by [[147edo]], which has 8. However, one of the P-rated intervals for 147edo is for 343/326, the best approximation of which cannot be reached by stacking three of 147edo's best tempered version of 7/4 and octave reducing, thus resulting in this interval's disqualification. Furthermore, the 147edo-tempered versions of six of the other 7 intervals in the starting interval set given a "P" rating in Hunt's system have absolute errors in cents that are ''greater'' than those of their 159edo-tempered counterparts which are also P-rated- a decisive loss for 147edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:13, 9 October 2020 (UTC)

:::: As for the remaining head to head comparison of 159edo and 205edo in terms of how good their representation is, one of the P-rated intervals for 205edo is 49/32, the best approximation of which cannot be reached by stacking two of 205edo's best tempered version of 7/4 and octave reducing, resulting in this interval's disqualification. Four of 205edo's remaining P-rated intervals are all solidly in the in the 5-limit chain, and another P-rated interval is 17/16- the 205edo-tempered version of which is better than the 159edo-tempered version- the final P-rated interval for 205edo is 3/2, and 159edo-tempered version of this interval has ''less'' absolute error in cents than the 205edo-tempered version, leaving 205edo with only 5 P-rated intervals that are not outperformed by their 159edo counterparts. This means a decisive loss for 205edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 02:40, 9 October 2020 (UTC)

:::: Sorry about the long string of comments... I hope you can get through them all, because I want to know your thoughts on the process I used and my reasoning for choosing 159edo over 205edo. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 03:09, 9 October 2020 (UTC)

:[...unindenting...]
Xenwolf, do you have time to help me remake glyphs and stuff for a new notation system? I want to take the feedback from Sam and Kite into account for this... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:28, 13 October 2020 (UTC)

: That depends on how well you can explain what you need. I think it should be possible to describe a toolbox, graphical elements, layout aspects. A rough sketch might also help to illustrate things. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:46, 13 October 2020 (UTC)

:: Right. I hope my descriptions in the [[Talk:159edo_notation#My_Second_Idea_for_a_Notation_System|new section of the relevant talk page]] can be of help. The only issue I can think of so far is that I need to come up with a good way to represent the rastma... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:01, 13 October 2020 (UTC)

== New Interval Categorizations ==

Continuing our discussion from [[Talk:5/4#"classic"_misleading|the 5/4 talk page]], do you think my proposal for new interval categorizations is at least half decent? I mean, if "classic" is too ambiguous, we need to find better descriptors for intervals like 5/4, don't we? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:56, 9 October 2020 (UTC)

: Sorry, I'm not in the mood to participate in this discussion right now. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 17:36, 9 October 2020 (UTC)

:: Ah. Perhaps we can have this discussion at another time then. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:30, 9 October 2020 (UTC)

== Another Comma ==

Hey Xenwolf, I've found this unnoticeable comma- 1771561/1769472- that marks the difference between three 128/121 semitones and one 32/27 minor third, and I would like to give it a name... Since the 3-limit and the 11-limit are both major navigational primes, I think we can call this comma the "nexusma", or the "nexus comma" or something like that... What do you think? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 06:06, 14 October 2020 (UTC)

: Sorry I don't see how you reach "nexus" here. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:27, 14 October 2020 (UTC)

:: Tempering out 1771561/1769472 leads to the joining of two navigational primes limits- the 3-limit and the 11-limit- and "nexus" means "a connection or series of connections linking two or more things". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:53, 14 October 2020 (UTC)

:: If "nexus" isn't a good basis for a name, what's another term that reflects this joining of two navigational primes? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:39, 14 October 2020 (UTC)

::: If I understand you right, you say 3 and 11 are "navigational primes"; That they are primes is of course already known to me, but I lack any idea what exactly you could mean by "navigational".
::: BTW: your image [[:File:Possible Quartertone Accidentals.png]] looks quite clear to me. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:01, 14 October 2020 (UTC)

:::: Navigational primes are those that lay the groundwork for defining key signatures. The 3-limit defines the primary diatonic key signatures, while the 11-limit defines paradiatonic and secondary diatonic key signatures. While the 5-limit, the 7-limit and the 13-limit also help define key signatures, they only define the exact variant of any given key signature- for instance, in distinguishing an Intense Major key from the standard Pythagorean Major key. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:41, 14 October 2020 (UTC)

:::: Examples of primary diatonic key signatures include C Major, G Major, G-Sharp Minor, B-Flat Minor, and so on. Examples of secondary diatonic key signatures include G-Demisharp Major, F-Demisharp Minor, B-Demiflat Major, and D-Demisharp Minor. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:48, 14 October 2020 (UTC)

So, does my definition of "navigational primes" as per [[User:Aura/Aura%27s_Ideas_on_Tonality#Navigational_Primes_and_the_Parachromatic-Paradiatonic_Contrast|this page]] make sense? If so, does my idea of calling 1771561/1769472 the "nexusma", or the "nexus comma" also make sense? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:27, 15 October 2020 (UTC)

: Yeah, that kind of makes sense. But I'm not fully convinced by the high priority you assign to 11 after 3. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 17:50, 15 October 2020 (UTC)

:: So, anything I need to think about in terms of my reasoning for assigning the 11-limit such a high priority? What are the objections I need to answer? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:06, 15 October 2020 (UTC)

::: I currently have not the time to read and study a lot of text. I read your last additions but maybe not as carefully as you may expect. I have no experience with quartertone music so far, so I probably have difficulties with things that are obvious in your eyes. If I look at it from a mathematical perspective, I only see that the higher the p-limit, the higher the density of fractions between 1 and 2. But please don't let my personal objections stop you from working out your theories in the Wiki. You are welcome to do so in the main namespace of the wiki; it's really not that new pages would have to be created as subpages of the user page and then go through a review process. And I have far too little knowledge of and experience with microtonal music to be a suitable "examiner". --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:35, 15 October 2020 (UTC)

:::: Okay, if that's the case, do you think that Kite and Flora could be of help? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:58, 15 October 2020 (UTC)

::::: I'm not sure. Maybe. Kite does a lot of practical work in microtonality [[41edo]] guitars etc. Flora is new, but seems to have good mathematical skills. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:31, 15 October 2020 (UTC)

::::: Oh yes, regarding [[:File:Possible Quartertone Accidentals.png|the 12 sign symbols you suggested]], I was really close to starting the detail work, but then realized that we have to consider the graphical context. After all, these symbols will be on and between staves, and yet you have to be able to recognize them and distinguish them safely. So this will also make a bit more work. Maybe I'll try a first rough draft showing the 12 symbols in 2 positions each. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:31, 15 October 2020 (UTC)

:::::: Right then. In the meantime, I'd best get to work putting the theory I've come up with here down on the page detailing my Concepts of Tonality... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:35, 15 October 2020 (UTC)

:: All I know in this case is that if the 3-limit is used to assign pitch relations between the standard notes, and you want to have a standard for assigning pitch relations for keys like G-Demisharp Major, which Jacob Collier uses in his rendition of "In the Bleak Midwinter", we need some sort of relatively simple limit by which we can build off of the 3-limit in order to access such keys. Furthermore, we need to ensure maximal separation from the standard keys in a case like this. It may be true that when the rastma isn't tempered out, there's multiple possibilities, but given what I demonstrated on constructing a 9/8 whole tone using just four 11-limit intervals in my recent response to Kite's recent comments on [[Talk:159edo_notation#My_Second_Idea_for_a_Notation System|the talk page for 159edo notation]], I can't help but think that 33/32 is bound to be perhaps the most important among quartertones, especially in light of the one example of a stack of three 33/32 parachromatic quartertones plus a [[4096/3993]] paradiatonic quartertone adding up to a full 9/8 whole tone- you can't get much more straightforward in adding up quartertones than that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:19, 15 October 2020 (UTC)

::: Your Ideas seem interesting and may make sense musically. But the process of underpinning these musically appealing ideas with a solid theoretical foundation seems very complicated and nerve-racking to me. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:35, 15 October 2020 (UTC)

:::: It is a very complicated job, but someone has to do it, and since I work more extensively with the 11-limit than most people here, it looks like that job falls largely to me. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:42, 15 October 2020 (UTC)

:::: If you're looking for a definition of "parachromatic" and "paradiatonic" as it relates to quartertones, let's look at the traditional distinction between "diatonic" and "chromatic" amongst semitones. From my observations so far, two parachromatic quartertones add up to a chromatic semitone, while a parachromatic quartertone and a paradiatonic quartertone add up to make a diatonic semitone. Therefore, it takes three parachromatic quartertones and one paradiatonic quartertone to make a 9/8 whole tone. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:47, 15 October 2020 (UTC)

== Alpharabian Comma ==

Hey Xenwolf, I botched the title of the [[Alpharabian comma]] page, as the word "comma" should not be capitalized. I'm hoping you can fix it. Thanks! --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:15, 16 October 2020 (UTC)

== Link on Nexuma Page ==

Hey, Xenwolf, I figured that when you said the "demonstrably" link on the Nexuma page was questionable, you were talking about the way that link was written, but were you also talking about the content of that link? I asked Kite to look over that particular page to make sure the content there was up to snuff... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:56, 17 October 2020 (UTC)

: I find the linking style questionable, not the referred text.
: Nobody is happy to get a long text to find (theirselves) the answer for a seemingly simple question, so [[User:Aura/Aura's Ideas on Tonality #Navigational Primes and the Parachromatic-Paradiatonic Contrast|this "'demonstrably' trap"]] is (in my opinion) a good example for the problem referred by
:: [https://quoteinvestigator.com/2012/04/28/shorter-letter/ ''If I had more time, I would have written a shorter letter''].
: Well, of course not a big issue, but for me it's kind of important. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:56, 17 October 2020 (UTC)
:: Well, I've never been good with shorter stuff- it doesn't feel like I can say what I need to say in shorter writings. Oh, and the very first sentence of that lengthy page says, and I quote:
:::"It seems that some people in the community want to know how my system relates to the more well-known approach of Aaron Hunt- a simple question with a complicated answer."
:: I must confess, I'm on the Autism spectrum- I have Asperger's specifically- and yes verbose writing like that is classic Asperger's for you... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:13, 17 October 2020 (UTC)

::: Writing/reading is a great tool but it takes time. If we consider that writing time is spent once and reading time is again and again, we understand that it pays off to invest in a great reading experience. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:35, 17 October 2020 (UTC)

:: If someone needs to create a more reader-friendly version of my writings on the not-so-simple subject of music theory, then so be it. In the meantime, I can remove the "demonstrably" link. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:20, 17 October 2020 (UTC)

::: For working together on such ideas, it could be better to place them (maybe in parts) in the article namespace as soon as you feel that you are done with it... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:35, 17 October 2020 (UTC)

::: A small addition: I'm not sure that ''I'' am the only one who is interested in the relation of your system to the Hunt system. (I'm not even sure if the H-System has gained any special popularity at all.) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:50, 17 October 2020 (UTC)

:::: Who else do you think might be interested in my system besides you and Sam? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 05:27, 18 October 2020 (UTC)

::::: I think, it will interest a lot of people if it turns out to be consistent (I have to read [https://en.xen.wiki/index.php?title=User:Aura/Aura%27s_Ideas_on_Tonality&curid=8270&diff=0&oldid=51567 your latest additions (ca. 7000 characters)]) ... ---[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:44, 18 October 2020 (UTC)

== Music in an Approximation of 94edo ==

Hello, Xenwolf, have you noticed how on my user page there are two new songs? I just wondered if you had seen them- they were posted here because they were written in an approximation of 94edo, so there's that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:17, 21 October 2020 (UTC)

: Yes of course, quite nice compositions. Of course you have to stay in the background if it is to serve as music for a computer game or movie. To me, the tonal base mostly sounds close to 12edo - maybe my personal [[JND]] is a lot above average. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 07:05, 22 October 2020 (UTC)

:: It is no surprise that when you work in diatonic keys in other EDOs, you end up with a sound that is close to 12edo, but in this case, the sound is better. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 08:42, 22 October 2020 (UTC)

::: Well, there are some passages where I found the sound not better. I'll give the details later. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:01, 22 October 2020 (UTC)

:::: If you're talking about the parts where I used the grave fifth, well, I have to say that the dissonance of the grave fifth is actually a way of bringing out the functions of a Minor VI chord in Major, as ending the phrase with a dissonant grave fifth really seems to hit home that "we're not done yet". I mean, isn't that kind of the point of a deceptive cadence anyway? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:22, 22 October 2020 (UTC)

:::: On a similar note, dissonance of the fifth on the Major III chord in Minor is a way of preventing the tonicization of that chord as well as giving it more propulsive force. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:28, 22 October 2020 (UTC)

:::: With all that said, I have to admit that at the time I wrote these pieces, I didn't exactly have an appreciation for how the dissonance of the grave fifth affects the flow of the music. It's the same way with the 11-limit chords that I use in these songs. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:43, 22 October 2020 (UTC)

== Contributions ==

Hey, Xenwolf, I can't help but wonder what y'all think of my contributions to both this wiki and to microtonality in general at this point. I mean, I'm pretty new here and here I am seemingly upending stuff with new music theory and what not. Then there's the fact that I talk to people on this wiki ''a lot''... I hope I'm not being disruptive in the wrong sorts of ways... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:15, 29 October 2020 (UTC)

: I think it's all good. I think people are busy with their stuff, so the responses to contents is currently low. If you are on facebook, there are some groups, which are - as I remember - more responsive (I'm not there any more, it's too time wasting). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:22, 29 October 2020 (UTC)

:: Heh, I don't mess with Facebook. I have enough to keep track of on Reddit and Discord... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:28, 29 October 2020 (UTC)

::: Reddit seems me a better place, aren't some of the other xenharmonists active there? I try to restrict my ''social energy'' 😉 here in the Xenwiki. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:39, 29 October 2020 (UTC)

:::: Not going to lie, I don't know who's who on Reddit... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:00, 29 October 2020 (UTC)

== The Song that Started It All for Me ==

Hey, Xenwolf, I've finally gotten the courage to release "Folly of a Drunk"- the piece that started it all. It's now on my user page, and I want to hear what you think of it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:19, 29 October 2020 (UTC)

: Thanks so far, I'll soon take the time to listen to it; right now, I have to do some important (but completely unrelated) stuff. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:41, 29 October 2020 (UTC)

:: Right. I hope to hear what you have to say. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:50, 29 October 2020 (UTC)

:: So, do you have the chance to listen now? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:06, 29 October 2020 (UTC)

::: You should not have mentioned the name Jacob Collier, I did not know him at all, now I spent hours on YouTube and stirred up my whole environment (not to mention the age depression of the amateur musician).
::: I also heard your piece, it has some very interesting twists and turns, but on the other hand it is not easy to follow them. The more ornamental quarter notes for example at the beginning are of course no problem. Unfortunately, where the modulation enters unfamiliar paths, it becomes quite difficult to penetrate acoustically. Certainly these twists and turns seem surprising.But the overall logic is quite difficult for me to understand (also because my ear is very much at home in the range between meantone and Pythagorean tuning), maybe it would help to look into the notes. But the overall logic is quite difficult for me to understand (also because my ear is very much at home in the range between midrange and Pythagorean tuning), maybe it would help to look into the notes.
::: In conclusion, I must admit that I tend to respond more to contemplative pieces (much to the chagrin of my wife, who always has to listen to such "sad things") and your piece starts off in such a cheerful marching rhythm, which is quite a bit of an effort. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:47, 31 October 2020 (UTC)

:::: The song "Folly of a Drunk", is a song that is meant to go along with a scene of a book I'm trying to write. Specifically, as per the name, it goes together with a scene in which a character gets drunk and makes a fool of himself while humming snatches of this same tune- unaware that the song was written in part to basically make fun of the stupid things that drunks do. I hope this make some level of sense. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 12:46, 31 October 2020 (UTC)

::::: I also listened to the tune just now and I agree that melodic quartertones are easy for my ear to follow (albeit I’ll agree with George Secor that as a melodic step quartertone is a bit small and tends to be recognized more as a dynamics feature, like a glide, and not an element of melody; but here that glide-iness AFAIU is just bull’s eye), but the harmonic shifts are sudden and quick and I’m left puzzled but can’t grow an anticipation for harmonic movements. This is easily an effect of that this harmonic system is novel to me and those moves aren’t repeated several times like e. g. Sevish does. Aura, thank you for showing this piece to us, but I’d be glad if maybe in another piece the interesting harmony bits would be exposed in more detail and a bit slower for an untrained ear to follow! :) --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 18:51, 31 October 2020 (UTC)

:::::: Let's be honest, the sudden and quick modulations are a good reflection of a drunk's likelihood of following the first impulse that comes to mind, as well as the possibility of things going from good to either awkward or bad at the drop of a hat.

:::::: Believe it or not, one of the key notes in the modulation, D-Demisharp- the note situated at an 11/8 fourth above the main tonic of A-Natural- actually occurs once in the bass near the end of each major section of the song up until the modulation, and the same chord in which it occurs is actually a simpler and slightly modified version of one of the chords used in the modulation itself. If you want, I'll be happy to make separate practice pieces demonstrating the chord progressions in question. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:32, 31 October 2020 (UTC)

::::::: Yeah, it would be interesting to listen to. --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 19:54, 31 October 2020 (UTC)

:::::::: Right then. Let me get to work on it. For the record, I'll have to put all the elements of the individual chords together for these demos rather than staggering the chords like in the actual song. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:05, 31 October 2020 (UTC)

:::::::: Here's a practice piece containing the key chord progressions of "Folly of a Drunk" that you might have missed due to the speed of the piece... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:26, 1 November 2020 (UTC)

:::::::: [[File:Folly of a Drunk Quartertone Cadences.mp3]]

:::::::: One more thing... At the request of Kite, I've put the score for the song up on my user page, so if you want to check that out, feel free. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 10:52, 1 November 2020 (UTC)

::::::::: Thanks! I decided to move at least my part of the discussion to your page as it doesn’t concern Xenwolf. [[User talk:Aura#Harmony in Folly of a Drunk|Here.]] --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 14:27, 1 November 2020 (UTC)

:::: Xenwolf, I think I can explain the logic of some of the weirder chord progressions in the modulation as well as why they work. One thing I seem to notice is that root motion by 3/2 and 4/3 works musically because of a strong harmonic affiliation. This same mechanism is at play for root motion by 5/4, 8/5, 8/7 and 7/4. On the other hand, root motion by roughly 600 cents also works musically, but by a different mechanism- that of sheer contrast. Root motion by 11/8 and 16/11 essentially brings both mechanisms into play at once- harmonic affiliation because 11/8 and 16/11 are the 11th harmonic and 11th subharmonic respectively, and sheer contrast because these pitches are located between 525 cents and 675 cents. The fact that this works musically is attested to by the number of people who actually find Folly of a Drunk catchy and actually enjoy the strange, unexpected modulation. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:02, 1 November 2020 (UTC)

== How about a page for discussing the current wiki projects and ideas what to do and their state? ==

I have seen such a page on a couple of wikis but now I can’t find how it was called. Something like [[Xenharmonic Wiki:Things to do]] or [[Xenharmonic Wiki:Noticeboard]]? I think a page like that would be good to make a rough list of mechanical mundane tasks a user like me may be able to do. I noticed you added a monzo and other information to an interval page and wondered if there many pages like this to help with. I already thought about writing a code snippet to print an interval’s mathematical stats like monzo formatted with use of this wiki’s templates, if it would be useful. Then it would find a rightful place in a section of this “what’s up now” page.

On minutiae: the page itself might contain concise desctiptions of various things and tasks and have links to subpages dedicated to them where they can be further guided with help messages and specs if needed, discussed on <code>Talk:</code>s etc., and <code>Talk:</code> for the central page would naturally be a place to discuss interesting global movements which one is shy to post right into the central page. (Like, “we need these pages made clearer” doesn’t need any discussion but “we need to style the wiki in Comic Sans” obviously does.)

Though by no means I propose strict organization: first and foremost just a dump of what everyone considers useful and interesting to do together and have help with, and in which manner it’s seen to be to do best, and what useful tools are suggested — all like that.

Anything in that vein. What do you think? (If there’s already a page with that purpose, yay! I didn’t search very thoroughly.) --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 15:18, 5 November 2020 (UTC)

: I fully agree with you in this. There are pages that could have turned into this root page, the one linked in the sidebar as ''[[Xenharmonic Wiki:Conventions|Conventions]]'' is such a thing, but its discussion is quite old. I was also looking for a suitable place where proposals could be published that - after reaching an acceptable positive quota - could turn into conventions. What I think is obvious: all that should take place in the Project namespace ([{{SERVER}}/w/Special:AllPages?from=&to=&namespace=4 ''Xenharmonic Wiki:...'']). Find a good root name for such a community project and we'll start it right now! 🙂 There is already a lot to do, for instance provide support for archiving outdated discussions. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:49, 5 November 2020 (UTC)

:: Cool! Yeah I agree about placing it in XW namespace, as <code>Help:</code> looks like it’s more for established tools, not discussion. So I’ll write something on [[Xenharmonic Wiki:Things to do]], and later if a better name arrives, let it be renamed. --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 17:13, 5 November 2020 (UTC)

::: Great! I am looking forward to joining the project! We will probably have to reintegrate things like [[Migration FAQ]], [[Wikifuture]], and [[Bugs]]/[[Talk:Bugs]] sometime. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 17:23, 5 November 2020 (UTC)

== Previewing math ==

Did you notice previewing on edit doesn’t display math? (Test: <math>\cos\frac{\pi}7</math>.) Looking at the HTML code, it seems MathJax script isn’t added for the editing page. Maybe it can be configured somewhere? (I know it’s possibly excluded when editing because it’s heavy, but maybe that won’t end up as an issue?) --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 15:54, 9 November 2020 (UTC)

: I don't observe that. It takes a bit time, but works (I changed your test for testing: <math>\cos\frac{\pi}{17}</math>). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 15:59, 9 November 2020 (UTC)

:: Oh… :( In my case it shows up as precisely this: <code><nowiki>[math]\cos\frac{\pi}{17}[/math]</nowiki></code>. I’m not sure it can shed some light on the issue but it’s all I have. Checked ad-blocking extensions and found none that could cut MathJax off. I’ll check my wiki preferences, maybe I switched something off unknowingly… (But math shows up normally when I load the page not as a preview, in case I may have written that unclearly.) --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 17:21, 9 November 2020 (UTC)
:: Oops, it gets rendered when the page is loaded normally. Changed to <code><nowiki><no</nowiki>wiki</code>. --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 17:22, 9 November 2020 (UTC)

== Quick Questions ==

Would you mind if I ask several quick questions? At the moment, I have four:

# External links cause rendering of the big margin after the anchor text before next work; it breaks the layout and the look pretty badly. Can it be fixed?
# I found another problem: there is the URL probably registered as the user: ../w/User:Contribution, so it appears in the “Special pages” list. At the same time, the page shows the contributions. Don't you think it needs some fix? — [[User:SAKryukov|SA]] 08:26, 27 November 2020 (UTC)
# The problems with that very bad yet important page MicrotonalInstruments referenced from the main navigation bar: it gives the title header "MicrotonalInstruments", must become "Microtonal Instruments", at the same time, the change should not break possible existing links (redirection?). (I want to wikify this page well because I already put some important fixes. But they go nowhere, because it is mostly dirty HTML inside wiki, not wiki — not maintainable. Before it is wikified, further effort would be a waste of time. I would do it, but not at once, and only when I'm tired of main work, that will require keeping this page "Under construction" for a short period of time.) — [[User:SAKryukov|SA]] 17:44, 27 November 2020 (UTC)
# Do we have a proper place for posting publications, like articles? It seems obvious: no. Say, we have the section "Theory", but no publications can be added to any of the first 3 items, which are already the self-consistent publications, only a new tool can be added to "Useful Tools". But not every publication can be classified as "Theory" or "Tools". So, don't you think we need a section "Articles" or "Publications" referenced from the main toolbar and the page similar to Practice/Instruments, Practice/Software, or Practice/Projects? — [[User:SAKryukov|SA]] 19:19, 27 November 2020 (UTC)

On the MicrotonalInstruments item above: I've found your comment in the history: "please resist any dd-"workarounds" the wiki will get fixed soon". I totally agree. I was about to show to you this kind of work-around, sorry that I make some redundant noise. I'm interested in resolving of the issue with the page name and "MicrotonalInstruments" vs. "Microtonal Instruments". When I have time, I can start to wikify the page without waiting to the fix of externally reference margin and other fixes. Would you agree is the only reasonable way to fix this content is to wikify it first? If I start, could we possibly clash if you do some fixes in parallel? Hope not... — [[User:SAKryukov|SA]] 19:07, 27 November 2020 (UTC)
By the way, I didn't get notification on your comment I mentioned above, just happened to look in the history and see it, even though this page is on my Watchlist. It is supposed to work this way? — [[User:SAKryukov|SA]] 19:07, 27 November 2020 (UTC)

(Just for the record: we do have the history of changes and archiving, but these wiki techniques are badly outdated and not so operational. The civilized approach is the coupling with some appropriate revision control system, the way it is done by GitHub and its embedded Wiki (multiple standards with the default in the form of Markdown). By the way, I'm one of the collaborates at Microsoft Visual Studio Code, the author of Markdown extension written in JavaScript; it does a lot of things related to the document self-consistency, automatic TOC and links with advanced options, and, importantly, does typographic corrections on output, for example, converts --, ---, or "" into typographically correct Unicode, and a lot more, anyway, I got tons of experience with that. These typographical problems are very irritating to me. I examine the possibility of improving things by Mediawiki scripting — not at all sure if it may make sense. First of all, not so unsafe. Then, corrections wiki to wiki is bad: wiki source should remain clear, the corrections should be done on the fly between wiki and resulting HTML rendering, but it may work only globally, not on the per-user basis. Besides, JavaScript is badly outdated here. So, probably nothing would pay off the effort.) — [[User:SAKryukov|SA]] 19:05, 27 November 2020 (UTC)

Thank you! <dd>— [[User:SAKryukov|SA]] ([[User talk:SAKryukov|talk]]), 21:46, 25 November 2020 (UTC)</dd>

: If I understand you correctly, you asking for the space after external links? This is an issue that is seemingly caused by the update. We have to wait for it to be fixed at least until next week, I fear. Unfortunately, I can't tell you more about this. I'm not the maintainer of the wiki nor have access to the configuration, so we have to be patient ... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 23:35, 25 November 2020 (UTC)

:: That's right, after the external links. I will be patient, no problem with that :-). Thank you anyway. I'm an impossible perfectionist and think about changing the layouts in case the problem is permanent. — [[User:SAKryukov|SA]] ([[User talk:SAKryukov|talk]]), 04:57, 26 November 2020 (UTC)

: Yes, there is a user named [[User:Contribution|Contribution]]. It may be confusing sometimes but I think there is nothing to fix. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:53, 27 November 2020 (UTC)

:: I don't know who did it, but I can see that the problem was just fixed completely, maybe even better than I expected. Whoever took care of that matter, I would like to express my full satisfaction. Thank you, people! — [[User:SAKryukov|SA]], ''Wednesday 2020 December 9, 22:00 UTC''

::: Could it really be that you did no browser refresh for such a long time? The issue was already found and fixed on 30 November 2020. There was a configuration issue that caused the CSS being expected in the wrong path. Aura told me around the same day that the problems he reported were gone so I expected you would also observe it. Unfortunately no measures were (or could be?) taken to force a cache invalidation. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:55, 9 December 2020 (UTC)

== To delete ==

Sorry, I created this page by paste "typo", it has to be deleted:
https://en.xen.wiki/w/Pagename
Please, what to do next time if such thing happens? — Thank you. — [[User:SAKryukov|SA]] 03:08, 28 November 2020 (UTC)

: Deletion done. In cases like this, place <code><nowiki>{{delete}}</nowiki></code> into the page and describe why in the summary, this way it will be listed in [[:Category:Pages nominated for deletion]]. The details may change in future to support an accessible discussion for the more difficult cases. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:43, 28 November 2020 (UTC)
: PS: sorry to bother again: what you are doing by indenting your signature might look great for you but decreases the usability for others. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:43, 28 November 2020 (UTC)

:: Thank you for the deletion. After you've done it, I've found this procedure in the documentation. — [[User:SAKryukov|SA]], ''Wednesday 2020 December 9, 06:21 UTC''

:: The indented signature? First, this is my old style, so I'm using a different template now, more compliant with your view on it, but... Then please explain what's wrong with the indented signature? I happened to indent it again, recently, but that was an ''ad hoc'' use in a special case: the last word in my post was the internal link to an existing page, so I found it inappropriate to have the signature on the same line referencing content unrelated to me. If you think this is wrong, what should be better? I do agree that simplicity and clarity has higher priority, but what's wrong with an extra indent, in the situation when pages are all stuffed with many of them? — [[User:SAKryukov|SA]], ''Wednesday 2020 December 9, 06:28 UTC''

== Space Tour ==

Hey Wolf, I've recently completed a massive 20-minute-long song called "Space Tour", and it's now available on my userpage. I hope you like it! --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 19:16, 3 December 2020 (UTC)

: Just listening. What I hear is great so far, thanks a lot for sharing. Reading the story is still on my todo list. BTW: great audio background for checking the last changes in the wiki. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:27, 3 December 2020 (UTC)

:: So Wolf, have you finished listening to the whole song? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 22:22, 3 December 2020 (UTC)

::: Of course. More than once. Maybe you should post it on a platform (SoundCloud?) where you can earn likes and reposts for it. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 23:40, 3 December 2020 (UTC)

:::: How about a link on Reddit? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:42, 3 December 2020 (UTC)

::::: Wha not, but I'm not the right person to ask, since I'm not active there. On SoundCloud I am --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 23:48, 3 December 2020 (UTC)

:: Thanks! You'll find the section between 13:19 and 14:32 to be quite intense though. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:29, 3 December 2020 (UTC)

::: Really interesting, but it doesn't stop there. It would be good to know which EDO is used where. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:40, 3 December 2020 (UTC)

:::: It's all in a near-perfect approximation of 159edo, but this EDO is mimicking other EDOs at different times, so there's that. So, I guess I'll have to highlight which parts of the song mimic which EDOs, including the transitions. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:47, 3 December 2020 (UTC)

:::: There you go, Wolf, I've added the info on which EDO is used and or mimicked in which parts of the song. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:19, 3 December 2020 (UTC)

::::: Thanks. But maybe it could be even more helpful in the song description ([[:File:Space Tour.mp3#Summary]]). The upload summary (cut if too long) gets transformed into the section "Summary" which can be edited later in the usual way. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:26, 3 December 2020 (UTC)

:::::: There, I've added the EDO-mimicry information to the #Summary section. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:35, 3 December 2020 (UTC)

:::::: Oh, and thanks for the info about how to alter the summaries of files. I needed that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:38, 3 December 2020 (UTC)

== User Categories ==

Since I am in the [https://en.wikipedia.org/wiki/Eastern_Time_Zone Eastern Time Zone], I think we need to add my user page to the correct categoy. I'm also a native speaker of English, though I do engage in conlanging. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:42, 8 December 2020 (UTC)

: Absolutely. Until now we only had UTC±%d-categories, but this is sub-optimal if you live in a time zone that implements DST. So I added new time zone categories right now [[:Category:User in EST/EDT]], which should meet your requirements and [[:Category:User in CET/CEST]] where I will move my user page now, more will follow at request. Maybe also [[:Category:User on Discord]] could be interesting to you - would you think this is the correct name? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 17:12, 8 December 2020 (UTC)

:: [[:Category:User on Discord]] is definitly an interesting category, though so far it seems only me and Arseniiv are there at the moment. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:32, 8 December 2020 (UTC)

: Ah, here is also [[:Category:User en-N]]. To add your user page to this category, place <code><nowiki>[[Category:User en-N]]</nowiki></code> into it (without the ''code'' and ''nowiki'' formatting). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 17:17, 8 December 2020 (UTC)

:: Right --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:32, 8 December 2020 (UTC)

::: There is also no user in en-N, but the categories don't reflect the truth. Nobody is forced to add their user page to one of these categories, but I think it would be helpful to have some more grouping information. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 17:35, 8 December 2020 (UTC)

:::: Well, I added my user profile to en-N, so that's one. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:37, 8 December 2020 (UTC)

::::: Great :) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 17:41, 8 December 2020 (UTC)

:::::: Thanks. For the record, it seems that [[:Category:User on facebook]] needs to be moved to [[:Category:User on Facebook]], though I guess we should make double sure before making this move. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:44, 8 December 2020 (UTC)

== Posting on the same page in parallel ==

I noticed that when I post on some page, and another participant is doing the same on the same page in parallel, sometimes I lose my new fragment of text. I assumed that I simply don't follow some correct order of operation. Any advice? — thank you! — [[User:SAKryukov|SA]], ''Wednesday 2020 December 9, 05:38 UTC''

: Well, edit conflicts sometimes happen, especially when the other person doesn't know about what you're doing. It's not your fault, at least to my knowledge. Xenwolf may know more, but in some respects, I doubt he'd say something much different that what I'm saying here. The only other thing he'd probably say is something to the effect that rapid chats are better kept to platforms like Discord and Facebook and Reddit. Unfortunately, as I've mentioned to him, I don't have Facebook and many of the microtonalists that I'm aware of do. Hopefully once we expand to Discord, this problem will be at least partially taken care of. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 05:44, 9 December 2020 (UTC)

: I should have also mentioned that Xenwolf has also suggested that to me that I type out what I want to say on a separate document and correct it there before I post here in the User Talk pages, but I have to admit I'd sooner see more chats on Discord. If Xenwolf has anything to add to this, especially if it's stuff I don't know about or have forgotten about, then he should respond to us himself, but since I'm not an admin, I wouldn't know. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 05:54, 9 December 2020 (UTC)

:: Yes, a separate document. It's worse than I thought, as I assumed I've done something inaccurately, but you say it's not the reason. Yes, a separate document is what I actually do, but I thought there is a really correct way. In the Wiki systems I worked with, such conflicts are well resolved. — [[User:SAKryukov|SA]], ''Wednesday 2020 December 9, 06:10 UTC''

::: It is? Well, chances are it's just a matter of poor timing then. I do know that when I've been on the receiving end of edit conflicts where I lose my text there is a procedure to make sure your text gets in- look to see what you typed as opposed to what the other person typed, and then see if you can insert your text into the edit window in the correct spot without deleting the other person's text. If there are any more details that need to be resolved, or elements of the procedure that need a better explanation, Xenwolf should know about them. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 06:13, 9 December 2020 (UTC)

Sorry for the confusion Wolf, could you perhaps walk SA through the procedure of how to deal with those edit conflicts in which it's your own comments that get lost? I now think that advice for that particular scenario is what SA was asking for initially, but I misunderstood him as asking about why it is that some edit conflicts happen and why they eliminate one person's comments at one time and the other person's comments at another time. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 07:06, 9 December 2020 (UTC)

: The wiki software is not a valid forum or chat surrogate. It's optimized for collaboratively editing content. There is a chat linked in the side bar, maybe this could be populated to, but others may be even better. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:49, 9 December 2020 (UTC)
: Edit conflicts typically happen if editors work through an intended plan save by save, but this plan isn't visible to others. The wiki software ''traditionally''(see below) detects conflicts by comparing the base revision of your edit with the last saved revision. In case the last save was after you started editing, you get a warning when you hit [Save changes], this warning includes two boxes, the upper is the text of you collision "opponent", the lower is your text. You may now resolve the conflict by hand. I personally prefer to copy my text before saving (especially in talks with Aura, no offense intended, I just do it, also in other circumstances on other MediaWiki-based wikis). Another option is to copy your changes from the lower box into the upper box, then save it, than apply the "opponent's" edit by help of the history (this option has the downside that others already saw your edit and will probably try the same in parallel). You can (and perhaps should) deliberately provoke an editing conflict by performing two edits in the described manner on a personal page (i.e. in your own user namespace) with two browser tabs. This way the aspects will be much clearer to you than from my dry description. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:49, 9 December 2020 (UTC)
: I know that there are platforms that are much better in formal conflict resolution (i.e. merging edits), especially the git-based wiki solutions. But this doesn't help here. MediaWiki has many advantages but as a community project itself it's road map looks somewhat unprofessional to developers new to it. (BTW: they'll move to [[GitLab]] soon) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:49, 9 December 2020 (UTC)
: I said ''traditionally'' because the wiki software obviously had improvements in this aspect. I know of "edit conflicts" that have been silently resolved maybe in other sections, maybe if the line distance is higher than one. After the upgrade to 1.35, also the change diffs look different than before, that is, more helpful. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:49, 9 December 2020 (UTC)

== SoundCloud ==

Thank you for suggesting to look into SoundCloud!

I only want to have the links for those who see this site for the first time, as in my case:
: [[SoundCloud|SoundCloud]]
: — [[User:SAKryukov|SA]], ''Wednesday 2020 December 9, 06:03 UTC''

:: Sorry, it's not clear to me what you you are trying to say. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:14, 9 December 2020 (UTC)

== Island Comma a.k.a. Parizeksma‎ ==

Hey, Xenwolf, it appears that the name "parizeksma" is rather well known among the Japanese-speaking members of the Xenharmonic community. Perhaps we should create a corresponding page on 676/675 for the Japanese version of this Wiki- or at least talk to one of the users who can. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:07, 20 December 2020 (UTC)

: Interesting. But I'm not sure if we will find someone who is able to start this Japanese page who is currently active. Did you think of [[User:Triethylamine]]? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:18, 20 December 2020 (UTC)

:: Yes, and I am in fact trying to message them. However, it seems Triethylamine doesn't understand English- so I used Google translate to translate my messages to them. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:21, 20 December 2020 (UTC)

:: Since we seem to be on the subject of translating stuff to other languages, do you think we could work together to translate some of my stuff in to German as well? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:28, 20 December 2020 (UTC)

::: We could try. I think you should also have a look on [https://www.deepl.com/home DeepL] (a Germany-based service that turned out to be really good for translating between German and English and vice versa). The question is what would be the best place for the German translations. Maybe [https://de.xen.wiki/w/Hauptseite the German Xenwiki]? If you register there, I'll approve the account. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:44, 20 December 2020 (UTC)

:::: Truth be told, I don't know much German at all, so even though the German Xenwiki is the best place for this information, we'll have to talk through the text we want to put there. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:59, 20 December 2020 (UTC)

:::: I've made the application there. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:05, 20 December 2020 (UTC)

:::: I didn't follow the link in time to get confirmed as I needed to translate. Sorry about that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:10, 20 December 2020 (UTC)

:::: When I try to follow the link, it now says: "Invalid confirmation code. The confirmation period may have passed. Please try to repeat the confirmation." --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:12, 20 December 2020 (UTC)

:::: In German, the page says: "Ungültiger Bestätigungscode. Möglicherweise ist der Bestätigungszeitraum verstrichen. Versuche bitte, die Bestätigung zu wiederholen." --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:14, 20 December 2020 (UTC)

::::: Not sure, what happened, I accepted the account request. Please try again! --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:24, 20 December 2020 (UTC)

::::: You may try the same name, don't forget to add a valid email address. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:27, 20 December 2020 (UTC)

:::::: Okay, so that's fixed, now I seem to have mistyped my password for the German Xenwiki and I now need to get it corrected. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:28, 20 December 2020 (UTC)

::::::: Please try again. Your account is (again) [[:de:User:Aura]] --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:32, 20 December 2020 (UTC)

:::::::: Okay, I'm in. I guess I have to be careful how I type. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:34, 20 December 2020 (UTC)

:::::::: I'm curious now. How do I provide an interwiki link between my user pages? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:36, 20 December 2020 (UTC)

::::::::: Interwiki links are made by adding the language prefix <code><nowiki>[[en:User:Aura]]</nowiki></code> or <code><nowiki>[[de:User:Aura]]</nowiki></code> (these are shown outside the content area) and normal links <code><nowiki>[[:en:User:Aura]]</nowiki></code> or <code><nowiki>[[:de:User:Aura]]</nowiki></code> --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:53, 20 December 2020 (UTC)

:::::::::: Okay, so, since we're both on both Wikis I need to know how to properly apply what you're saying here. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:52, 20 December 2020 (UTC)

:::::::::: The only thing I could think of to do was to copy the interwiki code from your user page to mine. I hope you don't mind. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:59, 20 December 2020 (UTC)

== Concept translations from English to German ==

Hey, Xenwolf, it looks like we've managed to translate "Antitonic" in to German as "Antitonika". I hope we can get to some of these other concepts of mine soon. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:47, 20 December 2020 (UTC)

: Well, I'm not totally sure if this is the exact translation. But let's see... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 23:50, 20 December 2020 (UTC)

:: Well, according to what I'm seeing, the Tonic is either 1) the first note of a diatonic scale; the keynote, or 2) the triad built on the tonic note, while "Tonika" is the name for the root note of a scale and the triad on this first level. Since notes that I'm calling "Antitonics" are notes that harmonically oppose the Tonic due to being in the vicinity of 600 cents away from the Tonic (hence the "anti-" prefix), and the various types of chords that I'm referring to as "Antitonic chords" are those that are built on Antitonic notes, it really does make sense to translate "Antitonic" as "Antitonika". That said, "Antitonika" is likely a new term for German- you won't find it elsewhere with comparable meaning since it's used to translate "Antitonic", and I can't even find the musical sense of that English term on Wiktionary- it is likely that I actually coined the term "Antitonic" in English as far as any sort of musical sense goes. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 00:09, 21 December 2020 (UTC)

:: As to some of the other terms, I can only assume that "Contralead", and "Contramediant" best translate into German as "Kontraleitton", a "Kontramediante" respectively on the basis of "Lead" and "Mediant" translating to "Leitton" and "Mediante" respectively. However, although the term "Subdominant" from traditional music theory translates to "Subdominante", the idea of Treble-Down tonality forces a terminological shift- while the traditional term "Subdominant" translates to "Subdominante", the fact that the corresponding function occurs on the note above the Dominant ("Dominante" in German) in Treble-Down tonality means this perfect fourth scale degree has to be renamed- thus, "Serviant", which is my new term for the perfect fourth scale degree, translates to "Serviante" in German. While "Doppeldominante" from German translates to English as "Supertonic" in traditional music theory, and "Doppelsubdominante" likewise translates to "Subtonic", the problems are twofold- in English, "Supertonic" refers to the note located a whole tone above the Tonic, while "Subtonic" refers to the note located a whole tone below the Tonic, and simultaneously, the term "Doppelsubdominante" needs to be replaced by the term "Doppelserviante" due to the existence of Treble-Down tonality. Therefore, in Treble-Down tonality, "Supertonic" translates to "Doppelserviante" and "Subtonic" translates to "Doppeldominante". As to the terms "Varicant" and "Contravaricant"- which you seem to have taken a fancy to- those terms would most likely translate into German as "Varicante" and "Kontravaricante". Similarly, "Semiserviant" and "Semidominant" translate to "Semiserviante" and "Semidominante" respectively. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 01:06, 21 December 2020 (UTC)

== 6250/6237 ==

I can't find the name of this comma in the Huygens-Fokker Foundation's list of intervals. I think we need to come up with a name for it. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:36, 21 December 2020 (UTC)

: Well, seems so. But have you an idea what [[6250/6237]] means, how is it tempered out, if it is even relevant? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 23:48, 21 December 2020 (UTC)

:: Okay, let me look at this comma some and see what I can find out. I already can tell that this comma is relevant considering that it involves the whole 11-limit. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:20, 23 December 2020 (UTC)

:: So, I just ran the numbers through Wolfram Alpha, and it seems that 6250/6237 is tempered out by both 53edo and 159edo despite their differing patent vals for both 7 and 11. It also seems that 6250/6237 is only slightly smaller than Mercator's comma at 3.60472 cents. It appears that when this comma is tempered out, [[160/77]]- which is the difference between [[5/2]] and [[77/64]]- is equated with a stack of four [[6/5]] minor thirds, and a stack of five [[5/4]] major thirds is equated with a stack consisting of an [[octave]] plus [[81/64]] plus [[77/64]]. Upon further calculations, it appears that 6250/6237 is also the difference between the [[keenanisma]] and the [[kleisma]], as well as the difference between the keenanisma and the undecimal hemifourths comma (160083/160000; needs a better name). Moreover, I've found that 6250/6237 is also the difference between the [[amity comma]] and the [[symbiosma|symbiotic comma]], as well as the sum of the [[lehmerisma]] and the wizardharry comma (4000/3993). --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:27, 23 December 2020 (UTC)

:: Let's also run this by Flora and see what she thinks. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:11, 23 December 2020 (UTC)

:: Hey, Xenwolf, I hope you like the name "liganellus comma" for 6250/6237. I know that Flora doesn't like me attaching the "-ma" suffix to the "u" in words like "nexuma" and "liganelluma", but as I told her, "sm" clusters are sometimes prone to becoming pronounced like "spm", and this is even true for words like "small"- which I'm liable to pronounce as [ˈspmɑɫ]- and I don't want to end up pronouncing "nexma" as [ˈnæ̠kspmə]. Meanwhile, I don't know of a single case in Latin where a double "l" is followed directly by an "m". I hope that makes sense for why I pick some of the names I pick for commas. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:10, 25 December 2020 (UTC)

::: I think the name is okay. But I think the argument to prevent the possibility of mispronunciation is rather weak in a global community. The question for me would be how to correctly build English names from ''liganellus'', for example why not ''liganellic''? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:43, 25 December 2020 (UTC)

:::: Well, it is what it is. As to how to correctly build English names from words like "nexus" and "liganellus", "liganellic" makes sense for a good adjective corresponding to "liganellus", but the right adjective for "nexus" would be "nexal"- yes, "nexal" is a word in English that means "relating to a nexus". --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:46, 25 December 2020 (UTC)

:::: Anyway, should I change "nexuma" and "liganelluma" to something else, and move the "nexuma" page accordingly? I know we can keep the names "nexus comma" and "liganellus comma", but still. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:53, 25 December 2020 (UTC)

:::: Hmm... would "nexisma" be a good replacement for "nexuma"? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:57, 25 December 2020 (UTC)

:::: I just realized something- although the argument to prevent the possibility of mispronunciation may be rather weak in a global community on account of the need for translingual names, it is not entirely without merits, as language-specific names for certain intervals are known to exist. Therfore, the name "nexuma" doesn't have to be replaced- rather, it can be noted in the article as purely an English-exclusive alternate name. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 18:24, 26 December 2020 (UTC)

== Comma Tables on 53edo and 159edo pages ==

Hey, Xenwolf, I've been trying to go through the list of commas to find out which commas are tempered out by 53edo and 159edo, and I'm starting to think that a comma table would be useful for both pages. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:18, 23 December 2020 (UTC)

== 625/624 ==

Hey, Xenwolf, I've found another comma that seems to need a name- [[625/624]]. This comma seems to be like the liganellus comma in that it binds well-known temperaments together- in this case, Catakleismic, Tritikleismic, Quadritikleismic, Octoid, Benediction, Sqrtphi, Ekadash, Countercata, Widefourth, Portentious, Yajna, Enlil, Hanuman, Marvel and Agni. Since this comma seems to be used so much, so on one hand, I could see the name reflecting its usage in extensions. On the other hand, I do see that tempering out this comma not only equates [[25/24]] with [[26/25]], splitting [[13/12]] in half and going part of the way towards splitting the [[9/8]] whole tone into three (the other comma needing to be tempered in order to finish the job being 676/675), but also equates [[39/32]] with the interval that results from stacking four [[5/4]] major thirds then octave-reducing. With all this in mind, perhaps we should call this comma the "vinctrias comma". Any thoughts? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:33, 26 December 2020 (UTC)

Never mind, it Looks like 625/624 is already called the "tunbarsma". Talk about an embarassing case of "open mouth and insert foot". I still like the name "vinctrias" though, so perhaps that name can be given to the temperament that tempers out 625/624 and 676/675. Sorry about all of this mess. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 23:56, 26 December 2020 (UTC)

== 936/935 ==

Hey, Xenwolf, I now know that all 13-limit superparticular commas have been named, but is the same thing true with all the 17-limit superparticulars? If not, I'm thinking 936/935 needs a name. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:52, 28 December 2020 (UTC)

: Sorry, I don't see an urgent need (compare [[Special:WhatLinksHere/936/935]]). If you really find names that clarify things, there will be nobody to disagree. In other words, I find it rather boring and also not very purposeful to discuss mediocre names. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:27, 28 December 2020 (UTC)

== Telicity ==

Hey, Xenwolf, I'm trying to iron out the kinks in my concept of "telicity", and I'm wondering if we should actually make an article on it. So far, here's what I have:

'''Telicity''' is a property of [[EDO]]s, which involves the given EDO being able to stack a number of instances of a given prime's [[patent interval]] to connect with an interval belonging to a chain created by lower prime's [[patent interval]] without either accumulating 50% relative error or more at any point in the process on the part of either prime's interval chain, or, creating as mismatch in results between the [[direct mapping]] and the more complicated traditional mapping for any interval along the chain. Furthermore, since the 2-prime simply results in manifestations of the [[unison]] at different registers, thus leading to things like [[octave reduction]], the 2-prime is not a factor that affects what qualifies as telicity ''unless'' an interval in 2-prime chain itself serves as the target of a higher prime's interval chain.

Given this definition, two things are immediately evident. Firstly, any sort of telicity involving the 2-prime cannot afford to temper out commas greater than half an EDO-step in size due to the unison being such a foundational interval to both EDOs and JI, and, the resultant inability to temper out commas greater than half a step in size without exceeding the 50% relative error threshold. Secondly, the only type of telicity available to the 3-prime is 3-to-2 telicity, as 2 is the only positive prime lower than 3, and since octave equivalency renders the unison as the only available target, that means that the 3-prime requires a complete [[circle of fifths]] without accumulating 50% relative error or more. However, higher primes have more options for achieving a form of telicity as there are multiple lower primes to chose from to potentially connect with, For instance, the 5-prime has both 5-to-3 and 5-to-2 telicity available to it.

Combinations of primes are more complicated, but it's safe to say that there are more types of telicity available in such cases- namely "full telicity" and "partial telicity". Full telicity for combinations involving multiple primes occurs when the EDO in question is able to stack a number of instances of a given combination's patent interval to connect with an interval belonging to a chain created by the patent interval for a prime that is lower than the lowest prime in the initial combination after octave reduction is taken into account. In contrast, partial telicity for combinations involving multiple primes occurs when the EDO in question is able to stack a number of instances of a given combination's patent interval to connect with an interval belonging to a chain created by the patent interval for a prime that is lower than the highest prime in the initial combination after octave reduction is taken into account.

Given that different EDOs can temper out different commas to achieve the same type of telicity- for example, [[12edo]] tempers out the [[Pythagorean comma]] to achieve 3-to-2 telicity, while [[53edo]] tempers out [[Mercator's comma]] to achieve 3-to-2 telicity- it can thus be argued that sequences of different EDOs demonstrating one or more types of telicity can be compiled. For instance, the first seven EDOs to demonstrate 3-to-2 telicity specifically are {{EDOs| 2, 5, 12, 24, 53, 106, 159 }}.

Any thoughts? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 17:46, 19 January 2021 (UTC)

: I think it's best you just start the article and then we discuss any questions or issues that may arise together on its talk page. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:02, 19 January 2021 (UTC)

== How do I make a template compatible with tables? ==

I just made the template ''User:FloraC/Collapsed box'', but it breaks whenever a table is present. I suppose you know how to resolve it.

You might want to check my sandbox and comment on my latest tests. The template ''temperament data'' is something similar to infobox interval and et. The ''collapsed box'' is nothing but a general formatting device. Let me know if either of them makes anything better. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 05:59, 31 January 2021 (UTC)

: The problem occurs whenever pipe chars (<code><nowiki>|</nowiki></code>) are passed to a template. Replacing pipes by <code><nowiki>{{!}}</nowiki></code> each will solve the problem, see following example:
<div style="margin-left: 1.5em; padding: 0 0.5em; border: 1px solid #ddf; background-color: #fafafa">
{{User:FloraC/Collapsed box
| title="bla"
| text=
{{{!}} class="wikitable"
! head1
! head2
{{!}}-
{{!}} cell1
{{!}} cell2
{{!}}-
{{!}} cell3
{{!}} cell4
{{!}}}
}}
</div>
: This, of course, defeats the idea of making collapsible content easier to write. If we'd automatically produce ''Approximate ratios'' from mapping and odd-limit, this could be solved by generating HTML tables with Lua. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:29, 31 January 2021 (UTC)

== Audio file types ==

I noticed that an internal link on the previously uploaded .mp3 file renders a nice player on the referencing page, which is often used on this site for presenting music pieces and illustrations.

What audio (or other media) file types are supported in the same way? I would mostly care about Opus in its own container.
These days, the most usable Web standard is Opus, and it provides the best combination of compression, quality, and latency. MP3 is not open source and was rendered obsolete more than a decade ago. It can be clearly seen in the Web video.

And what about other types? — [[User:SAKryukov|SA]], ''Monday 2021 February 15, 18:23 UTC''

: If you go onto the upload page, you'll see a list of file types that are supported (<code>png, gif, jpg, jpeg, webp, mid, mov, scl, mp3, mus2, ogg, pdf, rtf, svg, wav, wma, xlsx, zip, mscz, flac, mkv, mp4, oga, ogv, webm</code>). I saw that Wikipedia (Commons) also has <code>opus</code> in this list, but did not find any example. So it's hard to see how a/the web player might look. Can you show a live example in some other wiki? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:00, 17 February 2021 (UTC)

:: Thank you. The list of files is pretty good , but Opus is missing :-) It's very good that WebP and WebM are supported, they are currently the best and SVG is extremely important, I already knew it is supported well. No, I don't know examples on other Wiki, I only know how MP3 works. It's just I tried to ask instead of trying out. If referencing MP3 is rendered as a standard HTML5 audio element, it would be reasonable to expect that the same thing happens to, say, Ogg, but I cannot be quite sure. — [[User:SAKryukov|SA]], ''Wednesday 2021 February 17, 18:51 UTC''

::: I requested the addition of opus to the list and it seems that this will be implemented soon. But it of course doesn't make much sense if nobody actually uses it. I expected you would already have some pieces to upload? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:35, 18 February 2021 (UTC)

== Cannot see watchlist notifications anymore ==

I used to have the notifications, but I found some latest updates on the pages I watch — they did not trigger the notifications. Could you point out what could be wrong? Thank you — [[User:SAKryukov|SA]], ''Monday 2021 February 15, 18:30 UTC''

: I think you are talking about email notifications about changes on pages you watch. A notification is sent with the first change only and then gets muted until you visit the page again. In the notification, there are two links: one showing the diff for the change itself, one for the diff between the state before that change and the current state. This is what I know about the mediawiki notification system. I personally don't use email notification on this wiki, maybe I should switch it on to see if there is an issue. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 07:34, 17 February 2021 (UTC)

:: As I see now, there is no switch about email notifications in the preferences? Do you actually receive email notifications? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:05, 17 February 2021 (UTC)

::: Well, not recently. For example, I did not receive a notification on your post to this section. — [[User:SAKryukov|SA]], ''Wednesday 2021 February 17, 17:03 UTC''

:::: As I found out, there was no email notification. It is due to limitations of the email service being used. You may consider to use [[Wikipedia:Atom (Web standard)|Atom]] for this which is available for recent changes, and watchlist and some other pages. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:39, 18 February 2021 (UTC)

== Request to review my improvement on a template ==

I made a version of ''Template:Wedgie'' currently as ''User:FloraC/Multival'', with the inclusion of legend and selection of number of bracket pairs as in ''User:Arseniiv/Val'''. I hope this will make for a fair replacement. Just make sure there's no overlooked aspects.

Btw shall we deprecate ''Template:OEIS'' since "OEIS" is a valid interwiki prefix? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 04:00, 10 March 2021 (UTC)

: The template looks quite okay whereas I suggest to implement the number of brackets by a named parameter, something like <code>brackets=3</code> or <code>levels=3</code> or <code>pairs=3</code>. This way nobody will be confused about the order of parameters. I observe that 1 to 4 pairs are supported. Since I still don't understand wedgies and multivals: comes this limitation with the concept itself or is it due to the template? As a side note, the need of such paired switch statements in the template is the exact purpose for having modules enabled in this wiki... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:07, 10 March 2021 (UTC)

:: I'll make it a <code>rank=3</code>. I think not supporting more pairs beyond four is due to both the definition of the wedgie and the implementation of the template. More pairs are reasonable through logical extrapolation, but practically it looks rather unwieldy (proportionally to the template itself), and I believe some alternative notations should come to help in those cases. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:08, 10 March 2021 (UTC)

:: I doubt they'll become practical any time soon but higher-dimensional wedgies are in principle possible (for rank 5 and higher temperaments). [[User:IlL|Inthar]] ([[User talk:IlL|talk]]) 15:08, 10 March 2021 (UTC)

: I think [[Template:OEIS]] is fine as it has prefix with the link to clarify what OEIS means. So I'd not recommend to deprecate one of the two ways to link to sequences. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:07, 10 March 2021 (UTC)

:: Let's integrate the interwiki link into the OEIS template. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:08, 10 March 2021 (UTC)

::: That's a good idea. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:47, 10 March 2021 (UTC)

== May I request a new username? ==

Can I create a new account that I can name more "accessibly" (like "User:Inthar") instead of the current abstruse one? [[User:IlL|Inthar]] ([[User talk:IlL|talk]]) 23:50, 12 April 2021 (UTC)

: In fact I already thought about exactly that. It should be possible. I'll read a bit about it first, and after that, do it. Do you know that this will be result in a redirect from the old name to the new one (which I find makes sense)? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 05:55, 13 April 2021 (UTC)

:: Yes, that would be okay. [[User:IlL|Inthar]] ([[User talk:IlL|talk]]) 05:57, 13 April 2021 (UTC)

::: All should be done now (including renaming of pages and talk in the user namespace). :) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:07, 13 April 2021 (UTC)

:::: Thanks [[User:IlL|Inthar]] ([[User talk:IlL|talk]]) 06:23, 13 April 2021 (UTC)

== Comma Names, and a Preexisting Chart ==

Hey, Xenwolf, I haven't been able to get in touch with [[User:Spt3125|Spt3125]], and they seem to be the one to have [[User:Spt3125/R2_2.3.11|first documented]] the existence Nexus comma, the Alpharabian comma and the Betarabian comma, even though they didn't name said commas. I don't know if this person is on Facebook or what. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 01:48, 14 April 2021 (UTC)

I'm hoping that Sept3125 doesn't mind me naming the commas as I did in their absence... --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 01:49, 14 April 2021 (UTC)

: I'm pretty sure you are using the wrong user name, try [[User:Spt3125]] instead. However, I don't think there will be any problem with the naming of commas. Let's just see how it plays out, it is a wiki after all. :) Best regards --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 07:02, 14 April 2021 (UTC)

:: Thanks for the correction! --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:08, 14 April 2021 (UTC)

::: You should be able to [https://en.xen.wiki/w/Special:EmailUser/Spt3125 contact Spt3125 via wikimail], did you already try this? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 09:32, 15 April 2021 (UTC)

:::: Thanks for the tip! Done. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:16, 15 April 2021 (UTC)

== Proposal: prefer rewording to adding redirects ==

I'm deleting ''meantone-family'' since I've reworded the article so that it no longer involves the hyphen. I don't reckon Wikipedia would add a redirect whenever there's such a phrase to be linked, so we perhaps should follow. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 14:04, 10 June 2021 (UTC)

: Okay, I agree with you. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:29, 10 June 2021 (UTC)

== 11- and 13-limit coditone temperament ==

I revised technical data for 11- and 13-limit [[Ditonmic family #Coditone|coditone]] temperament. The coditone temperament can be described as '''50&53 temperament''' for 7, 11, and 13 prime limits, tempering out 225/224, 351/350, 385/384, and 847/845 in the 13-limit (with wedgie of {{Multival|13 2 30 -19 -5 …}} on 13-limit). I get information of coditone temperament from [http://www.huygens-fokker.org/docs/lintemps.html List of temperaments] in [http://www.huygens-fokker.org/scala Scala] and [http://x31eq.com/cgi-bin/rt.cgi?ets=50+53&limit=13 13-limit Coditone] in [http://x31eq.com/temper/ Temperament finding scripts]. I renamed "coditonic" for 11-limit 3de&53 and 13-limit 3def&53 temperaments (with wedgie of {{Multival|13 2 30 34 48 …}} on 13-limit) on 10 June 2021. Deal? --[[User:Xenllium|Xenllium]] ([[User talk:Xenllium|talk]]) 10:50, 11 June 2021 (UTC)

: Hi Xenllium,
: I'm afraid I can't help you in this matter.
: My problem is based on the way mathematicians use (their) language: Brevity they perceive as supreme and as pure beauty. But exactly this point leads into a disastrous didactics: between "initiates" and "novices" there is a huge gap that can only be overcome with pain (and most of this pain is endured by the novices).
: I've been successful in programming for about 3 decades now, and in a wide variety of languages, most of which take up much more space than mathematical notation (yes, I've also tried Haskell, which seemed to me a promising contribution to the fusion of the two worlds, but unfortunately also takes a bit more time than I've - so far - been able to spend on it).
: So, conversely, I would be grateful if you could pass on to me some of the mathematical knowledge you clearly have. My services in return could be in the areas of MediaWikis (syntax, templates) and Lua modules.
: I think with your current problem Flora could help you or Mike Battaglia or Cmloegcmluin, maybe also Inthar or Aura. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:25, 11 June 2021 (UTC)

: I think 11-limit coditone was meant to be 50 & 53, as in the temperament finder. The original data on this wiki could be a mistake. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 05:55, 12 June 2021 (UTC)

== Discord link should be on sidebar ==

I think the Discord would probably be a more useful resource than the currently inactive IRC chat. [[User:Inthar|Inthar]] ([[User talk:Inthar|talk]]) 19:02, 2 July 2021 (UTC)

: Sounds reasonable, what is this link? You know than I'm not on Discord. I'll be now, again, away for a couple of hours, you may add it to [[:Category:User on Discord]] or ask [[User:FloraC|FloraC]] to add it to [[MediaWiki:Sidebar]] (maybe between FB and IRC). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:26, 2 July 2021 (UTC)

:: https://discord.com/invite/FSF5JFT is the discord link, FloraC wasn't authorized to make the edit. --[[User:Xenoindex|Xenoindex]] ([[User talk:Xenoindex|talk]]) 12:12, 3 July 2021 (UTC)

::: I see, thanks Xenoindex for letting me know. What would you suggest as text? What's the group name? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:30, 3 July 2021 (UTC)

:::: "XA Discord" would be perfect. --[[User:Xenoindex|Xenoindex]] ([[User talk:Xenoindex|talk]]) 12:38, 3 July 2021 (UTC)

::::: Thanks, done. Let me know if there are any problems. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:44, 3 July 2021 (UTC)

:::::: We got a problem, the link doesn't show on the main page for logged out users. But, it does show on some special pages for some reason. --[[User:Xenoindex|Xenoindex]] ([[User talk:Xenoindex|talk]]) 13:43, 3 July 2021 (UTC)

::::::: FloraC is currently working on it. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 15:21, 3 July 2021 (UTC)

:::::::: We've figured out what the problem was, the wiki caches need to be purged as they are loading older versions of pages. I managed to do this on the main page by appending "?action=purge" to the URL and clicking the purge button but many other pages remain without the discord link unless someone purges or edits them. A mass-purge of all caches explained here: https://www.mediawiki.org/wiki/Manual:Interface/Sidebar#Troubleshooting should resolve the problem completely. --[[User:Xenoindex|Xenoindex]] ([[User talk:Xenoindex|talk]]) 08:16, 4 July 2021 (UTC)

::::::::: Thanks for letting me know, so a temporary problem. Please give me an example where the sidebar is the old one. To me, all seem to be correct (I tried [[Special:Random|Random page]] which is also part of the sidebar). Maybe it's just your browser cache? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 11:20, 4 July 2021 (UTC)

:::::::::: [[18edo]], [[14/9]], and [[21/16]] each have the old sidebar as of writing this message, they may appear correct if any of the pages have since been edited. I found these particular examples by hitting random page while logged out. Be sure to check while logged out, all sidebars appear correct to users who are logged in for some reason. Also, I know it's not my browser cache because I get the same result on an alternate browser I don't use. --[[User:Xenoindex|Xenoindex]] ([[User talk:Xenoindex|talk]]) 11:54, 4 July 2021 (UTC)

::::::::::: Please try the following on one of them: click on edit, then save it without doing an actual change. If the sidebar was incorrect before, is it correct after? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:07, 4 July 2021 (UTC)

:::::::::::: Saving a change without changing anything doesn't register as an actual change so I made a small change to [[14/9]] and yes it did correct it. --[[User:Xenoindex|Xenoindex]] ([[User talk:Xenoindex|talk]]) 13:48, 4 July 2021 (UTC)

::::::::::::: What do you mean by ''“register as”''? Pressing "Save changes" without changing anything ''is'' possible, I just tried it. That an actual change causes a purge was expected. Please try it again. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:36, 4 July 2021 (UTC)

:::::::::::::: Just tried it again on [[21/16]] and it didn't appear to correct the sidebar, and by register I meant that it doesn't show up in recent changes or otherwise appear to do anything. --[[User:Xenoindex|Xenoindex]] ([[User talk:Xenoindex|talk]]) 14:41, 4 July 2021 (UTC)

::::::::::::::: I see, thanks for testing. So we must wait for [[User:Tyler Henthorn]] to fix it. I already informed him via E-Mail about the issue. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 15:11, 4 July 2021 (UTC)

:::::::::::::::: After hitting random page a couple hundred times while logged out I can't seem to find any pages with old sidebars. Not sure what happened back there but I'm calling this problem solved. Thank you for all your help, XA Discord will be happy about this. --[[User:Xenoindex|Xenoindex]] ([[User talk:Xenoindex|talk]]) 15:27, 4 July 2021 (UTC)

::::::::::::::::: This is what Tyler told me: ''“I deleted and rebuilt the file cache as a quick fix.”'' I think that's what worked in the end. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:11, 4 July 2021 (UTC)

::::: PS: FloraC now has the required privileges. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:46, 3 July 2021 (UTC)

== EDO vs. edo (and MOS vs. mos) ==

Hey Xenwolf. Last week, I added a topic on [https://en.xen.wiki/w/Xenharmonic_Wiki_talk:Conventions Xenharmonic Wiki talk: Conventions] and I thought you might be interested to have a look, since it is related to some page renaming you did the week before. If you'd like, we can discuss over there. --[[User: Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 03:34, 12 July 2021 (UTC)

: I think that this is not only a matter of taste and easy writing. I'll come back to this topic soon. Meanwhile I'm not forcing any of the directions but sticking to the old Nedo format will obviously do no harm. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 05:30, 12 July 2021 (UTC) PS: please sign your contributions on talk pages with <code><nowiki>--~~~~</nowiki></code> this automatically adds your name and a timestamp

:: I'm not very happy with the combination of both discussions. I'd tend to do discuss it term by term. I'll add some thoughts concerning ''EDO'' vs. ''edo'' in [[Xenharmonic Wiki talk:Conventions #EDO vs. edo (and MOS vs. mos)]] but don't know if some of them can be extrapolated to ''MOS'' vs. ''mos''. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:31, 12 July 2021 (UTC)

== My Second System for 159edo Notation ==

Hey, Xenwolf, have you seen the accidentals I finally came up with for Quartertones, Rastmas and Syntonic Commas? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:49, 15 July 2021 (UTC)

: I saw it right now. Looks interesting but a lot of symbols and combinations to learn. I think I would not be able to keep all of them in mind. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:03, 15 July 2021 (UTC)

:: I'm afraid some of that's unavoidable due to the size of 159edo and the need for accessibility by those not familiar with 53edo. That said, it's still a huge improvement over my first proposed system, as there's only sixteen additional symbols besides the traditional natural, sharp, flat, double sharp and double flat, as opposed to the multiple dozen additional symbols from the first round. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:24, 15 July 2021 (UTC)

== Regular Temperament Sections Disappearing ==

For some reason, I can't see the regular temperament sections of the pages when I'm logged out, and Shift-Refresh doesn't seem to be helping. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 13:56, 16 July 2021 (UTC)

Beyond that, I just added another comma to the list of commas tempered out by 159edo, and I can't see that comma on the list after logging out either, and again Shift-Refresh doesn't seem to be helping. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 14:35, 16 July 2021 (UTC)

: I tried to open some pages in Edge and observe that parts of pages don't appear (marked with '''cut''') while on some other pages all seem to be correct (marked by ''okay''): [[157edo]] '''cut''', [[28edo]] ''okay'', [[103edo]] '''cut''', [[104edo]] ''okay'', [[176edo]] '''cut'''. Can you confirm the observations for this list? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:44, 16 July 2021 (UTC)

:: I can confirm your observations for 157edo, and 176edo easily, though I've noticed that after logging in on Edge, all the parts of the pages seem to be present, while things are missing from these pages after logging out even using Google Chrome. I'm not quite sure what's missing from 103edo after logging out since I'm not quite as familiar with the contents of that page, but both of the pages that you've marked "okay" pages seem to be fine after logging out. I've also noticed that the list of prime harmonics on the 159edo page is in the wrong place after logging out- it's on the page, but in a different spot. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 15:38, 16 July 2021 (UTC)

::: It looks like a cache issue. Pages of the [https://en.xen.wiki/w/Special:AllPages?from=&to=&namespace=0 article namespace] (also called <code>(main)</code>) are not showing additions after [https://en.xen.wiki/index.php?title=MediaWiki%3ASidebar&type=revision&diff=73749&oldid=73598 13:06, 5 July 2021]. There are some exceptions for '''''moved''''' or '''''newly created''''' pages which I don't understand right now. I think that's something that should be reported to [[User:Tyler Henthorn]]. Unfortunately I have currently not the time to do it... --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 15:50, 16 July 2021 (UTC)

:::: I now reported the issue via PM to Tyler. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:25, 16 July 2021 (UTC)

== Suggested change to edo pages: odd harmonics instead of primes in edo approximation tables ==

Hello Xenwolf,

We (including [[User:SupahstarSaga]], [[User:Fredg999]] and I) would like to resurrect [[Xenharmonic_Wiki:Things_to_do#Odd_harmonics_table_instead_of_prime_harmonics_for_edos|an old suggestion of mine]], namely using odds instead of primes. This is because odd mappings give more information at a glance than primes: odd harmonic mappings don't always correspond to prime mappings (for example, a stack of two best 3's don't always make the best 9), and subgroup interpretations can sometimes care about ratios between odds harmonics, for example, 7/5 and 11/5. I made a template implementing this suggestion here: [[User:Inthar/Template:Harmonics_in_edo]]. We also want to do this with other equal-step tunings such as [[13edt]]. Tom Price also suggested an additional visual idea I really like. We could try implementing that with Lua, but in the meantime I think this will do.

I'd just like to reopen the discussion about this suggested change. Please let me know on the relevant discussion page if you have any concerns.

[[User:Inthar|Inthar]] ([[User talk:Inthar|talk]]) 21:15, 24 July 2021 (UTC)

== Organization of music references ==

After cleaning up (or setting up) the Music sections in a few edo pages ([[0edo]] through [[6edo]] so far), I've started to think that maintaining lists like these manually is probably the reason why they end up outdated most of the time. I thought, maybe a xenharmonic music database would be better suited for that, in which each piece could be tagged with its tuning(s), scale(s) if applicable, etc. And then I noted that the Wiki is basically a database of pages and other stuff, and that using the Wiki could be an option. Of course, music will have to be added manually, but that's the price for having a platform-independent database; the advantage to be able to filter by genre or by tuning seems to be worth the effort to me.

So I was wondering, are there technical issues that would arise if we were to create individual pages for each track instead of building large tables spread over multiple pages as we currently do? It seems to me that there are already a lot of pages because of all these intervals and scales having individual pages, so I don't see what sort of problem could arise, but I'm asking in case I'm missing something. Also, if you're aware of automating tools that could be helpful in setting up multiple pages (e.g. reading from a .csv file and creating pages in bulk), that could be handy as well. [[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 03:23, 26 July 2021 (UTC)

'''UPDATE:''' After discussing with [[User:Xenoindex|xenoindex]], we agreed that having single pages for each song would clutter the search results in the search bar. I came up with the idea to set up a parallel wiki, something like ''music.xen.wiki'', which could store those pages while avoiding the aforementioned problem. It would be easy to bridge those pages with the main wiki, although I guess that assumes linking to the English wiki only.

Also, I want to clarify that I'm not sure whether or not I will have a lot of time to spend on this project, especially since there are other things I want to work on as well. For now I'm just asking to know how it works in case I want to start. There is already one other user from XA Discord who mentioned being interested to contribute if we started though, so I wouldn't be alone. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 15:56, 29 July 2021 (UTC)

'''UPDATE 2:''' After discussing with [[User:SupahstarSaga|HEHEHE I AM A SUPAHSTAR SAGA]], maybe another wiki isn't necessary, but otherwise we agreed on the other core ideas. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 15:28, 30 July 2021 (UTC)

== Request for help on a new microtonal theory ==

Xenwolf, I know that you have much more experience in microtones than I do, so I would like you to take a look at my new microtonal theory, [[User:Userminusone/Intervallic Polarity|Intervallic Polarity]]. This is something that I think has useful implications, but right now, its definition is a bit shaky and also quite subjective. If you are willing, I would really appreciate it if you could give me your thoughts on this theory or maybe even help me refine and expand upon its definition. Best regards, [[User:Userminusone|Userminusone]] ([[User talk:Userminusone|talk]]) 21:54, 1 August 2021 (UTC)

: Sorry for my late response. I meanwhile tried twice to get an overview of your ideas and kept it on my todo list. Now I have to admit that I'm probably not able to contribute to this theory. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:19, 19 September 2021 (UTC)

== A clue on the telephone numbers problem ==

Looking forward to your comment on [[User talk:KingHyperio #Telephone numbers problem]]. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 19:11, 16 September 2021 (UTC)

: I just read about it (and already responded there). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:15, 19 September 2021 (UTC)

== Leantone Temperament ==

I saw that you were the last to edit a couple of the Leantone scale pages, and I wanted to ask if Leantone, as a 2.9.5.7.11 temperament, is meant to reach the 11 in 3 generators or 9? I’m likely going to add something on the subgroup temperaments page for it so I wanted to check. [[User:KingHyperio|KingHyperio]] ([[User talk:KingHyperio|talk]]) 16:07, 21 December 2021 (UTC)

Or if it does in some other number of generators [[User:KingHyperio|KingHyperio]] ([[User talk:KingHyperio|talk]]) 16:12, 21 December 2021 (UTC)

: I'm really sorry, but I have to admit that I have only made formal changes to these pages and have no experience with the actual content. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:32, 21 December 2021 (UTC)

Ok, thanks anyways [[User:KingHyperio|KingHyperio]] ([[User talk:KingHyperio|talk]]) 16:36, 21 December 2021 (UTC)

: From my understanding, the tempered 11th harmonic is reached in 3 periods (~1200¢ each) and 3 generators (~192.5¢ each). If you look at the reduced mapping on x31eq (http://x31eq.com/cgi-bin/rt.cgi?limit=2_9_5_7_11&ets=6_7d), the last column of the matrix will give you that information (the top "3" is the number of periods, the bottom "3" is the number of generators). This implies that 11/8 is mapped to 3 generators, for example. I hope this helps! --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 18:32, 21 December 2021 (UTC)

== 311 EDO huge table ==

311 EDO is a one-of-a-kind extremely consistent system to the point it can be said to be the first true melodic model of the harmonic series itself. Therefore to understand the structure of the harmonic series (at least in the 41-limit add-73) without making it impractical, it would be useful to use 311 EDO, and 311 EDO is a great alternative to cents for this reason (which requires smaller numbers and only round numbers) because of being distinctly consistent in the [[23-odd-limit]] and consistent in the 41-prime-limited 77-odd-limit with prime harmonic 73 included as the only prime over 41 and under 81 which is more in tune than out of tune (which is to say its step error is less than a quarter), but furthermore, because of it fitting the way 311 EDO maps the harmonic series by filling a gap and because of it being an odd prime with less error than all previous primes. 311 EDO is therefore a natural system to inspect when looking at ways of modelling higher-limit systems and has important connections with many simpler systems. Just one example would be [[Canousmic_temperaments#Superlimmal|Superlimmal]], the 29-limit 80&311 temperament. Another reason it is a one-of-a-kind system is that in terms of having rooted harmonics with less than 25% error each, I did a search before in Python 3 and there is nothing that beats it until over 20 thousand, meaning it is simultaneously the first and last EDO to truly approximate the harmonic series, and the fact it does it up to a very large subset of the 77-odd-limit makes it worth inspecting the structure of for anyone wishing to learn medium-to-high-complexity tempered JI/odd-limits. Sorry if I've overstressed my point. Also the other table has been there for as long as I remember, and I felt it was both incomplete and messy so I wanted a table from a more systematic approach. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:17, 27 December 2021 (UTC)

Oh one other thing, feel free to suggest ways of making the table prettier. For example, I was initially only putting the intervals of the form a/b for a>b and for a and b from 39 to 78 (not including primes >41 other than 73 and corresponding thusly to the 41-prime-limited add-73 77-odd-limit) but then I noticed the end of the table was sparse and some intervals were missing, so instead I put the octave-complement of each such interval too, but this made the organisation messier. It does mean however that the interval table could potentially have its size halved without any loss of information and with the only caveat that you'd have to calculate octave-complements of intervals yourself (both in terms of number of steps and in terms of JI intervals). I think my former method which lead to a more orderly organisation of odd-limit intervals per interval of 311 EDO was maybe better especially considering it lead to simpler code too. Once I or others decide which is the better method I may start hand-prettifying the table by adding consistently-mapped odd-limit intervals or commas for empty intervals of 311 EDO in the table. One example could be that 9801/9800, 441/440 and 385/384 are all mapped to 1\311, although my concern for giving interpretations like that is there is a gargantuan number of intervals that are mapped to one or two steps of 311 EDO, so maybe leaving them blank is more elegant. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 23:26, 27 December 2021 (UTC)

== Categorization of redirects ==

I see it fit to categorize temperament redirects cuz they're eventually to be expanded to full articles. For ratios redirecting to interval names, I'm not sure. They're essentially the same concept and will never be distinct articles. So the categories are duplicate, and the maintenance load also doubles. What's your take on this? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 12:52, 3 April 2022 (UTC)

: I find it generally useful to also make alternative names findable in categories (they are italicized to distinguish them). In the index of a book, there are sometimes short references instead of page numbers (I consider the categorization of redirects to be the wiki equivalent of this). But I'm not sure the categories are useful overall. Personally, I see them more as "fire stairs" to articles. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:22, 3 April 2022 (UTC)
== Step ratio terms in other languages ==
Kite has brought up what he sees as a possible issue in hard vs. soft terms ([[Talk:TAMNAMS#Hard_and_soft_in_French.2C_German.2C_etc.|here]]) when translated to European languages. Looking at the [https://en.wikipedia.org/wiki/Key_signature_names_and_translations Wikipedia page] he's linking to, there seems to be no conflict in Romance languages at least, and from my German knowledge there is no conflict between ''hart/weich'' and ''Dur/moll''. There could be other reasons literal translations of hard and soft are unsuitable, though (I don't know what [[de:Diskussion:Schrittverhältnis#Benennung|your comment]] on the German article for step ratio was pointing at). My suggestion would be to create a page for translating TAMNAMS hard and soft terms, specifically, and patiently wait for native speaker input. [[User:Inthar|Inthar]] ([[User talk:Inthar|talk]]) 14:52, 19 August 2022 (UTC)

: Concur. --[[User:Godtone|Godtone]] ([[User talk:Godtone|talk]]) 19:30, 19 August 2022 (UTC)

:: Thanks for letting me know, I replied in [[Talk:TAMNAMS#Hard and soft in French, German, etc.]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 20:29, 31 August 2022 (UTC)

== Maintenance bot ==

Hi Xenwolf, I notice that we sometimes do manual cleaning which could be automated by bots, such as fixing double redirects. I stumbled upon this yesterday: https://www.mediawiki.org/wiki/Manual:Pywikibot/redirect.py

Do you think there's a chance it could be installed on this wiki? Unless there's already something similar available that I don't know of yet? --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 16:11, 8 October 2022 (UTC)

: I don't think anything like this exists yet. The person who takes care of the server side installation is [[User:Tyler Henthorn|Tyler Henthorn]], maybe you can share your ideas with him. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:06, 13 October 2022 (UTC)

== In-browser sound generation ==

Hi Xenwolf!

My in-browser sound generation project ([[User:Plumtree/Sound]]) is essentially ready. Could you review [[User:Plumtree/common.js]] and [[User:Plumtree/common.css]] and, if there're no issues, include those globally?

The best option would've been [[mw:Extension:Gadgets]] for JS and [[mw:Extension:TemplateStyles]] for CSS. Alas, they aren't installed. I've asked [[User:Tyler Henthorn]] for them but his last edit was more than a year ago and it's unlikely he'll answer any time soon.

What does JS do?
* It reacts to clicks on HTML elements with class <code>sequence-audio</code>. When one is clicked, it reads its <code>data-sequence</code> attribute and plays the encoded pattern.
* If <code>data-lock</code> attribute is set, it also adds the <code>sequence-audio-playing</code> class and ignores further clicks for the duration of the sequence.
* Timbres defined by their harmonic spectra are supported. Builtins are <code>sine</code>, <code>semisine</code>, <code>flute</code>, <code>violin</code>; you can supply custom ones using <code>data-timbre-X</code> attributes.
* A sequence consists of the following elements, separated by whitespaces:
** <code>wait:DURATION</code> - adds DURATION ms to the global time shift, which starts at 0.
** <code>FREQUENCY:DURATION:GAIN:SHIFT:INSTRUMENT</code> - plays FREQUENCY for DURATION ms with GAIN with timbre specified with INSTRUMENT. It starts at global shift + SHIFT ms, and global shift isn't modified. INSTRUMENT's default is <code>sine</code>; SHIFT's default is <code>0</code>.
* For example, sequences used for interval demonstration look like this: <code>440:1000:0.1 660:1000:0.1:500 wait:2000 660:1000:0.1 440:1000:0.1:500 wait:2000 440:1000:0.1 660:1000:0.1</code>.
* Modern browsers support Web Audio API quite well and I don't expect any compatibility issues.

What does CSS handle?
* Background colour of <code>.sequence-audio-button</code> elements depending on their state.
* Cursor styles upon <code>.sequence-audio-button</code> elements so that they're interpreted as interactive.
* Additionally, <code>.white-key</code> and <code>.black-key</code> elements have the corresponding colours. Those may be used to build interactive keyboards for ETs.

Examples (all require [[User:Plumtree/common.js]] and [[User:Plumtree/common.css]] to be properly viewed):
* [[User:Plumtree/Sound]] - mostly tests of intervals.
* [[User:Plumtree/Sandbox/Interval]] - actually tests of intervals as they're going to be included into [[Template:Infobox Interval]].
* [[User:Plumtree/Audio]] - the template which is currently the main interface for this JS.

[[User:Plumtree|Plumtree]] ([[User talk:Plumtree|talk]]) 17:52, 16 October 2022 (UTC)

== Thank you for reconstructing my diagram on 10648/10647 ==

Thank you, Xenwolf, for reconstructing my diagram on the harmonisma, 10648/10647, and your helpful hint on formatting monospaced text for alignment.

Your reformatting gave me the opportunity to spot and correct my mistakes in the original diagram, which were of course my own responsibility. Thanks to your help, the corrected diagram should hopefully help readers to visualize the relationship between the 10648/10647 and the 352/351 and 364/363. [[User:Mschulter1325|Mschulter1325]] 19:38, 11 November 2022 (UTC)

: You're welcome, it was a pleasure to help. Shouldn't the chart be placed on page [[10648/10647]] itself after the corrections are made? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:03, 12 November 2022 (UTC)

Yes, it's corrected, and I just put some final touches on tidying up the alignment, so it should be ready to go on the article's page. Many thanks for your assistance! [[User:Mschulter1325|Mschulter1325]] 04:20, 15 November 2022 (UTC)

== Add HEJI font to CSS ==

Hi Xenwolf,

I'd like to add a bit of code to [[MediaWiki:Common.css]] so that we can use the HEJI2Text font on the wiki (instead of relying on a bunch of SVG images, namely), but I don't have admin access so I can't do it myself. Do you think you could add it?

<pre><nowiki>
/* use HEJI2Text font if class="heji" */
@font-face {
font-family: HEJI2Text;
src: url(https://plainsound.org/fonts/HEJI2Text.otf);
}
.heji {
font-family: HEJI2Text;
}
</nowiki></pre>
--[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 07:49, 3 January 2023 (UTC)

: Hi Fredg999, would you please try the additions needed within [[User:Fredg999/common.css|''your personal common.css'']] and prepare or collect some representative examples (maybe just links to pages)? This would also be a good basis to better understand the impact of this proposal on the site and for discussing individual points with other users. Best regards --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 18:06, 3 January 2023 (UTC)

:: I added a few examples to [[User:Fredg999/Sandbox#HEJI2Text testing area|''my personal Sandbox page'']]. Here is a screenshot of the result: https://drive.google.com/file/d/10ZLax9RYqQg3-mQtV9YeKPC--2VmvR43/view?usp=sharing
:: The main use case I have in mind is the [[Helmholtz-Ellis notation]] page, where we could improve the reference tables and give more examples efficiently using the HEJI font. I was thinking of adding a table that shows all symbols (a bit like the HEJI notation palette on [https://www.plainsound.org/HEJI/ Plainsound's HS CALC]), but also shows the character mapping, so that readers can learn to use the font more easily on the wiki and elsewhere.
:: Most symbols from the [[Alternative symbols for ups and downs notation]] could also be written using the HEJI font, since it provides symbols for each combination of the standard chromatic accidentals with one, two or three up or down arrows.
:: Many other pages about just intonation could benefit from HEJI symbols as well, such as interval tables on various EDO pages (for easy up/down symbols as a complement to their "text" version; e.g. [[22edo#Intervals]]), as well as the [[Overtone scale]] page, where notation would be another representation of the JI scales, alongside the solfege notations already present, for example.
:: --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 03:49, 4 January 2023 (UTC)

::: I added the font to [[MediaWiki:Common.css]]. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:52, 4 January 2023 (UTC)

MediaWiki:Common.css

2023-01-04T06:51:25Z

Xenwolf: add HEJI font as suggested in https://en.xen.wiki/index.php?title=User_talk:Xenwolf&oldid=100894#Add_HEJI_font_to_CSS

/* CSS placed here will be applied to all skins */

/* for [[Template::Monzo]] and [[Template::Val]] */
/* prevent line breaks within monzo and val notations */
span.monzo,
span.val {
white-space: nowrap;
}

/* text-align property for a small selection of table rows, default is set by the *-all class */
table.left-all td,
table.left-1 td:nth-child(1),
table.left-2 td:nth-child(2),
table.left-3 td:nth-child(3),
table.left-4 td:nth-child(4),
table.left-5 td:nth-child(5),
table.left-6 td:nth-child(6),
table.left-7 td:nth-child(7),
table.left-8 td:nth-child(8),
table.left-9 td:nth-child(9),
table.left-10 td:nth-child(10),
table.left-11 td:nth-child(11),
table.left-12 td:nth-child(12) {
text-align: left;
}
table.center-all td,
table.center-1 td:nth-child(1),
table.center-2 td:nth-child(2),
table.center-3 td:nth-child(3),
table.center-4 td:nth-child(4),
table.center-5 td:nth-child(5),
table.center-6 td:nth-child(6),
table.center-7 td:nth-child(7),
table.center-8 td:nth-child(8),
table.center-9 td:nth-child(9),
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User:Xenwolf/common.css

2023-01-04T06:48:23Z

Xenwolf: copy CSS from User:Fredg999/common.css

User talk:Xenwolf

2023-01-03T18:06:23Z

Xenwolf: /* Add HEJI font to CSS */ re

137edo

2022-11-27T12:48:01Z

Xenwolf: cleanup, simplify

{{Infobox ET}}
The '''137 equal division''' divides the octave into 137 equal parts of 8.759 cents each. It is the [[optimal patent val]] for 7-limit [[orwell]] temperament and for the planar temperament tempering out 2430/2401. It tempers out 2109375/2097152 (the semicomma) in the 5-limit; 225/224 and 1728/1715 in the 7-limit; 243/242 in the 11-limit; 351/350 in the 13-limit; 375/374 and 442/441 in the 17-limit; and 324/323 and 495/494 in the 19-limit. Since it is the 33rd [[prime number]], 137edo has no proper divisors aside from 1.

A diagram of 7-limit Orwell based on the 31\137edo generator:

[[File:137edo_MOS_031_demo_correction.png|alt=137edo_MOS_031_demo_correction.png|137edo_MOS_031_demo_correction.png]]

[[:File:137edo_MOS_031.svg|137edo_MOS_031.svg]]

[[Category:Equal divisions of the octave|###]] 
[[Category:Nuwell]]
[[Category:Orwell]]
[[Category:Prime EDO]]
[[Category:Semicomma]]

List of MOS scales in 17edo

2022-11-19T11:56:15Z

Xenwolf: categorize, plus some cleanup

Since 17 is a prime number, any interval can be repeatedly stacked to produce new intervals until all 17 tones are included. This page lists and visualizes the scales produced this way.

== Diagram of mosses of 17edo ==

The following diagram is a visualization of some of the mosses available in [[17edo]]. See [[MOSScales|moment of symmetry scales]] for background on this type of linear scale, and see [[horogram]] for background on this type of diagram.

[[File:17edo_horograms.jpg|alt=17edo_horograms.jpg|17edo_horograms.jpg]]

[[:File:17edo_horograms.pdf|17edo horograms.pdf]]

{| class="wikitable"
|-
! generator
! temperament
|-
| 2\17
| [[Bleu]]
|-
| 3\17
| [[Machine]]
|-
| 4\17
| [[Huxley]]
|-
| 5\17
| [[Maqamic]]/[[Hemif]]
|-
| 6\17
| [[Skwares]]
|-
| 7\17
| [[Supra]]
|-
| 8\17
| [[Progress]]
|}

See also: [[17edo neutral scale]]

== Mosses by generator pair ==
The following is a table that sorts all possible moment-of-symmetry scales by generator pair, including mos information, temperament-agnostic information, and temperament information. A few notes:

* The table denotes each family using a [[Horogram#Rectangular%20Horogram|rectangular horogram]], starting with 1L 1s and [[MOS Diagrams|adding notes]] until every note is added.
* For scales whose order of steps, from read left-to-right, starts with a large step and ends with a small step, the smaller of the two generators is the chroma-positive generator; otherwise, the larger of the two is the chroma-positive generator.
* [[TAMNAMS]] names are used wherever possible, except for scales with 4 or fewer notes and 1L ns scales for tidiness. Scales with at least four notes have clickable links to their corresponding mos page.

{| class="wikitable"
! colspan="21" |Single-Period Scales for 17 Equal Division of the Octave
|-
! colspan="17" |Steps for Generators 16\17 and 1\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="16" |16
| 1
| 1L 1s
| 16:1
|
|
|-
| colspan="15" |15
| 1
| 1
| 1L 2s
| 15:1
|
|
|-
| colspan="14" |14
| 1
| 1
| 1
| [[1L 3s]]
| 14:1
|
|
|-
| colspan="13" |13
| 1
| 1
| 1
| 1
| [[1L 4s]]
| 13:1
|
|
|-
| colspan="12" |12
| 1
| 1
| 1
| 1
| 1
| [[1L 5s]]
| 12:1
|
|
|-
| colspan="11" |11
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 6s]]
| 11:1
|
|
|-
| colspan="10" |10
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 7s]]
| 10:1
|
|
|-
| colspan="9" |9
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 8s]]
| 9:1
|
|
|-
| colspan="8" |8
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 9s]]
| 8:1
|
|
|-
| colspan="7" |7
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 10s]]
| 7:1
|
|
|-
| colspan="6" |6
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 11s]]
| 6:1
|
|
|-
| colspan="5" |5
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 12s]]
| 5:1
|
|
|-
| colspan="4" |4
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 13s]]
| 4:1
|
|
|-
| colspan="3" |3
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 14s]]
| 3:1
|
|
|-
| colspan="2" |2
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| [[1L 15s]]
| 2:1
|
|
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 17edo
| 1
|
|
|-
! colspan="17" |Steps for Generators 15\17 and 2\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="15" |15
| colspan="2" |2
| 1L 1s
| 15:2
|
|
|-
| colspan="13" |13
| colspan="2" |2
| colspan="2" |2
| 1L 2s
| 13:2
|
|
|-
| colspan="11" |11
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 3s]]
| 11:2
|
| bleu[4]
|-
| colspan="9" |9
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 4s]]
| 9:2
|
| bleu[5]
|-
| colspan="7" |7
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 5s]]
| 7:2
|
| bleu[6]
|-
| colspan="5" |5
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 6s]]
| 5:2
|
| bleu[7]
|-
| colspan="3" |3
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[1L 7s]]
| 3:2
|
| bleu[8]
|-
| 1
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| [[8L 1s]]
| 2:1
| subneutralic
| bleu[9]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 17edo
| 1
|
|
|-
! colspan="17" |Steps for Generators 14\17 and 3\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="14" |14
| colspan="3" |3
| 1L 1s
| 14:3
|
|
|-
| colspan="11" |11
| colspan="3" |3
| colspan="3" |3
| 1L 2s
| 11:3
|
|
|-
| colspan="8" |8
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| [[1L 3s]]
| 8:3
|
| machine[4]
|-
| colspan="5" |5
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| [[1L 4s]]
| 5:3
|
| machine[5]
|-
| colspan="2" |2
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| [[5L 1s]]
| 3:2
| machinoid
| machine[6]
|-
| colspan="2" |2
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| [[6L 5s]]
| 2:1
|
| machine[11]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 17edo
| 1
|
|
|-
! colspan="17" |Steps for Generators 13\17 and 4\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="13" |13
| colspan="4" |4
| 1L 1s
| 13:4
|
|
|-
| colspan="9" |9
| colspan="4" |4
| colspan="4" |4
| 1L 2s
| 9:4
|
|
|-
| colspan="5" |5
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| [[1L 3s]]
| 5:4
|
| huxley[4]
|-
| 1
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| colspan="4" |4
| [[4L 1s]]
| 4:1
| manual
| huxley[5]
|-
| 1
| 1
| colspan="3" |3
| 1
| colspan="3" |3
| 1
| colspan="3" |3
| 1
| colspan="3" |3
| [[4L 5s]]
| 3:1
| gramitonic
| huxley[9]
|-
| 1
| 1
| 1
| colspan="2" |2
| 1
| 1
| colspan="2" |2
| 1
| 1
| colspan="2" |2
| 1
| 1
| colspan="2" |2
| [[4L 9s]]
| 2:1
|
| huxley[13]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 17edo
| 1
|
|
|-
! colspan="17" |Steps for Generators 12\17 and 5\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="12" |12
| colspan="5" |5
| 1L 1s
| 12:5
|
|
|-
| colspan="7" |7
| colspan="5" |5
| colspan="5" |5
| 1L 2s
| 7:5
|
|
|-
| colspan="2" |2
| colspan="5" |5
| colspan="5" |5
| colspan="5" |5
| [[3L 1s]]
| 5:2
| tetric
| maqamic/hemif[4]
|-
| colspan="2" |2
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| colspan="2" |2
| colspan="3" |3
| [[3L 4s]]
| 3:2
| mosh
| maqamic/hemif[7]
|-
| colspan="2" |2
| colspan="2" |2
| colspan="2" |2
| 1
| colspan="2" |2
| colspan="2" |2
| 1
| colspan="2" |2
| colspan="2" |2
| 1
| [[7L 3s]]
| 2:1
| dicotonic
| maqamic/hemif[10]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 17edo
| 1
|
|
|-
! colspan="17" |Steps for Generators 11\17 and 6\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="11" |11
| colspan="6" |6
| 1L 1s
| 11:6
|
|
|-
| colspan="5" |5
| colspan="6" |6
| colspan="6" |6
| 2L 1s
| 6:5
|
|
|-
| colspan="5" |5
| colspan="5" |5
| 1
| colspan="5" |5
| 1
| [[3L 2s]]
| 5:1
| antipentic
| sqwares[5]
|-
| colspan="4" |4
| 1
| colspan="4" |4
| 1
| 1
| colspan="4" |4
| 1
| 1
| [[3L 5s]]
| 4:1
| checkertonic
| sqwares[8]
|-
| colspan="3" |3
| 1
| 1
| colspan="3" |3
| 1
| 1
| 1
| colspan="3" |3
| 1
| 1
| 1
| [[3L 8s]]
| 3:1
|
| sqwares[11]
|-
| colspan="2" |2
| 1
| 1
| 1
| colspan="2" |2
| 1
| 1
| 1
| 1
| colspan="2" |2
| 1
| 1
| 1
| 1
| [[3L 11s]]
| 2:1
|
| sqwares[14]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 17edo
| 1
|
|
|-
! colspan="17" |Steps for Generators 10\17 and 7\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="10" |10
| colspan="7" |7
| 1L 1s
| 10:7
|
|
|-
| colspan="3" |3
| colspan="7" |7
| colspan="7" |7
| 2L 1s
| 7:3
|
|
|-
| colspan="3" |3
| colspan="3" |3
| colspan="4" |4
| colspan="3" |3
| colspan="4" |4
| [[2L 3s]]
| 4:3
| pentic
| supra[5]
|-
| colspan="3" |3
| colspan="3" |3
| colspan="3" |3
| 1
| colspan="3" |3
| colspan="3" |3
| 1
| [[5L 2s]]
| 3:1
| diatonic
| supra[7]
|-
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| 1
| colspan="2" |2
| 1
| colspan="2" |2
| 1
| 1
| [[5L 7s]]
| 2:1
|
| supra[12]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 17edo
| 1
|
|
|-
! colspan="17" |Steps for Generators 9\17 and 8\17
! Mos
! Step Ratio
! TAMNAMS Name
! Temperament
|-
| colspan="9" |9
| colspan="8" |8
| 1L 1s
| 9:8
|
|
|-
| 1
| colspan="8" |8
| colspan="8" |8
| 2L 1s
| 8:1
|
|
|-
| 1
| 1
| colspan="7" |7
| 1
| colspan="7" |7
| [[2L 3s]]
| 7:1
| pentic
| progress[5]
|-
| 1
| 1
| 1
| colspan="6" |6
| 1
| 1
| colspan="6" |6
| [[2L 5s]]
| 6:1
| antidiatonic
| progress[7]
|-
| 1
| 1
| 1
| 1
| colspan="5" |5
| 1
| 1
| 1
| colspan="5" |5
| [[2L 7s]]
| 5:1
| balzano
| progress[9]
|-
| 1
| 1
| 1
| 1
| 1
| colspan="4" |4
| 1
| 1
| 1
| 1
| colspan="4" |4
| [[2L 9s]]
| 4:1
|
| progress[11]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| colspan="3" |3
| 1
| 1
| 1
| 1
| 1
| colspan="3" |3
| [[2L 11s]]
| 3:1
|
| progress[13]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| colspan="2" |2
| 1
| 1
| 1
| 1
| 1
| 1
| colspan="2" |2
| [[2L 13s]]
| 2:1
|
| progress[15]
|-
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 1
| 17edo
| 1
|
|
|}

[[Category:17edo]]
[[Category:MOS]]

35edo

2022-11-17T21:52:08Z

Xenwolf: /* Theory */ re-add odd harmonics table

{{Infobox ET}}
{{EDO intro|35}}

== Theory ==
As 35 is 5 times 7, 35edo allows for mixing the two smallest xenharmonic [[macrotonal edos]]: [[5edo]] and [[7edo]]. A single degree of 35edo represents the difference between 7edo's narrow fifth of 685.71¢ and 5edo's wide fifth of 720¢. Because it includes 7edo, 35edo tunes the 29th harmonic with +1 cent of error. 35edo can also represent the 2.3.5.7.11.17 [[Just_intonation_subgroups|subgroup]] and 2.9.5.7.11.17 subgroup, because of the accuracy of 9 and the flatness of all other subgroup generators (7/5 and 17/11 stand out, having less than 1 cent error). Therefore among whitewood tunings it is very versatile; you can switch between these different subgroups if you don't mind having to use two different 3/2s to reach the inconsistent 9 (a characteristic of whitewood tunings), and if you ignore [[22edo]]'s more in-tune versions of 35edo MOS's and consistent representation of both subgroups. 35edo has the optimal patent val for [[greenwood]] and [[secund]] temperaments, as well as 11-limit [[muggles]], and the 35f val is an excellent tuning for 13-limit muggles. 35edo is the largest edo with a lack of a diatonic scale.

{{Odd harmonics in edo|edo=35}}

== Notation ==
{| class="wikitable"
|-
! Degrees
! Cents
! colspan="3" | [[Ups and downs notation]]
! [[Dual-fifth tuning|Dual-fifth]] notation
based on closest 12edo interval
|-
| 0
| 0.000
| unison
| 1
| D
| 1sn, prime
|-
| 1
| 34.286
| up unison
| ^1
| ^D
| augmented 1sn
|-
| 2
| 68.571
| dup unison
| ^^1
| ^^D
| diminished 2nd
|-
| 3
| 102.857
| dud 2nd
| vv2
| vvE
| minor 2nd
|-
| 4
| 137.143
| down 2nd
| v2
| vE
| neutral 2nd
|-
| 5
| 171.429
| 2nd
| 2
| E
| submajor 2nd
|-
| 6
| 205.714
| up 2nd
| ^2
| ^E
| major 2nd
|-
| 7
| 240
| dup 2nd
| ^^2
| ^^E
| supermajor 2nd
|-
| 8
| 274.286
| dud 3rd
| vv3
| vvF
| diminished 3rd
|-
| 9
| 308.571
| down 3rd
| v3
| vF
| minor 3rd
|-
| 10
| 342.857
| 3rd
| 3
| F
| neutral 3rd
|-
| 11
| 377.143
| up 3rd
| ^3
| ^F
| major 3rd
|-
| 12
| 411.429
| dup 3rd
| ^^3
| ^^F
| augmented 3rd
|-
| 13
| 445.714
| dud 4th
| vv4
| vvG
| diminished 4th
|-
| 14
| 480
| down 4th
| v4
| vG
| minor 4th
|-
| 15
| 514.286
| 4th
| 4
| G
| major 4th
|-
| 16
| 548.571
| up 4th
| ^4
| ^G
| augmented 4th
|-
| 17
| 582.857
| dup 4th
| ^^4
| ^^G
| minor tritone
|-
| 18
| 617.143
| dud 5th
| vv5
| vvA
| major tritone
|-
| 19
| 651.429
| down 5th
| v5
| vA
| diminished 5th
|-
| 20
| 685.714
| 5th
| 5
| A
| minor 5th
|-
| 21
| 720
| up 5th
| ^5
| ^A
| major 5th
|-
| 22
| 754.286
| dup 5th
| ^^5
| ^^A
| augmented 5th
|-
| 23
| 788.571
| dud 6th
| vv6
| vvB
| diminished 6th
|-
| 24
| 822.857
| down 6th
| v6
| vB
| minor 6th
|-
| 25
| 857.143
| 6th
| 6
| B
| neutral 6th
|-
| 26
| 891.429
| up 6th
| ^6
| ^B
| major 6th
|-
| 27
| 925.714
| dup 6th
| ^^6
| ^^B
| augmented 6th
|-
| 28
| 960
| dud 7th
| vv7
| vvC
| diminished 7th
|-
| 29
| 994.286
| down 7th
| v7
| vC
| minor 7th
|-
| 30
| 1028.571
| 7th
| 7
| C
| superminor 7th
|-
| 31
| 1062.857
| up 7th
| ^7
| ^C
| neutral 7th
|-
| 32
| 1097.143
| dup 7th
| ^^7
| ^^C
| major 7th
|-
| 33
| 1131.429
| dud 8ve
| vv8
| vvD
| augmented 7th
|-
| 34
| 1165.714
| down 8ve
| v8
| vD
| diminished 8ve
|-
| 35
| 1200
| 8ve
| 8
| D
| 8ve
|}

=== Chord Names ===
Ups and downs can be used to name 35edo chords. Because every interval is perfect, the quality can be omitted, and the words major, minor, augmented and diminished are never used. An up or down immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Alterations are always enclosed in parentheses, additions never are.

0-10-20 = C E G = C = C or C perfect

0-9-20 = C vE G = Cv = C down

0-11-20 = C ^E G = C^ = C up

0-10-19 = C E vG = C(v5) = C down-five

0-11-21 = C ^E ^G = C^(^5) = C up up-five

0-10-20-30 = C E G B = C7 = C seven

0-10-20-29 = C E G vB = C,v7 = C add down-seven

0-9-20-30 = C vE G B = Cv,7 = C down add-seven

0-9-20-29 = C vE G vB = Cv7 = C down seven

For a more complete list, see [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].

== JI Intervals ==
(Bolded ratio indicates that the ratio is most accurately tuned by the given 35edo interval.)

{| class="wikitable"
|-
| Degrees
| Cents value
| Ratios in 2.5.7.11.17 subgroup
| Ratios with flat 3
| Ratios with sharp 3
| Ratios with best 9
|-
| 0
| 0.000
| '''1/1'''
| (see comma table)
|
|
|-
| 1
| 34.286
| '''50/49''', '''121/119''', 33/32
| '''36/35'''
| 25/24
| '''81/80'''
|-
| 2
| 68.571
| 128/125
| '''25/24'''
| 81/80
|
|-
| 3
| 102.857
| '''17/16'''
| '''15/14'''
| '''16/15'''
| '''18/17'''
|-
| 4
| 137.143
|
| '''12/11''', 16/15
|
|
|-
| 5
|171.429
| '''11/10'''
|
| 12/11
| '''10/9'''
|-
| 6
| 205.714
|
|
|
| '''9/8'''
|-
| 7
| 240
| '''8/7'''
|
| 7/6
|
|-
| 8
| 274.286
| '''20/17'''
| '''7/6'''
|
|
|-
| 9
| 308.571
|
| '''6/5'''
|
|
|-
| 10
|342.857
| '''17/14'''
|
| 6/5
| '''11/9'''
|-
| 11
| 377.143
| '''5/4'''
|
|
|
|-
| 12
| 411.429
| '''14/11'''
|
|
|
|-
| 13
| 445.714
| '''22/17''', 32/25
|
|
| '''9/7'''
|-
| 14
| 480
|
|
| 4/3, '''21/16'''
|
|-
| 15
|514.286
|
| '''4/3'''
|
|
|-
| 16
| 548.571
| '''11/8'''
|
|
|
|-
| 17
| 582.857
| '''7/5'''
| '''24/17'''
| 17/12
|
|-
| 18
| 617.143
| '''10/7'''
| '''17/12'''
| 24/17
|
|-
| 19
| 651.429
| '''16/11'''
|
|
|
|-
| 20
|685.714
|
| '''3/2'''
|
|
|-
| 21
| 720
|
|
| 3/2, '''32/21'''
|
|-
| 22
| 754.286
| '''17/11''', 25/16
|
|
| '''14/9'''
|-
| 23
| 788.571
| '''11/7'''
|
|
|
|-
| 24
| 822.857
| '''8/5'''
|
|
|
|-
| 25
|857.143
| '''28/17'''
|
| 5/3
| '''18/11'''
|-
| 26
| 891.429
|
| '''5/3'''
|
|
|-
| 27
| 925.714
| '''17/10'''
| '''12/7'''
|
|
|-
| 28
| 960
| '''7/4'''
|
|
|
|-
| 29
| 994.286
|
|
|
| '''16/9'''
|-
| 30
|1028.571
| '''20/11'''
|
|
| '''9/5'''
|-
| 31
| 1062.857
|
| '''11/6''', 15/8
|
|
|-
| 32
| 1097.143
| '''32/17'''
| '''28/15'''
| '''15/8'''
| '''17/9'''
|-
| 33
| 1131.429
|
|
|
|
|-
| 34
| 1165.714
|
|
|
|
|-
|3
|1200
|
|
|
|
|}

{| class="wikitable" style="text-align:center;"
|-
! Interval, complement
! Error (abs., in [[cent]]s)
|-
|[[7/5]] [[10/7]]
|0.3448
|-
|[[13/12]] [[24/13]]
|1.4296
|-
|[[9/8]] [[16/9]]
|1.8039
|-
|[[17/16]] [[32/17]]
|2.0984
|-
|[[11/8]] [[16/11]]
|2.7469
|-
|[[18/17]] [[17/9]]
|3.9024
|-
|[[11/9]] [[18/11]]
|4.5509
|-
|[[11/10]] [[20/11]]
|6.4247
|-
|[[14/11]] [[11/7]]
|6.0789
|-
|[[6/5]] [[5/3]]
|7.0703
|-
|[[7/6]] [[12/7]]
|7.4151
|-
|[[8/7]] [[7/4]]
|8.8259
|-
|[[14/13]] [[13/7]]
|8.8447
|-
|[[16/15]] [[15/8]]
|8.8742
|-
|[[5/4]] [[8/5]]
|9.1707
|-
|[[10/9]] [[9/5]]
|10.9747
|-
|[[12/11]] [[11/6]]
|13.494
|-
|[[3/2]] [[4/3]]
|16.241
|-
|[[15/14]] [[28/15]]
|16.5858
|-
|
|
|}

== Rank-2 temperaments ==
{| class="wikitable"
|-
! | Periods

per octave
! | Generator
! | Temperaments with

flat 3/2 (patent val)
! | Temperaments with sharp 3/2 (35b val)
|-
| | 1
| | 1\35
| |
| |
|-
| | 1
| | 2\35
| |
| |
|-
| | 1
| | 3\35
| |
| | [[Ripple|Ripple]]
|-
| | 1
| | 4\35
| | [[Greenwoodmic_temperaments#Secund|Secund]]
| |
|-
| | 1
| | 6\35
| colspan="2" | Messed-up [[Chromatic_pairs#Baldy|Baldy]]
|-
| | 1
| | 8\35
| |
| | Messed-up [[Orwell]]
|-
| | 1
| | 9\35
| | [[Myna|Myna]]
| |
|-
| | 1
| | 11\35
| | [[Muggles]]
| |
|-
| | 1
| | 12\35
| |
| | [[Avicennmic_temperaments#Roman|Roman]]
|-
| | 1
| | 13\35
| colspan="2" | Inconsistent 2.9'/7.5/3 [[Sensi]]
|-
| | 1
| | 16\35
| |
| |
|-
| | 1
| | 17\35
| |
| |
|-
| | 5
| | 1\35
| |
| | [[Blackwood]] (favoring 7/6)
|-
| | 5
| | 2\35
| |
| | [[Blackwood]] (favoring 6/5 and 20/17)
|-
| | 5
| | 3\35
| |
| | [[Blackwood]] (favoring 5/4 and 17/14)
|-
| | 7
| | 1\35
| | [[Apotome_family|Whitewood]]/[[Apotome_family#Redwood|Redwood]]
| |
|-
| | 7
| | 2\35
| | [[Greenwoodmic_temperaments#Greenwood|Greenwood]]
| |
|}

== Scales ==
A good beginning for start to play 35-EDO is with the Sub-diatonic scale, that is a [[MOS]] of 3L2s: 9 4 9 9 4.

== Commas ==
35 EDO [[tempers out]] the following [[comma]]s. (Note: This assumes the [[val]] {{val| 35 55 81 98 121 130 }}.)

{| class="commatable wikitable center-1 center-2 right-4 center-5"
|-
! [[Harmonic limit|Prime limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
| 3
| [[2187/2048]]
| {{monzo| -11 7 }}
| 113.69
| Lawa
| Apotome, Whitewood comma
|-
| 5
| [[6561/6250]]
| {{monzo| -1 8 -5 }}
| 84.07
| Quingu
| Ripple comma
|-
| 5
| <abbr title="10077696/9765625">(15 digits)</abbr>
| {{monzo| 9 9 -10 }}
| 54.46
| Quinbigu
| [[Mynic comma]]
|-
| 5
| [[3125/3072]]
| {{monzo| -10 -1 5 }}
| 29.61
| Laquinyo
| Small diesis, Magic comma
|-
| 7
| [[405/392]]
| {{monzo| -3 4 1 -2 }}
| 56.48
| Ruruyo
| Greenwoodma
|-
| 7
| [[16807/16384]]
| {{monzo| -14 0 0 5 }}
| 44.13
| Laquinzo
| Cloudy
|-
| 7
| [[525/512]]
| {{monzo| -9 1 2 1 }}
| 43.41
| Lazoyoyo
| Avicenna
|-
| 7
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.79
| Zotrigu
| Starling comma, Septimal semicomma
|-
| 11
| [[99/98]]
| {{monzo| -1 2 0 -2 1 }}
| 17.58
| Loruru
| Mothwellsma
|-
| 13
| [[66/65]]
| {{monzo| 1 1 -1 0 1 -1 }}
| 26.43
| Thulogu
| Winmeanma
|}
<references/>

== Music ==
* [http://soonlabel.com/xenharmonic/archives/2348 Little Prelude & Fugue, "The Bijingle" by Claudi Meneghin]
* [https://www.archive.org/download/Transcendissonance/05Self-destructingMechanicalForest-CityOfTheAsleep.mp3 Self-Destructing Mechanical Forest] by Chuckles McGee (in Secund[9])
* [https://youtu.be/07-wj6BaTOw "G2 Manifold"] by E8 Heterotic (uses a combination of 5-EDO and 7-EDO, which can be classified as a 35-EDO subset.)

[[Category:35edo]]
[[Category:Equal divisions of the octave|##]] 
[[Category:Listen]]
[[Category:Dual-fifth]]

Chain-of-fifths notation

2022-11-16T10:23:36Z

Xenwolf: /* Edos up to 100 */ more obvious table syntax

The '''circle-of-fifths notation''' (aka '''extended Pythagorean notation''') is suitable to open up the variety of tones of a selection of [[edo]]s and [[regular temperament]]s of fifth generator. The principle is based on one of the intervals taking over the role of the fifth of the traditional classical notation system (in [[12edo]] or the [[meantone]] tuning). The classical notation system uses seven root notes and accidentals (♯, ♭ and their multiples) to sharpen and flatten these root notes by the same amount (which is an octave-reduced stack of 7 fifths).

Edos that are best supported by this system are those whose fifth does not deviate too much from the pure fifth [[3/2]] (702{{cent}}) and that can be represented by only one ring of fifths. [[24edo]], as a counter-example to this, contains two rings. If we as well demand that whole tones (2 × P5 - P8), diatonic semitones (3 × P8 - 5 × P5), and chromatic semitones (shifts caused by one accidental, 7 × P5 - 4 × P8), use a positive number of steps, we exclude all edos below 12 and also {{EDOs| 13, 16, 18, and 23 }}. They make more sense notated as subsets. For example, 13edo can be notated as a subset of [[26edo]].

The '''neutral circle-of-fifths notation''' (aka '''quartertone notation''') uses an extended accidental set including '''demisharps''' and '''demiflats'''. It works for any tuning system generated by a neutral third. The [[mohaha]] temperament and its typical edo tunings ([[17edo]], 24edo, [[31edo]], [[38edo]], [[45edo]]) are well represented by this system.

== Edos up to 100 ==
Edos up to 100 are listed in the following tables. The unit (if not stated otherwise) is ''steps'' of the corresponding edo which is given in the first column of each row. The list contains only those edos whose all degrees can be reached by stacking the [[direct approximation]] of the fifth in the respective edo.

{| class="wikitable center-all"
|-
|+ Edos fit for circle-of-fifths notation
|-
! Edo
! Fifth
! Fifth-detuning abs(¢), rel(%)
! Whole tone
! Diatonic semitone
! Chromatic semitone
|-
! [[12edo|12]]
| 7 || -2.0 ( -2.0%) || 2 || 1 || 1
|-
! [[17edo|17]]
| 10 || +3.9 ( +5.6%) || 3 || 1 || 2
|-
! [[19edo|19]]
| 11 || -7.2 (-11.4%) || 3 || 2 || 1
|-
! [[22edo|22]]
| 13 || +7.1 (+13.1%) || 4 || 1 || 3
|-
! [[26edo|26]]
| 15 || -9.6 (-20.9%) || 4 || 3 || 1
|-
! [[27edo|27]]
| 16 || +9.2 (+20.6%) || 5 || 1 || 4
|-
! [[29edo|29]]
| 17 || +1.5 ( +3.6%) || 5 || 2 || 3
|-
! [[31edo|31]]
| 18 || -5.2 (-13.4%) || 5 || 3 || 2
|-
! [[32edo|32]]
| 19 || +10.5 (+28.1%) || 6 || 1 || 5
|-
! [[33edo|33]]
| 19 || -11.0 (-30.4%) || 5 || 4 || 1
|-
! [[37edo|37]]
| 22 || +11.6 (+35.6%) || 7 || 1 || 6
|-
! [[39edo|39]]
| 23 || +5.7 (+18.6%) || 7 || 2 || 5
|-
! [[40edo|40]]
| 23 || -12.0 (-39.9%) || 6 || 5 || 1
|-
! [[41edo|41]]
| 24 || +0.5 ( +1.7%) || 7 || 3 || 4
|-
! [[42edo|42]]
| 25 || +12.3 (+43.2%) || 8 || 1 || 7
|-
! [[43edo|43]]
| 25 || -4.3 (-15.3%) || 7 || 4 || 3
|-
! [[45edo|45]]
| 26 || -8.6 (-32.3%) || 7 || 5 || 2
|-
! [[46edo|46]]
| 27 || +2.4 ( +9.2%) || 8 || 3 || 5
|-
! [[47edo|47]]
| 27 || -12.6 (-49.3%) || 7 || 6 || 1
|-
! [[49edo|49]]
| 29 || +8.2 (+33.7%) || 9 || 2 || 7
|-
! [[50edo|50]]
| 29 || -6.0 (-24.8%) || 8 || 5 || 3
|-
! [[53edo|53]]
| 31 || -0.1 ( -0.3%) || 9 || 4 || 5
|-
! [[55edo|55]]
| 32 || -3.8 (-17.3%) || 9 || 5 || 4
|-
! [[56edo|56]]
| 33 || +5.2 (+24.2%) || 10 || 3 || 7
|-
! [[59edo|59]]
| 35 || +9.9 (+48.7%) || 11 || 2 || 9
|-
! [[61edo|61]]
| 36 || +6.2 (+31.7%) || 11 || 3 || 8
|-
! [[63edo|63]]
| 37 || +2.8 (+14.7%) || 11 || 4 || 7
|-
! [[64edo|64]]
| 37 || -8.2 (-43.8%) || 10 || 7 || 3
|-
! [[65edo|65]]
| 38 || -0.4 ( -2.3%) || 11 || 5 || 6
|-
! [[67edo|67]]
| 39 || -3.4 (-19.2%) || 11 || 6 || 5
|-
! [[69edo|69]]
| 40 || -6.3 (-36.2%) || 11 || 7 || 4
|-
! [[70edo|70]]
| 41 || +0.9 ( +5.3%) || 12 || 5 || 7
|-
! [[71edo|71]]
| 42 || +7.9 (+46.8%) || 13 || 3 || 10
|-
! [[73edo|73]]
| 43 || +4.9 (+29.8%) || 13 || 4 || 9
|-
! [[74edo|74]]
| 43 || -4.7 (-28.7%) || 12 || 7 || 5
|-
! [[75edo|75]]
| 44 || +2.0 (+12.8%) || 13 || 5 || 8
|-
! [[77edo|77]]
| 45 || -0.7 ( -4.2%) || 13 || 6 || 7
|-
! [[79edo|79]]
| 46 || -3.2 (-21.2%) || 13 || 7 || 6
|-
! [[80edo|80]]
| 47 || +3.0 (+20.3%) || 14 || 5 || 9
|-
! [[81edo|81]]
| 47 || -5.7 (-38.2%) || 13 || 8 || 5
|-
! [[83edo|83]]
| 49 || +6.5 (+44.8%) || 15 || 4 || 11
|-
! [[88edo|88]]
| 51 || -6.5 (-47.7%) || 14 || 9 || 5
|-
! [[89edo|89]]
| 52 || -0.8 ( -6.2%) || 15 || 7 || 8
|-
! [[90edo|90]]
| 53 || +4.7 (+35.3%) || 16 || 5 || 11
|-
! [[91edo|91]]
| 53 || -3.1 (-23.2%) || 15 || 8 || 7
|-
! [[94edo|94]]
| 55 || +0.2 ( +1.4%) || 16 || 7 || 9
|-
! [[95edo|95]]
| 56 || +5.4 (+42.9%) || 17 || 5 || 12
|-
! [[97edo|97]]
| 57 || +3.2 (+25.9%) || 17 || 6 || 11
|-
! [[98edo|98]]
| 57 || -4.0 (-32.6%) || 16 || 9 || 7
|-
! [[99edo|99]]
| 58 || +1.1 ( +8.9%) || 17 || 7 || 10
|}

{| class="wikitable center-all"
|-
|+ Edos fit for neutral circle-of-fifths notation
|-
! Edo
! Fifth
! Fifth-detuning abs(¢), rel(%)
! Whole tone
! Diatonic semitone
! Chromatic semitone
|-
! [[17edo|17]]
| 10 || +3.9 ( +5.6%) || 3 || 1 || 2
|-
! [[24edo|24]]
| 14 || -4.0 (-4.0%) || 4 || 2 || 2
|-
! [[27edo|27]]
| 16 || +9.2 (+20.6%) || 5 || 1 || 4
|-
! [[31edo|31]]
| 18 || -5.2 (-13.4%) || 5 || 3 || 2
|-
! [[37edo|37]]
| 22 || +11.6 (+35.6%) || 7 || 1 || 6
|-
! [[38edo|38]]
| 22 || -7.2 (-22.9%) || 6 || 4 || 2
|-
! [[41edo|41]]
| 24 || +0.5 ( +1.7%) || 7 || 3 || 4
|-
! [[44edo|44]]
| 26 || +7.1 (+26.2%) || 8 || 2 || 6
|-
! [[45edo|45]]
| 26 || -8.6 (-32.3%) || 7 || 5 || 2
|-
! [[52edo|52]]
| 30 || -9.6 (-41.8%) || 8 || 6 || 2
|-
! [[55edo|55]]
| 32 || -3.8 (-17.3%) || 9 || 5 || 4
|-
! [[58edo|58]]
| 34 || +1.5 ( +3.6%) || 10 || 4 || 6
|-
! [[61edo|61]]
| 36 || +6.2 (+31.7%) || 11 || 3 || 8
|-
! [[65edo|65]]
| 38 || -0.4 ( -2.3%) || 11 || 5 || 6
|-
! [[69edo|69]]
| 40 || -6.3 (-36.2%) || 11 || 7 || 4
|-
! [[71edo|71]]
| 42 || +7.9 (+46.8%) || 13 || 3 || 10
|-
! [[75edo|75]]
| 44 || +2.0 (+12.8%) || 13 || 5 || 8
|-
! [[78edo|78]]
| 46 || +5.7 (+37.3%) || 14 || 4 || 10
|-
! [[79edo|79]]
| 46 || -3.2 (-21.2%) || 13 || 7 || 6
|-
! [[86edo|86]]
| 50 || -4.3 (-30.7%) || 14 || 8 || 6
|-
! [[89edo|89]]
| 52 || -0.8 ( -6.2%) || 15 || 7 || 8
|-
! [[92edo|92]]
| 54 || +2.4 ( +18.3%) || 16 || 6 || 10
|-
! [[95edo|95]]
| 56 || +5.4 (+42.9%) || 17 || 5 || 12
|-
! [[99edo|99]]
| 58 || +1.1 ( +8.9%) || 17 || 7 || 10
|}

== Expansions ==
* [[Syntonic-rastmic subchroma notation]] – built on neutral circle-of-fifths notation
* [[Ups and downs notation]] – built on circle-of-fifths notation
** Neutral ups and downs notation (→ [[Alternative symbols for ups and downs notation]])
* [[Sagittal notation]] (''evo flavor'') – built on circle-of-fifths notation or neutral circle-of-fifths notation

== See also ==
* [[Nominal-accidental chain]]
* [[Circle of fifths]]
* [[Fifthspan]]
* [[User:Xenwolf/cofn]] – sortable table with more intervals (all fifths within the interval [4\7, 3\5], the "[[diatonic range]]")

[[Category:Notation]]
[[Category:Method]]
[[Category:Fifth]]

27edo

2022-11-15T13:51:44Z

Xenwolf: /* Music */ +1 (-1)

{{Infobox ET}}

'''27 equal divisions of the octave''' ('''27edo'''), or '''27(-tone) equal temperament''' ('''27tet''', '''27et''') when viewed from a [[regular temperament]] perspective, is the tuning system derived by dividing the [[octave]] into 27 [[equal]]ly large steps. Each step represents a frequency ratio of the 27th root of 2, or 44.4 [[cent]]s.

== Theory ==

If octaves are kept pure, 27edo divides the [[octave]] in 27 equal parts each exactly 44.444… [[cent]]s in size. However, 27 is a prime candidate for [[octave shrinking]], and a step size of 44.3 to 44.35 cents would be reasonable. The reason for this is that 27edo tunes harmonics [[3/1|3]], [[5/1|5]], and [[7/1|7]] sharply. The optimal step size for octave-shrinking in the 7-limit is 44.3071 cents, which rougly corresponds to 27.0837-edo.

Assuming however pure octaves, 27 has a fifth sharp by slightly more than nine cents and a 7/4 sharp by slightly less, and the same 400 cent major third as [[12edo]], sharp 13+2/3 cents. The result is that [[6/5]], [[7/5]] and especially [[7/6]] are all tuned more accurately than this. It can be considered the superpythagorean counterpart of [[19edo]], as its 5th is audibly indistinguishable from 1/3 [[septimal comma]] superpyth in the same way that 19edo is audibly indistinguishable from [[1/3 syntonic comma meantone]], resulting in three of them reaching a near perfect minor third/major sixth in both.

27edo, with its 400 cent major third, tempers out the [[diesis]] of [[128/125]], and also the septimal comma, [[64/63]] (and hence [[126/125]] also). These it shares with 12edo, making some relationships familiar, and as a consequence they both support augene temperament. It shares with [[22edo]] tempering out the allegedly Bohlen-Pierce comma [[245/243]] as well as 64/63, so that they both support the [[superpyth]] temperament, with quite sharp "superpythagorean" fifths giving a sharp [[9/7]] in place of meantone's 5/4.

Though the [[7-limit]] tuning of 27edo is not highly accurate, it nonetheless is the smallest equal division to represent the 7-odd-limit both [[consistent]]ly and distinctly – that is, everything in the [[7-odd-limit]] diamond is uniquely represented by a certain number of steps of 27edo. It also represents the 13th harmonic very well, and performs quite decently as a 2.3.5.7.13 temperament. It also approximates [[19/10]], [[19/12]], and [[19/14]], so 0-7-13-25 does quite well as a 10:12:14:19; the major seventh 25\27 is less than a cent off from 19/10. Octave-inverted, these also form a quite convincing approximation of the main Bohlen-Pierce triad, 3:5:7, making it the smallest edo that can simulate tritave harmony, although it rapidly becomes quite rough if extended to the 9 and above, unlike a true tritave based system.

Its step, as well as the octave-inverted and octave-equivalent versions of it, holds the distinction for having around the highest [[harmonic entropy]] possible and thus is, in theory, most dissonant, assuming the relatively common values of ''a'' = 2 and ''s'' = 1%. This property is shared with all edos between around 24 and 30. Intervals smaller than this tend to be perceived as unison and are more consonant as a result; intervals larger than this have less "tension" and thus are also more consonant.

The 27-note system or one similar like a well temperament can be notated very easily, by a variation on the quartertone accidentals. In this case a sharp raises a note by 4 edosteps, just one edostep beneath the following nominal (for example C to C# describes the approximate 10/9 and 11/10 interval) and the flat conversely lowers: these are augmented unisons and diminished unisons. Just so, one finds that an accidental can be divided in half, and this fill the remaining places without need for double sharps and double flats. Enharmonically then, E double flat means C half sharp. In other words, the resemblance to quarter tone notation differs in enharmonic divergence. The notes from C to D are C, D flat, C half-sharp, D half-flat, C sharp, D. Unfortunately, some ascending intervals appear to be descending on the staff. Furthermore, the 3rd of a 4:5:6 or 10:12:15 chord must be notated as either a 2nd or a 4th. The composer can decide for him/herself which addidional accidental pair is necessary if they will need redundancy to remedy these problems, and to keep the chromatic pitches within a compass on paper relative to the natural names (C, D, E etc.). Otherwise it is simple enough, and the same tendency for A# to be higher than Bb is not only familiar, though here very exaggerated, to those working with the Pythagorean scale, but also to many classically trained violinists.
=== Odd harmonics ===
{{Harmonics in equal|27}}

== Intervals ==
{| class="wikitable center-all right-2 left-3"
|-
! #
! Cents
! Approximate Ratios*
! colspan="3" | [[Ups and Downs Notation]]
! Solfege
|-
| 0
| 0.00
| [[1/1]]
| P1
| perfect unison
| D
| do
|-
| 1
| 44.44
| [[28/27]], [[36/35]], [[39/38]], [[49/48]], [[50/49]], [[81/80]]
| ^1, m2
| up unison, minor 2nd
| ^D, Eb
| di
|-
| 2
| 88.89
| [[16/15]], [[21/20]], [[25/24]], [[19/18]], [[20/19]]
| ^^1, ^m2
| dup unison, upminor 2nd
| ^^D, ^Eb
| ra
|-
| 3
| 133.33
| [[15/14]], [[14/13]], [[13/12]]
| vA1, ~2
| downaug 1sn, mid 2nd
| vD#, vvE
| ru
|-
| 4
| 177.78
| [[10/9]]
| A1, vM2
| aug 1sn, downmajor 2nd
| D#, vE
| reh
|-
| 5
| 222.22
| [[8/7]], [[9/8]]
| M2
| major 2nd
| E
| re
|-
| 6
| 266.67
| [[7/6]]
| m3
| minor 3rd
| F
| ma
|-
| 7
| 311.11
| [[6/5]], [[19/16]]
| ^m3
| upminor 3rd
| Gb
| me
|-
| 8
| 355.56
| [[16/13]]
| ~3
| mid 3rd
|^Gb
| mu
|-
| 9
| 400.00
| [[5/4]], [[24/19]]
| vM3
| downmajor 3rd
| vF#
| mi
|-
| 10
| 444.44
| [[9/7]], [[13/10]]
| M3
| major 3rd
| F#
| mo
|-
| 11
| 488.89
| [[4/3]]
| P4
| perfect 4th
| G
| fa
|-
| 12
| 533.33
| [[27/20]], [[48/35]], [[19/14]], [[26/19]]
| ^4
| up 4th
| Ab
| fih
|-
| 13
| 577.78
| [[7/5]], [[18/13]]
| ~4, ^d5
| mid 4th, updim 5th
| ^^G, ^Ab
| fi
|-
| 14
| 622.22
| [[10/7]], [[13/9]]
| vA4, ~5
| downaug 4th, mid 5th
| vG#, vvA
| se
|-
| 15
| 666.67
| [[40/27]], [[35/24]], [[19/13]], [[28/19]]
| v5
| down fifth
| G#
| sih
|-
| 16
| 711.11
| [[3/2]]
| P5
| perfect 5th
| A
| so/sol
|-
| 17
| 755.56
| [[14/9]], [[20/13]]
| m6
| minor 6th
| Bb
| lo
|-
| 18
| 800.00
| [[8/5]], [[19/12]]
| ^m6
| upminor 6th
| ^Bb
| le
|-
| 19
| 844.44
| [[13/8]]
| ~6
| mid 6th
| vA#
| lu
|-
| 20
| 888.89
| [[5/3]], [[32/19]]
| vM6
| downmajor 6th
| A#
| la
|-
| 21
| 933.33
| [[12/7]]
| M6
| major 6th
| B
| li
|-
| 22
| 977.78
| [[7/4]], [[16/9]]
| m7
| minor 7th
| C
| ta
|-
| 23
| 1022.22
| [[9/5]]
| ^m7
| upminor 7th
| Db
| te
|-
| 24
| 1066.67
| [[28/15]], [[13/7]], [[24/13]]
| ~7
| mid 7th
| ^Db
| tu
|-
| 25
| 1111.11
| [[15/8]], [[40/21]], [[48/25]], [[19/10]], [[36/19]]
| vM7
| downmajor 7th
| vC#
| ti
|-
| 26
| 1155.56
| [[27/14]], [[35/18]], [[96/49]], [[49/25]], [[160/81]]
| M7
| major 7th
| C#
| da
|-
| 27
| 1200.00
| 2/1
| P8
| 8ve
| D
| do
|}
<nowiki/>* based on treating 27edo as a 2.3.5.7.13.19 subgroup temperament; other approaches are possible.

Combining ups and downs notation with [[color notation]], qualities can be loosely associated with colors:

{| class="wikitable center-all"
|-
! quality
! [[color name]]
! monzo format
! examples
|-
| rowspan="2" | minor
| zo
| {a, b, 0, 1}
| 7/6, 7/4
|-
| fourthward wa
| {a, b}, b < -1
| 32/27, 16/9
|-
| upminor
| gu
| {a, b, -1}
| 6/5, 9/5
|-
| rowspan="2" | mid
| tho
| {a, b, 0, 0, 0, 1}
| 13/12, 13/8
|-
| thu
| {a, b, 0, 0, 0, -1}
| 16/13, 24/13
|-
| downmajor
| yo
| {a, b, 1}
| 5/4, 5/3
|-
| rowspan="2" | major
| fifthward wa
| {a, b}, b > 1
| 9/8, 27/16
|-
| ru
| {a, b, 0, -1}
| 9/7, 12/7
|}
All 27edo chords can be named using ups and downs. Alterations are always enclosed in parentheses, additions never are. An up or down after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13). Here are the zo, gu, ilo, yo and ru triads:

{| class="wikitable center-all"
|-
! [[Color notation|color of the 3rd]]
! JI chord
! notes as edosteps
! notes of C chord
! written name
! spoken name
|-
| zo
| 6:7:9
| 0-6-16
| C Eb G
| Cm
| C minor
|-
| gu
| 10:12:15
| 0-7-16
| C ^Eb G
| C^m
| C upminor
|-
| ilo
| 18:22:27
| 0-8-16
| C vvE G
| C~
| C mid
|-
| yo
| 4:5:6
| 0-9-16
| C vE G
| Cv
| C downmajor or C down
|-
| ru
| 14:18:21
| 0-10-16
| C E G
| C
| C major or C
|}
For a more complete list, see [[Ups and Downs Notation #Chords and Chord Progressions]]. See also the [[22edo]] page.

== JI approximation ==

=== 15-odd-limit interval mappings ===
The following table shows how [[15-odd-limit intervals]] are represented in 27edo. Prime harmonics are in '''bold'''; inconsistent intervals are in ''italic''.
{| class="wikitable center-all"
|+ Direct mapping (even if inconsistent)
|-
! Interval, complement
! Error (abs, ¢)
|-
| [[7/6]], [[12/7]]
| 0.204
|-
| ''[[15/11]], [[22/15]]''
| ''3.617''
|-
| '''[[16/13]], [[13/8]]'''
| '''3.917'''
|-
| [[6/5]], [[5/3]]
| 4.530
|-
| [[10/9]], [[9/5]]
| 4.626
|-
| [[7/5]], [[10/7]]
| 4.734
|-
| [[14/13]], [[13/7]]
| 5.035
|-
| [[13/12]], [[24/13]]
| 5.239
|-
| ''[[11/9]], [[18/11]]''
| ''8.148''
|-
| '''[[8/7]], [[7/4]]'''
| '''8.952'''
|-
| '''[[4/3]], [[3/2]]'''
| '''9.156'''
|-
| [[9/7]], [[14/9]]
| 9.360
|-
| [[13/10]], [[20/13]]
| 9.770
|-
| ''[[11/10]], [[20/11]]''
| ''12.774''
|-
| '''[[5/4]], [[8/5]]'''
| '''13.686'''
|-
| [[15/14]], [[28/15]]
| 13.891
|-
| [[18/13]], [[13/9]]
| 14.395
|-
| ''[[12/11]], [[11/6]]''
| ''17.304''
|-
| ''[[14/11]], [[11/7]]''
| ''17.508''
|-
| '''[[11/8]], [[16/11]]'''
| '''17.985'''
|-
| [[9/8]], [[16/9]]
| 18.312
|-
| [[15/13]], [[26/15]]
| 18.926
|-
| ''[[16/15]], [[15/8]]''
| ''21.602''
|-
| [[13/11]], [[22/13]]
| 21.901
|}

{| class="wikitable center-all"
|+ Patent val mapping
|-
! Interval, complement
! Error (abs, ¢)
|-
| [[7/6]], [[12/7]]
| 0.204
|-
| '''[[16/13]], [[13/8]]'''
| '''3.917'''
|-
| [[6/5]], [[5/3]]
| 4.530
|-
| [[10/9]], [[9/5]]
| 4.626
|-
| [[7/5]], [[10/7]]
| 4.734
|-
| [[14/13]], [[13/7]]
| 5.035
|-
| [[13/12]], [[24/13]]
| 5.239
|-
| '''[[8/7]], [[7/4]]'''
| '''8.952'''
|-
| '''[[4/3]], [[3/2]]'''
| '''9.156'''
|-
| [[9/7]], [[14/9]]
| 9.360
|-
| [[13/10]], [[20/13]]
| 9.770
|-
| '''[[5/4]], [[8/5]]'''
| '''13.686'''
|-
| [[15/14]], [[28/15]]
| 13.891
|-
| [[18/13]], [[13/9]]
| 14.395
|-
| '''[[11/8]], [[16/11]]'''
| '''17.985'''
|-
| [[9/8]], [[16/9]]
| 18.312
|-
| [[15/13]], [[26/15]]
| 18.926
|-
| [[13/11]], [[22/13]]
| 21.901
|-
| ''[[16/15]], [[15/8]]''
| ''22.842''
|-
| ''[[14/11]], [[11/7]]''
| ''26.936''
|-
| ''[[12/11]], [[11/6]]''
| ''27.141''
|-
| ''[[11/10]], [[20/11]]''
| ''31.671''
|-
| ''[[11/9]], [[18/11]]''
| ''36.297''
|-
| ''[[15/11]], [[22/15]]''
| ''40.827''
|}

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal 8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 43 -27 }}
| [{{val| 27 43 }}]
| -2.89
| 2.88
| 6.50
|-
| 2.3.5
| 128/125, 20000/19683
| [{{val| 27 43 63 }}]
| -3.88
| 2.74
| 6.19
|-
| 2.3.5.7
| 64/63, 126/125, 245/243
| [{{val| 27 43 63 76 }}]
| -3.70
| 2.39
| 5.40
|-
| 2.3.5.7.13
| 64/63, 91/90, 126/125, 169/168
| [{{val| 27 43 63 76 100 }}]
| -3.18
| 2.39
| 5.39
|-
| 2.3.5.7.13.19
| 64/63, 76/75, 91/90, 126/125, 169/168
| [{{val| 27 43 63 76 100 115 }}]
| -3.18
| 2.18
| 4.92
|}

27et (27eg val) is lower in relative error than any previous equal temperaments in the 13-, 17-, and 19-limit. The next equal temperaments doing better in those subgroups are 31, 31, and 46, respectively.

27et is particularly strong in the 2.3.5.7.13.19 subgroup. The next equal temperament that does better in this subgroup is 53.

=== Rank-2 temperaments ===
* [[List of 27edo rank two temperaments by badness]]
* [[List of edo-distinct 27e rank two temperaments]]

{| class="wikitable center-all left-3 left-4"
|-
! Periods per octave
! Generator
! Temperaments
! MOS Scales
|-
| 1
| 1\27
| [[Quartonic]]/quarto
|
|-
| 1
| 2\27
| [[Octacot]]/octocat
| [[1L_12s]], [[13L_1s]]
|-
| 1
| 4\27
| [[Tetracot]]/modus/wollemia
| [[1L_5s]], [[6L_1s]], [[7L_6s]], [[7L_13s]]
|-
| 1
| 5\27
| [[Machine]]/kumonga
| [[1L_4s]], [[5L_1s]], [[5L_6s]], [[11L_5s]]
|-
| 1
| 7\27
| [[Myna]]/coleto/minah/[[oolong]]
| [[4L_3s]], [[4L_7s]], [[4L_11s]], [[4L_15s]], [[4L_19s]]
|-
| 1
| 8\27
| [[Beatles]]/ringo
| [[3L_4s]], [[7L_3s]], [[10L_7s]]
|-
| 1
| 10\27
| [[Sensi]]/sensis
| [[3L_2s]], [[3L_5s]], [[8L_3s]], [[8L_11s]]
|-
| 1
| 11\27
| [[Superpyth]]
| [[5L_2s]], [[5L_7s]], [[5L_12s]], [[5L_17s]]
|-
| 1
| 13\27
| Fervor
| [[2L_3s]], [[2L_5s]], [[2L_7s]], [[2L_9s]], [[2L_11s]], etc ... [[2L_23s]]
|-
| 3
| 1\27
| [[Semiaug]]/hemiaug
|
|-
| 3
| 2\27
| [[Augmented]]/[[Augene]]/ogene
| [[3L_3s]], [[3L_6s]], [[3L_9s]], [[12L_3s]]
|-
| 3
| 4\27
| [[Oodako]]/[[terrain]]
| [[3L_3s]], [[6L_3s]], [[6L_9s]], [[6L_15s]]
|-
| 9
| 1\27
| Terrible version of [[Ennealimmal]] /niner
| [[9L_9s]]
|}

=== Commas ===
27edo [[tempers out]] the following [[commas]]. (Note: This assumes the [[val]] {{val| 27 43 63 76 93 100 }}.)

{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
! [[Harmonic Limit|Prime Limit]]
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref>
! [[Monzo]]
! [[Cent]]s
! [[Color name]]
! Name(s)
|-
| 5
| [[128/125]]
| {{monzo| 7 0 -3 }}
| 41.06
| Trigu
| Diesis, augmented comma
|-
| 5
| [[20000/19683]]
| {{monzo| 5 -9 4 }}
| 27.66
| Saquadyo
| Minimal diesis, Tetracot comma
|-
| 5
| [[78732/78125]]
| {{monzo| 2 9 -7 }}
| 13.40
| Sepgu
| Medium semicomma, Sensipent comma
|-
| 5
| <abbr title="7629394531250/7625597484987">(26 digits)</abbr>
| {{monzo| 1 -27 18 }}
| 0.86
| Satritribiyo
| [[Ennealimma]]
|-
| 7
| [[686/675]]
| {{monzo| 1 -3 -2 3 }}
| 27.99
| Trizo-agugu
| Senga
|-
| 7
| [[64/63]]
| {{monzo| 6 -2 0 -1 }}
| 27.26
| Ru
| Septimal comma, Archytas' comma, Leipziger Komma
|-
| 7
| [[50421/50000]]
| {{monzo| -4 1 -5 5 }}
| 14.52
| Quinzogu
| Trimyna
|-
| 7
| [[245/243]]
| {{monzo| 0 -5 1 2 }}
| 14.19
| Zozoyo
| Sensamagic
|-
| 7
| [[126/125]]
| {{monzo| 1 2 -3 1 }}
| 13.79
| Zotrigu
| Septimal semicomma, Starling comma
|-
| 7
| [[4000/3969]]
| {{monzo| 5 -4 3 -2 }}
| 13.47
| Rurutriyo
| Octagar
|-
| 7
| [[1728/1715]]
| {{monzo| 6 3 -1 -3 }}
| 13.07
| Triru-agu
| Orwellisma, Orwell comma
|-
| 7
| <abbr title="420175/419904">(12 digits)</abbr>
| {{monzo| -6 -8 2 5 }}
| 1.12
| Quinzo-ayoyo
| [[Wizma]]
|-
| 7
| [[2401/2400]]
| {{monzo| -5 -1 -2 4 }}
| 0.72
| Bizozogu
| Breedsma
|-
| 7
| [[4375/4374]]
| {{monzo| -1 -7 4 1 }}
| 0.40
| Zoquadyo
| Ragisma
|-
| 7
| <abbr title="250047/250000">(12 digits)</abbr>
| {{monzo| -4 6 -6 3 }}
| 0.33
| Trizogugu
| [[Landscape comma]]
|-
| 11
| [[99/98]]
| {{monzo| -1 2 0 -2 1 }}
| 17.58
| Loruru
| Mothwellsma
|-
| 11
| [[896/891]]
| {{monzo| 7 -4 0 1 -1 }}
| 9.69
| Saluzo
| Pentacircle
|-
| 11
| [[385/384]]
| {{monzo| -7 -1 1 1 1 }}
| 4.50
| Lozoyo
| Keenanisma
|-
| 13
| [[91/90]]
| {{monzo| -1 -2 -1 1 0 1 }}
| 19.13
| Thozogu
| Superleap
|}
<references/>

== Music ==
* [https://www.archive.org/details/MusicForYourEars Music For Your Ears] ([https://www.archive.org/download/MusicForYourEars/musicfor.mp3 play]) by [[Gene Ward Smith]] The central portion is in 27edo, the rest in [[46edo]].
* [http://micro.soonlabel.com/gene_ward_smith/Others/Igs/Sad%20Like%20Winter%20Leaves.mp3 Sad Like Winter Leaves] by [[Igliashon Jones]] {{dead link}}
* [[:File:Superpythagorean_Waltz.mp3|Superpythagorean Waltz]] by [[Igliashon Jones]]
* [https://pixelarchipelago.bandcamp.com/track/stuttering-anticipation-27edo Stuttering Anticipation] by [[Igliashon Jones]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of27sonatina.mp3 Galticeran Sonatina] by [[Joel Taylor]]
* [https://www.youtube.com/watch?v=7QcwKlK6z4c miniature prelude and fugue] by [[Peter Kosmorsky]]
* [http://micro.soonlabel.com/27edo/daily20111202-deep-chasm-zeta-cp-1.mp3 Chicago Pile-1] by [[Chris Vaisvil]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Perc-Sitar.mp3 Tetracot Perc-Sitar] (on [https://soundcloud.com/dustin-schallert/tetracot-perc-sitar SoundCloud]) by [[Dustin Schallert]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Jam.mp3 Tetracot Jam] (on [https://soundcloud.com/dustin-schallert/tetracot-jam SoundCloud]) by [[Dustin Schallert]]
* [http://micro.soonlabel.com/gene_ward_smith/Others/Schallert/Tetracot%20Pump.mp3 Tetracot Pump] (on [https://soundcloud.com/dustin-schallert/tetracot-pump SoundCloud]) by [[Dustin Schallert]]
* [https://soundcloud.com/dustin-schallert/27-edo-guitar-1 27-EDO Guitar 1] by [[Dustin Schallert]]

== See also ==
* [[Lumatone mapping for 27edo]]

[[Category:27edo| ]] 
[[Category:Equal divisions of the octave|##]] 
[[Category:Augene]]
[[Category:Listen]]
[[Category:Twentuning]]
[[Category:Zeta]]

TAMNAMS

2022-11-15T13:19:01Z

Xenwolf: fix typo

'''TAMNAMS''' (read "tame names"; from '''''T'''emperament-'''A'''gnostic '''M'''os '''NAM'''ing '''S'''ystem''), devised by the XA Discord, is a system of temperament-agnostic names for scales (designed especially with small octave-equivalent [[mos]]ses in mind), their intervals and their associated generator ranges, taking into account the relative sizes of large and small steps.

== Step ratio spectrum ==
=== Simple step ratios ===
The TAMNAMS system names nine specific simple [[Blackwood's R|L:s ratios]]. These correspond to the simplest edos that have the mos scale.

{| class=wikitable
|-
|+ Step ratio names
|-
! TAMNAMS Name
! Ratio
! Diatonic example
|-
| Equalized
| L:s = 1:1
| [[7edo]]
|-
| Supersoft
| L:s = 4:3
| [[26edo]]
|-
| Soft (or monosoft)
| L:s = 3:2
| [[19edo]]
|-
| Semisoft
| L:s = 5:3
| [[31edo]]
|-
| Basic (or quintessential)
| L:s = 2:1
| [[12edo]]
|-
| Semihard
| L:s = 5:2
| [[29edo]]
|-
| Hard (or monohard)
| L:s = 3:1
| [[17edo]]
|-
| Superhard
| L:s = 4:1
| [[22edo]]
|-
| Collapsed
| L:s = 1:0
| [[5edo]]
|}

For example, the 5L2s (diatonic) scale of 19edo has a step ratio of 3:2, which is ''soft''. We call the 19edo diatonic scale ''soft diatonic''. Tunings of a mos with L:s larger are ''harder'', and tunings with L:s smaller are ''softer''.

The two extremes, equalized and collapsed, are degenerate cases. An equalized mos has L equal to s, so the mos pattern is no longer apparent. A collapsed mos has s = 0, merging adjacent tones s apart into a single tone. In both cases, the mos structure is no longer valid.

=== Step ratio ranges ===
In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying mos tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic. Note that the soft-of-basic range is always strictly proper while the hard-of-basic range is often improper but is always proper in the case that there is 1 small step per period in the mos pattern.

By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier ''strict'' can be used, for example ''strict hyposoft''.
{| class="wikitable"
|+Intermediate ranges
!TAMNAMS Name
!Range
|-
|Hyposoft
|3:2 ≤ L:s ≤ 2:1
|-
|Ultrasoft
|1:1 ≤ L:s ≤ 4:3
|-
|Parasoft
|4:3 ≤ L:s ≤ 3:2
|-
|Quasisoft
|3:2 ≤ L:s ≤ 5:3
|-
|Minisoft
|5:3 ≤ L:s ≤ 2:1
|-
|Minihard
|2:1 ≤ L:s ≤ 5:2
|-
|Quasihard
|5:2 ≤ L:s ≤ 3:1
|-
|Parahard
|3:1 ≤ L:s ≤ 4:1
|-
|Ultrahard
|4:1 ≤ L:s ≤ 1:0
|-
|Hypohard
|2:1 ≤ L:s ≤ 3:1
|}

=== Central spectrum ===
'''Equalized''': L/s = 1/1 (trivial/pathological)

::: ('''Ultrasoft''' range here, may also be called ''pseudoequalized'' if especially close to equalized.)

:: '''Supersoft''': L/s = 4/3

::: ('''Parasoft''' range here.)

: '''Soft''': L/s = 3/2

::: (Beginning of '''hyposoft''' range here.)

::: ('''Quasisoft''' range here.)

:: '''Semisoft''': L/s = 5/3

::: ('''Minisoft''' range here.)

::: (End of '''hyposoft''' range here.)

'''Quintesssential''': L/s = 2/1

::: (Beginning of '''hypohard''' range here.)

::: ('''Minihard''' range here.)

:: '''Semihard''': L/s = 5/2

::: ('''Quasihard''' range here.)

::: (End of '''hypohard''' range here.)

: '''Hard''': L/s = 3/1

::: ('''Parahard''' range here.)

:: '''Superhard''': L/s = 4/1

::: ('''Ultrahard''' range here, may also be called ''pseudocollapsed'' if especially close to collapsed.)

'''Collapsed''': L/s = 1/0 = infinity (trivial/pathological)

== Naming mos intervals ==
To denote interval classes within the mos, TAMNAMS uses the generic prefix ''mos-'', or the specific prefixes and abbreviations listed under ''mos pattern names''. One might be tempted to
generalize diatonic 1-indexed ordinal names: ''In 31edo's ultrasoft [[mosh]] scale, the perfect mosthird (aka Pmosh3rd) is a neutral third and the major mosfifth (aka Lmosh5th) is a perfect fifth.''

The way intervals are named above (and in 12edo theory) has a problem. An interval that's n steps wide is named ''(n+1)th''. This means that adding two intervals is more complicated than it should be. Stacking two fifths makes a ninth, when naively it would make a tenth. We're used to this for the diatonic scale, but when dealing with unfamiliar scale structures, it can be very confusing.

Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.

In contexts where it doesn't cause ambiguity, ''k-mosstep'' can be shortened to ''k-step''. ''k-step'' is also generalizable to non-mos scale types such as 3-step-size scales; see below for naming in scales with 3 step sizes.

(The ordinal names could still be suggestive for e.g. (tunings of) heptatonic mosses where the ordinal names tend to match up well with diatonic ordinal categories.)
{| class="wikitable"
|+Example: 3L4s
!Interval name
!Abbreviation
!10edo Size
!Gens up
|-
|Perfect mosunison
|P0ms
|0\10
|0
|-
|Minor mosstep (or small mosstep)
|m1ms
|1\10
| -3
|-
|Major mosstep (or large mosstep)
|M1ms
|2\10
|4
|-
|Diminished 2-mosstep
|d2ms
|2\10
| -6
|-
|Perfect 2-mosstep
|P2ms
|3\10
|1
|-
|Minor 3-mosstep
|m3ms
|4\10
| -2
|-
|Major 3-mosstep
|M3ms
|5\10
|5
|-
|Minor 4-mosstep
|m4ms
|5\10
| -5
|-
|Major 4-mosstep
|M4ms
|6\10
|2
|-
|Perfect 5-mosstep
|P5ms
|7\10
| -1
|-
|Augmented 5-mosstep
|A5ms
|8\10
|6
|-
|Minor 6-mosstep
|m6ms
|8\10
| -4
|-
|Major 6-mosstep
|M6ms
|9\10
|3
|-
|Perfect mosoctave
|P7ms
|10\10
|0
|}

TAMNAMS uses the following modifiers to denote different interval sizes within a mos interval class:
* For multiples of the period plus or minus 0 or 1 generators: ''perfect''. (Diatonic examples: perfect mos4th (Pmos4th), perfect mos5th (Pmos5th), perfect mos8th (Pmos8th), perfect mos12th (Pmos12th), etc.)
* For generic interval classes with 2 specific sizes of intervals therein (which are therefore separated by a chroma of c = L - s), ''major'' and ''minor'' are used to distinguish the larger (L) and smaller (s) intervals. Note that the generator, its period-equivalents, and the generator's period-complement and its period-equivalents are the only intervals excluded from this rule due to their inclusion in the previous rule. Diatonic examples: major mos2nd (abbreviated Lmos2nd), minor mos3rd (abbreviated smos3rd), major mos3rd (Lmos3rd), etc.)
* For nL ns scales, there's an exception to the above two rules. Only multiples of the period (1\n) are called ''perfect''. Other intervals are called major or minor, despite being period-equivalent to a generator. The reason for this exception is that otherwise all intervals would be called ''perfect'', leading to ambiguity.
* If you subtract a chroma from a perfect (Pmos) or minor (smos) interval, it becomes ''diminished'' (d; dmos). If you subtract two chromas instead, it becomes ''doubly diminished'' (dd; ddmos). (Diatonic examples: diminished mos3rd (dmos3rd), diminished mos4th (dmos4th), doubly diminished mos5th (ddmos5th), etc.)
** When modifying unisons or octave multiples, ''mosdiminished'' and ''mosaugmented'' could be used (e.g. ''mosdiminished octave'' instead of ''diminished mosoctave''), because the unison and the octave don't change depending on the mos pattern, but the meanings of ''augmented'' and ''diminished''.
* If you add a chroma to a perfect (Pmos) or major (Lmos) interval, it becomes ''augmented'' (A; Amos). If you add two chromas instead, it becomes ''doubly augmented'' (AA; AAmos). (Diatonic examples: augmented mos2nd (Amos2nd), augmented mos4th (Amos4th), doubly augmented mos5th (AAmos5th).)
* The pattern continues, ddd for triply diminished and AAA for triply augmented. Note that applying this operation more than 3 times is an unlikely usecase, and a shorthand notaton of d^3 and A^3 or an alternative notation or terminology entirely would likely be preferable in such circumstances, hence repetition of the corresponding letter is a sufficient system.

Other interval names:
* ''moschroma'' or ''chroma'': L − s
* ''mosdiesis'': |chroma − s| = |L − 2s|

== Naming mos degrees ==
To denote degrees in a given mos (or altered mos) mode, we use the term ''k-mosdegree'', abbreviated as kmd (or ''k-degree'' and kd if context allows). Just like for mos interval names, we use 0-indexing, so the perfect 0-mosdegree is the tonic. The modifiers ''perfect'', ''minor'', ''major'', ''augmented'' and ''diminished'' can be used just like for mos interval names: for example, ''minor 3-mosdegree'' (m3md) denotes the degree that lies a minor 3-mosstep above the tonic. Modifiers can be omitted when clear from context.

To denote a chord or a mode on a given degree, write the chord or the mode in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the 0-369-646 chord can be written 0-4-7\13, P0ms-M2ms-M4ms or 7|0 0-2-4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0-369-646), or the chord 0-369-646 on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal: Naming mos modes|below]] for the convention we have used to name the mode).

== Mos pattern names ==
NOTE: Names are finalized, prefixes and abbreviations are still open to change.

TAMNAMS suggests the following names for selected small mosses. These names are optional; interval size names and step ratio names can be combined with conventional ''xL ys'' names. For example: ''21edo is the soft [[5L 3s]] tuning and its major mosthird is a neutral third of size 342.9 cents.''

Some of the names come from older temperament-agnostic mos names, such as names (such as ''mosh'') from [[Graham Breed]]'s [[mos naming#Graham_Breed.27s_naming_scheme|mos names]]. These names have been coined so that mosses can be discussed more independently of RTT temperaments. Sometimes the prefix has a different source than the scale name for euphonic reasons.

1L ns names are named with the an- prefix if they are generalised names and anti- prefix if the name for the corresponding nL1s scale assumed a period of an octave.

This list is maintained by [[User:Inthar]] and [[User:Godtone]].
{| class="wikitable center-all"
|+ TAMNAMS moss names
!colspan=6| 2-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix>used in interval, degree and mode names, e.g. ''perfect 3-oneirostep, perfect 3-oneirodegree, oneiro-3-up''</ref> !! Abbreviation<ref name="abbr">written abbreviations of prefixes, e.g. ''P3neiros, P3neirod, on-3|''</ref> !! Allows non-octave tunings?<ref name="general">whether the name can be used for mosses with no octaves; lightly tempered octaves are allowed; names for mosses with more than 5 notes do not admit nonoctave tunings because the names are specific to the corresponding valid tuning range</ref> !! Etymology
|-
| [[1L 1s]] || trivial || triv- || trv || Yes; can have any period || the simplest valid mos pattern
|-
| [[1L 1s]] || monowood || monowd- || wood || No; must have octave period || blackwood[10] & whitewood[14] generalized to n-wood for nL ns
|-
!colspan=6| 3-note mosses (non-octave<ref name=general/>)
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! (Non-octave periods allowed)<ref name=general/> !! Etymology
|-
| [[1L 2s]] || antrial || atri- || atri || Yes; can have any period || broader range than trial so named w.r.t. it (anti-trial; antial; antrial)
|-
| [[2L 1s]] || trial || tri- || tri || Yes; can have any period || from tri- for 3
|-
!colspan=6| 4-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Allows non-octave tunings?<ref name=general/> !! Etymology
|-
| [[1L 3s]] || antetric || atetra- || att || Yes; can have any period || broader range than tetric so named w.r.t. it (anti-tetric; antetric)
|-
| [[2L 2s]] || biwood || biwd- || bw || No; two periods must be an octave || from 2-wood
|-
| [[3L 1s]] || tetric || tetra- || tt || Yes; can have any period || from tetra- for 4
|-
!colspan=6| 5-note mosses (non-octave<ref name=general/>)
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! (Non-octave periods allowed)<ref name=general/> !! Etymology
|-
| [[1L 4s]] || pedal || ped- || ped || || [[#Pedal (1L 4s)|one big toe and four small toes]]
|-
| [[2L 3s]] || pentic || pent- || pt || || common pentatonic; from penta- for 5
|-
| [[3L 2s]] || antipentic || apent- || apt || || opposite pattern of common pentatonic mos
|-
| [[4L 1s]] || manual || manu- || manu || || one thumb and four longer fingers
|-
!colspan=6| 6-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Notes on tuning<ref name=general/> !! Etymology
|-
| [[1L 5s]] || antimachinoid || amech- || amech || || opposite pattern of machinoid
|-
| [[2L 4s]] || malic || mal- || mal || antrial mos with 2 periods per octave || apples have two concave ends, lemons have two pointy ends.
|-
| [[3L 3s]] || triwood || triwud- || trw || trivial mos with 3 periods per octave || from 3-wood
|-
| [[4L 2s]] || citric || citro- || cit || trial mos with 2 periods per octave || parent mos of lemon and lime
|-
| [[5L 1s]] || machinoid || mech- || mech || || from [[machine]] temperament
|-
!colspan=6| 7-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! (Octave periods only.)<ref name=general/> !! Etymology
|-
| [[1L 6s]] || onyx || on- || on || || [[#Onyx (1L 6s)|from a ''lot'' of naming puns]]
|-
| [[2L 5s]] || antidiatonic || pel- || pel || || pel- is from pelog
|-
| [[3L 4s]] || mosh || mosh- || mosh || || Graham Breed's name; from "mohajira-ish"
|-
| [[4L 3s]] || smitonic || smi- || smi || || from "sharp minor third"
|-
| [[5L 2s]] || diatonic || ''none'' || ''none'' || ||
|-
| [[6L 1s]] || arch(a)eotonic || arch- || arch || || originally a name for 13edo's 6L 1s
|-
!colspan=6| 8-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Notes on tuning<ref name=general/> !! Etymology
|-
| [[1L 7s]] || antipine || apine- || apine || || opposite pattern of pine
|-
| [[2L 6s]] || subaric || subar- || subar || antetric mos with 2 periods per octave || largest subset mos of jaric and taric
|-
| [[3L 5s]] || checkertonic || check- || chk || || from the [[Kite Giedraitis's Categorizations of 41edo Scales|Kite guitar checkerboard scale]]
|-
| [[4L 4s]] || tetrawood; diminished || tetwud- || ttw || trivial mos with 4 periods per octave || from 4-wood
|-
| [[5L 3s]] || oneirotonic || oneiro- || onei || || originally a name for 13edo's 5L 3s
|-
| [[6L 2s]] || ekic || ek- || ek || tetric mos with 2 periods per octave || from temperaments [[echidna]] and [[hedgehog]]
|-
| [[7L 1s]] || pine || pine- || pine || || from [[porcupine]] temperament
|-
!colspan=6| 9-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Notes on tuning<ref name=general/> !! Etymology
|-
| [[1L 8s]] || antisubneutralic || ablu- || ablu || || opposite pattern of subneutralic
|-
| [[2L 7s]] || balzano || bal- /bæl/ || bal || || from Balzano scale in 20edo which is 2L 7s
|-
| [[3L 6s]] || tcherepnin || cher- || ch || antrial mos with 3 periods per octave || common name
|-
| [[4L 5s]] || gramitonic || gram- || gram || ||from "grave minor third"
|-
| [[5L 4s]] || semiquartal || cthon- || cth || || from "half fourth" and "chthonic"
|-
| [[6L 3s]] || hyrulic || hyru- || hyru || trial mos with 3 periods per octave || allusion to [[triforce]] temperament
|-
| [[7L 2s]] || superdiatonic || arm- || arm || || common name, arm- is from [[Armodue]]
|-
| [[8L 1s]] || subneutralic || blu- || blu || || blu- is from [[bleu]] temperament
|-
!colspan=6| 10-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Notes on tuning<ref name=general/> !! Etymology
|-
| [[1L 9s]] || antisinatonic || asina- || asi || || opposite pattern of sinatonic
|-
| [[2L 8s]] || jaric || jara- || jar || pedal mos with 2 periods per octave || from temperaments [[pajara]], [[injera]] and [[diaschismic]]
|-
| [[3L 7s]] || sephiroid || seph- || seph || || from [[sephiroth]] temperament
|-
| [[4L 6s]] || lime || lime- || lime || pentic mos with 2 periods per octave || limes/4L 6s's steps tend to be smaller than lemons/6L 4s's steps
|-
| [[5L 5s]] || pentawood || penwud- || pw || trivial mos with 5 periods per octave || from 5-wood
|-
| [[6L 4s]] || lemon || lem- || lem || anpentic mos with 2 periods per octave || from [[lemba]] temperament
|-
| [[7L 3s]] || dicoid /'daɪˌkɔɪd/ or zaltertic || dico- or zal- || dico or zal || || from exotemperaments [[Dicot family#Dichotic|dichotic]] and [[dicot]] (dicoid), from "central Zalzalian third" for neutral third (zaltertic)
|-
| [[8L 2s]] || taric || tara- || tar || manual mos with 2 periods per octave || from Hindi ''aṭhārah'' '[[#Taric (8L 2s)|18]]'
|-
| [[9L 1s]] || sinatonic || sina- || si || || from [[sinaic]]
|}
<references/>
=== Reasoning for the names ===
The goal of TAMNAMS mos names is to choose memorable but aesthetically neutral names.

All names ending in -oid refer to an exotemperament which, when including extreme tunings, covers the entire range of the corresponding octave-period mos, such that many edos with simple step ratios for that mos will correspond to valid tunings, if not by patent val, then with a small number of warts.

All names for mosses with five or less notes - excluding (mono)wood and biwood (which like all n-wood mosses are specific to octave tuning) - require that some small integer multiple of the period is equal to an octave, under the reasoning that mosses with five or less notes are common and broad in tuning enough that they are much more likely to find interest in non-octave contexts. Because of this, their names were chosen to be extremely general, both to avoid bias/being too flavorful and (correspondingly) so that the terms could validly be reused for any mos for which the period is not equal to a (potentially tempered) octave.

Any multiperiod mos with more than five notes was given a name that wasn't reliant on the name of a mos with five or less notes as such names were based on those mos names formerly requiring an octave tuning (which is to say some small integer multiple of their period must be equal to a (potentially slightly tempered) octave).

Former names like "orwelloid" and "sensoid" were abandoned because the names were too temperament-specific in the sense that even considering extreme tunings didnt cover the whole range of the mos. The remaining temperament-based names have been abstracted or altered heavily, namely "pine", "hyrulic", "jaric", "ekic" and "lemon".

The inclusion of mos names for "multiperiod" mosses was from a desire to have all ten-note-and-under mosses named for completeness, which is also what prompted some of the reconsiderations mentioned earlier. Similarly, the inclusion of mosses of the form 1L ns using the "anti-" prefix (or an- for less-than-six-note mosses) was also for a practical consideration; although the tuning range is very unhelpful for knowing what such a mos will sound, it is nonetheless useful for describing structure in situations where one does not want to use the mathematical name, especially given that in such situations the tuning will likely be specified somewhere already. Jaric and taric specifically were chosen over bipedal and bimanual because of this, and to a lesser extent, lemon and lime were chosen over antibipentic and bipentic respectively (and for consistency with that their parent MOSS, 4L2s, is named citric).

The distinction between using the prefixes "anti-" vs "an-" for reversing the number of large vs. small steps is also not as trivial as it may sound. In the case of mosses with six or more notes, as the period is always an octave, there is a very large tuning range for the 1L ns mosses (hence the original reason for omitting such mosses), but the "anti-" prefix shows that what is significant is that it has the opposite structure to the corresponding nL 1s mos while pointing out the resulting ambiguity of range. In the case of mosses with five or less notes, as the period is not known and therefore could be very small, this is not as much of a concern as fuller specification is likely required anyway, especially in the case of larger periods, so the name should not be tediously long as the name refers to a very simple mos pattern, and for related reasons, the name shouldn't give as much of a sense of one 'orientation' of the structure being more 'primary' than the other, while with mosses with more than five notes, this suggestion of sense is very much intended, because it will almost always make more sense to talk about the (n+1)L 1s child mos of whatever 1L ns mos you want to speak of.

=== Name-specific reasonings ===
==== Pedal (1L 4s) ====
Pedals are operated with feet, which have one large toe and four small toes. Also comes from words like "bipedal", where in TAMNAMS, "bipedal" would literally mean a pedal scale with a period equal to half of some chosen interval, although such a scale would have either two right feet or two left feet depending on orientation chosen. If you think "car"/"vehicle" when you think "pedal" and don't think (or want to think) much about feet then you can think about "[[beep]]ing" (as [[beep]] is the 7-limit 4&5 exotemperament). Because this name relies so heavily and fundamentally on there being 1 large and 4 small steps per period, it is appropriate to generalise for any size of period you would want. In that regard, same goes for manual, pentic and anpentic.
==== Malic (2L 4s) and citric (4L 2s) ====
Malic derives from Latin ''malus'' 'apple'. An apple has two concave ends, and large steps in a scale with more small steps are hole-like, hence the two large steps in malic. Citric (4L 2s) is named after the child mosses of citric, namely lemon (6L 4s) and lime (4L 6s). Unlike apples, lemons have two convex pointy ends, and small steps in a scale with more large steps are pointy, hence the two small steps. Malic and citric acids are both ubiquitous in food and biology, thus justifying their use for fairly small mos scales.

==== Machinoid (5L 1s) ====
[[Machine]] is the 5&6 temperament in the 2.9.7.11 subgroup with a comma list of 64/63 and 99/98.

Its list of EDO tunings is {{ val list | 5, 6, (5+5=10e,) 11, 12, 16, 17, (5+10e+12=21be,) 22, 23, (5+5+5+5+6=26qe,) 27, 28, 33 }} with non-patent val EDOs in brackets but included for demonstrating virtual completeness of the tuning range and the unusually large [[33edo]] tuning being to show [[11edo]]'s strength as a tuning.

==== Onyx (1L 6s) ====
"1Ln-ic's" and "nL1-ic's (like, the -ic suffix applied to MOSS names, collectivised for 1Lns and nL1s) sounds like "one-el-en-ics" or "en-el-one-ics" which abbreviated sort of sounds like "one-ics" => "onyx". Then "onyx" sounds sort of like "one-six". Furthermore the onyx mineral comes in many colours and types, which seems fitting given this is the parent scale for a wide variety of MOSSes; specifically of interest being 7L 1s (pine), 8L 1s (subneutralic) and 9L 1s (sinatonic). Finally, the name "onyx" is also supposed to be vaguely reminiscent of "anti-archaeotonic" as "chi" (the greek letter) is written like an "x" (this is related to why "christmas" is abbreviated sometimes as "X-mas") and other than that, the letters "o" and "n" and their sounds are also present in "archaeotonic", and "x" is vaguely reminiscent of negation and multiplication. There is also something like a "y" sound in "archaeotonic" in the "aeo" part (depending partially on your pronounciation).
==== Subaric (2L 6s) ====
This name alludes to the fact that 2L 6s is the largest proper '''sub'''set mos of both j'''aric''' (2L 8s) and t'''aric''' (8L 2s).
==== Jaric (2L 8s) ====
This name alludes to a few highly notable and generally inaccurate (with the exception of diaschismic) temperaments that exist in the tuning range of this MOSS. Specifically, notice how the letters and sound of "jaric" has (or is intended to have) a lot of overlap with [[pajara]], [[diaschismic]] and [[injera]] (listed in order of increasingly sharp fourths; note that diatonic fourths and 4-jarasteps are equated in jaric, a notable property).
==== Taric (8L 2s) ====
Taric was named based on it being the only octave-tuned TAMNAMS pattern with a [[#Simple step ratios|basic]] tuning of [[18edo]] (because [[5L 6s]] has more than 10 notes so is out of the scope of TAMNAMS, although not necessarily out of the scope of extensions) and it was also named based on rhyming with jaric (as they share the parent mos [[2L 6s]]).
==== Sephiroid (3L 7s) ====
[[Sephiroth]] is the 3&10 temperament in the 2.5.7.11.13.17.21 subgroup with commas including 65/64, 85/84, 221/220, 105/104, 169/168, 170/169, 221/220, 273/272, 275/273.

Its list of patent val EDO tunings is {{ val list | 3, 10, 13, 16, 23, 26 }} with non-patent val tunings including 6eg, 7e*, 19eg, 20e, 29g, 32egq, 33ce, 36c.

* Extreme tunings even occasionally go outside of this range like with 7e, but this would never be considered a good tuning.

(Note that ''q'' in the above is a placeholder symbol meaning that the generator 21 is warted.)

Note therefore how practically a full range of tunings is covered both in breadth and depth.
==== Dicoid/Zaltertic (7L 3s) ====
[[Dicot family#Dichotic|Dichotic]] is the 7&10 temerament in the 11-limit with commas including 25/24, 45/44, 55/54, 56/55, 64/63 and is an extension of the 5-limit exotemperament [[dicot]] which tempers 25/24, equating 5/4 and 6/5 into a neutral third sized interval, which is the generator. To help justify using these temperament for inspiration for the name, note that:

Its list of patent val EDO tunings is {{ val list | 7, 10, 17 }} with non-patent val tunings including 14cd(=7+7), 20e(=10+10), 24cd(=17+7), 27ce(=17+10).

Note there are many more warted tunings than this with even more extreme tunings, which makes it reasonable to associate the exotemperament with the range of vaguely saner tunings.
==== On the term ''diatonic'' ====
In TAMNAMS, ''diatonic'' exclusively refers to 5L 2s. Other diatonic-based scales (specifically with 3 step sizes or more), such as [[Zarlino]], [[blackdye]] and [[diasem]], are called ''[[Detempering|detempered]]'' (if the philosophy is [[RTT]]-based) or ''deregularized/detuned'' (RTT-agnostic) ''diatonic scales''. The adjectives ''diatonic-like'' or ''diatonic-based'' may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate.

(The choice of how to define ''diatonic'' isn't bound by history, since many other terms have different meanings depending on the historical musical system referred to, for example the ''enharmonic scale'' may refer to a chain-of-fifths-based scale with 12edo enharmonics not equated, or to an ancient Greek genus.)

== Proposal: Naming mos modes ==
For any mos pattern, TAMNAMS allows one to use a modified version of [[UDP notation]] to name a given mos's mode. We use "xL ys k|" to denote the mode of the mos xL ys that has k generators above the tonic and n − 1 − k generators below the tonic. For example, "5L 3s 5|" for LsLLsLLs, read "5 ell 3 ess 5 pipe". We skip the number of chroma-positive generators down and the number of periods, which are redundant though these are required by standard UDP notation. The | symbol is read "pipe" instead of "up", because "up" here may be interpreted as part of the accidental alteration modifier (see below).

For an altered mode we can use any accidental alteration whose meaning is clear. For non-diatonic mosses, the degree modified is indicated using TAMNAMS's 0-indexing convention. For example, LsLsLLLs can be written "5L 3s 5| @4d" (read "5L 3s 5 pipe at-4-degree"), using the @ accidental from [[diamond-mos notation]]. Using this convention, any mode of any mos can be referred to without introducing new mode names to memorize.

For a mos pattern given a name in TAMNAMS, there is also the option of using the prefix for the pattern instead of saying "xL ys": the 5L 3s mode LsLLsLLs can be called "oneiro-5-pipe" and written "onei-5|".

== Proposal: Extensions for Descendent MOSes ==
{{see also| TAMNAMS Extension}}
{{see also| User:Frostburn/TAMNAMS Extension}}

There is currently a proposal for a series of systematic extensions to this system for naming MOSes descended from the main ones listed here, as well as a few others. These extensions are currently being worked on mainly by [[User:Frostburn|Frostburn]].

== Non-mos scales ==
=== Intervals in arbitrary scales ===
Zero-indexed interval names are also used for arbitrary scales, so we can still call a k-step interval a ''k-step'' and the corresponding degree the ''k-degree''. But instead of ''k-mosstep'' and ''k-mosdegree'', we use ''k-scalestep'' and ''k-scaledegree'' for arbitrary scales.

=== Proposal: Naming 3-step-size scales' step ratios ===
Analogously to 2-step-size scales including mosses, scales with three step sizes L > M > S, including [[MV3]] scales, can also be defined by their L:M:S ratios. Here TAMNAMS names the L/M ratio and then the M/S ratio as if these were mos step ratios: for example, [[21edo]] [[diasem]] (5L 2M 2s, LMLSLMLSL or its inverse) has a step ratio of L:M:S = 3:2:1, so we name it ''soft-basic diasem''.

For step ratios where one ratio is unspecified:
* x:y:z (where x:y is known but y:z is not) is called ''(hardness term for x/y)-any''. x:x:1 is called ''equalized-any'' or ''LM-equalized''.
* x:y:z (where y:z is known but x:y is not) is called ''any-(hardness term for y/z)''. x:1:1 is called ''any-equalized'' or ''MS-equalized''.

=== 3-step scale pattern names ===

=== Naming MV3 intervals ===
[[MV3]] scales, such as [[diasem]], have at most 3 sizes for each interval class. For every interval class that occurs in exactly 3 sizes, we use ''large'', ''medium'' and ''small k-step''. For every interval class that occurs in 2 sizes, we use ''large k-step'' and ''small k-step''. If an interval class only has one size, then we call it ''perfect k-step''.

== Appendix ==

=== Derivation of the step ratio names ===
The idea is to start with the simplest ratios (L/s = 1/0 and L/s = 1/1) and derive more complex ratios through repeated application of the [[mediant]] (aka Farey addition) to adjacent fractions.

* Applying the mediant to the starting intervals 1/0 and 1/1 gives (1+1)/(1+0) = 2/1, and as this is the simplest possible ratio where the large and small step are distinguished and nonzero, it is called the ''quintessential'' (''quintess.'' or ''essential'' for short) or ''basic'' tuning. (Note that if applying the mediant to 1/0 seems confusing, think of it as equivalent to applying the mediant to 0/1 and 1/1 and the ratios as flipped, thus representing s/L rather than L/s when written this way.)

* As L/s = 1/1 represents L and s being equal in size, it is called ''equalized''.

* As L/s = 1/0 represents s = 0, it is called ''collapsed'', as the small scale steps collapse to zero cents and disappear.

* The mediant of 1/1 and 2/1 is 3/2, thus making the scale sound mellower/softer, and as this is the simplest (in the sense of lowest [[Odd limit#Relationship_to_other_limits|integer limit]]) ratio to represent such a property, it is simply called the ''soft'' tuning.

* Analogously, the mediant of 2/1 and 1/0, 3/1, is called the ''hard'' tuning. Thus you can say that a step ratio tuning is ''hard of'' or ''soft of'' another step ratio tuning.

* To get something between soft and basic we take the mediant again and get 5/3 for ''semisoft'', and analogously 5/2 for ''semihard''. To get something more extreme we take the mediant of 1/0 with 3/1 for a harder-than-hard tuning, giving us 4/1 for ''superhard'' and analogously 4/3 for ''supersoft''.

There are also tertiary names beyond the above:

* Anything softer than supersoft is ''ultrasoft,'' and anything harder than superhard is ''ultrahard''. Something between soft and supersoft is ''parasoft'', as ''para-'' means both ''beyond'' and ''next to''. Something between hard and superhard is ''parahard''.

* Something between soft and basic is ''hyposoft'' as it is less soft than soft. Something between hard and basic is ''hypohard'' for the same reason. Between semisoft and quintessential is ''minisoft'' and between semihard and quintessential is ''minihard''.

* Finally, between soft and semisoft is ''quasisoft'' as such scales may potentially be mistaken for soft or semisoft while not being either - hence the use of the prefix ''quasi-'', and between hard and semihard is ''quasihard'' for the same reason.

The reasoning for the ''para- super- ultra-'' progression (note that ''super-'' is the odd one out as it refers to an exact ratio) is it mirrors naming for shades of musical intervals and because ''parapythagorean'' is between ''pythagorean'' and ''superpythagorean''.

This results in the ''central spectrum'' - an elegant system which names all exact L/s ratios in the 5-integer-limit excepting only 5/1 and 5/4 which are disincluded intentionally for a variety of reasons: to keep the maximum corresponding notes per period in an [[EPD|equal pitch division]] low, because it keeps the 'tree' of mediants complete to a certain number of layers, and because their disinclusion gives a roughly-equally-spaced set of ratios, with the regions between 4/3 and 1/1 and between 4/1 and 1/0 being the only exceptions - corresponding to extreme tunings. Note that filling in those extreme regions is the purpose of the extended spectrum.
=== Extending the spectrum's edges ===
Extending the spectrum builds on the central spectrum and relies on a few key observations. Firstly, as periods and mosses come in wildly different shapes and sizes, and as we want to represent a somewhat representative variety of ''simple'' tunings for the step ratio for a given mos pattern and period, the notion of ''simple'' used will correspond to the number of equally-spaced tones per period required. This is expressed as [number of large steps in pattern]*L + [number of small steps in pattern]*s, where L and s are from the step ratio itself, L/s, and are assumed to be coprime. Then, in order to not introduce bias to mos patterns with more L's or more s's, we should assume that both are equally likely and thus weight both equally, which means that the resulting minimum number of tones per period for a ratio L/s is L+s. The next observation is that the large values of L/s can be a lot more consequential than the ones close to 1/1 due to the fact that small steps are guaranteed to be smaller than large steps and that we don't know how many small steps there are compared to large steps, and therefore the ''hard'' end of the spectrum is more vast, and analogously, L/s values close to 1/1 will tend to be inconsequential and for very close values likely impractical to distinguish - in the extremes only serving small tuning adjustments rather than melodic properties. This leads to another observation: mos patterns with periods tuned to step ratios, while related to temperaments, ''are not'' temperaments - instead forming a sort of amalgamative superset of temperaments if you want to force a temperament interpretation, and thus their main function is in melodic structure, with temperaments informing potential harmonies and microtunings. Thus, the spectrum should be kept minimal and simple so that it is both generally hearable and not too specific.

The most obvious adjustment to the edges is to draw a distinction between ''ultrasoft'' and ''pseudoequalized'' by adding a step ratio corresponding to ''semiequalized'', and between ''ultrahard'' and ''pseudocollapsed'' by adding a step ratio corresponding to ''semicollapsed''. Thus:

'''Ultrasoft''' is between '''supersoft''' and '''semiequalized''' and '''pseudoequalized''' is between '''semiequalized''' and '''equalized'''.

'''Ultrahard''' is between '''superhard''' and '''semicollapsed''', and '''pseudocollapsed''' is between '''semicollapsed''' and '''collapsed'''.

Then all that's left is to decide what the step ratios for semicollapsed and semiequalized should be. In order to keep the spacing (of the s/L ratios when graphed, or to a lesser extent the L/s ratios if you see the roughly gradual increase in spacing in that form) roughly consistent with all the other ratios, '''semiequalized''' should be L/s = 6/5 rather than L/s = 5/4. Then note the complexity of L/s = 6/5 is 6+5=11, so to find the corresponding complexity for '''semicollapsed''' we use L/s = 10/1 as 10+1=11 too. Then finally, to preserve some of the symmetry, we include L/s = 6/1 as '''extrahard'''. Although L/s = 10/1 for '''semicollapsed''' may seem a little extreme of a boundary, L/s = 12/1 would actually be what is the most ''equally spaced'' continuing on from 6/1 for the same reason that L/s = 6/5 is the most ''equally spaced''. Note that while the range from '''superhard''' to '''semicollapsed''' is '''ultrahard''', the region may be split into two sub-ranges:

'''superhard''' (L/s=4/1) to '''extrahard''' (L/s=6/1) is '''hyperhard''' (4 < L/s < 6).

'''extrahard''' (L/s=6/1) to '''semicollapsed''' (L/s=10/1) is '''clustered''' (6 < L/s < 10).

With the inclusion of these 3 new L/s ratios nearer the edges of the spectrum and names for the range divisions they create, we get the extended spectrum, summarised and detailed above, just for the regions affected to avoid repetition.

=== Extended spectrum ===
'''Equalized''': L/s = 1/1 (trivial/pathological)

::: ('''Pseudoequalized''' range here.)

:: '''Semiequalized''': L/s = 6/5

::: ('''Ultrasoft''' range here.)

:: '''Supersoft''': L/s = 4/3

(4/3 < L/s < 4/1 range here, called the '''nonextreme''' range, detailed by central spectrum.)

:: '''Superhard''': L/s = 4/1

::: (Beginning of '''ultrahard''' range here.)

::: ('''Hyperhard''' range here.)

:: '''Extrahard''': L/s = 6/1

::: ('''Clustered''' range here.)

::: (End of '''ultrahard''' range here.)

::'''Semicollapsed''': L/s = 10/1

::: ('''Pseudocollapsed''' range here.)

'''Collapsed''': L/s = 1/0 = infinity (trivial/pathological)
=== Terminology and final notes ===
A ratio of L/s = k/1 can be called ''k-hard'' and a ratio of L/s = k/(k-1) can analogously be called ''k-soft'', so the simplest ultrasoft tuning is 5-soft or ''pentasoft'', the simplest hyperhard tuning is 5-hard or ''pentahard'', the simplest clustered tuning is 7-hard or ''heptahard'', 8-hard is ''octahard'', 9-hard is ''nonahard'', and finally, the characteristic simple ultrahard tuning is 6-hard or ''extrahard'', as previously discussed, which can be seen to be similar to ''hexahard'' - hopefully helping with memorisation.

A perhaps useful (or otherwise mildly amusing) mnemonic is ''2-soft is too soft to be hard and 2-hard is too hard to be soft'', representing that 2-soft = 2-hard = 2/1 = '''basic'''.

Note that often the central spectrum will be sufficient for exploring a mos pattern-period combination, and the extended spectrum is intended more for (literally) edge cases where it may be useful. Often if a temperament interpretation doesn't seem to show up for a mos pattern-period combination, it just means the temperament needs a more complex mos pattern to narrow down the generator range. An example of this phenomena is the highly complex mos pattern of [[12L 17s]] represents near-Pythagorean tunings well due to having a generator of a fourth or a fifth bounded between those of [[12edo]] and those of [[29edo]], which are roughly equally off but in opposite directions, and many important near-Pythagorean systems show up in just the ratios of the central spectrum alone.

[[Category:MOS]]

TAMNAMS

2022-11-15T12:36:01Z

Xenwolf: /* Simple step ratios */ format table, link edo pages

'''TAMNAMS''' (read "tame names"; from '''''T'''emperament-'''A'''gnostic '''M'''os '''NAM'''ing '''S'''ystem''), devised by the XA Discord, is a system of temperament-agnostic names for scales (designed especially with small octave-equivalent [[mos]]ses in mind), their intervals and their associated generator ranges, taking into account the relative sizes of large and small steps.

== Step ratio spectrum ==
=== Simple step ratios ===
The TAMNAMS system names nine specific simple [[Blackwood's R|L:s ratios]]. These correspond to the simplest edos that have the mos scale.

{| class=wikitable
|-
|+ Step ratio names
|-
! TAMNAMS Name
! Ratio
! Diatonic example
|-
|E qualized
| L:s = 1:1
| [[7edo]]
|-
| Supersoft
| L:s = 4:3
| [[26edo]]
|-
| Soft (or monosoft)
| L:s = 3:2
| [[19edo]]
|-
| Semisoft
| L:s = 5:3
| [[31edo]]
|-
| Basic (or quintessential)
| L:s = 2:1
| [[12edo]]
|-
| Semihard
| L:s = 5:2
| [[29edo]]
|-
| Hard (or monohard)
| L:s = 3:1
| [[17edo]]
|-
| Superhard
| L:s = 4:1
| [[22edo]]
|-
| Collapsed
| L:s = 1:0
| [[5edo]]
|}

For example, the 5L2s (diatonic) scale of 19edo has a step ratio of 3:2, which is ''soft''. We call the 19edo diatonic scale ''soft diatonic''. Tunings of a mos with L:s larger are ''harder'', and tunings with L:s smaller are ''softer''.

The two extremes, equalized and collapsed, are degenerate cases. An equalized mos has L equal to s, so the mos pattern is no longer apparent. A collapsed mos has s = 0, merging adjacent tones s apart into a single tone. In both cases, the mos structure is no longer valid.

=== Step ratio ranges ===
In between the nine specific ratios there are eight ranges of ratios. Each range has a name. These names are useful for classifying mos tunings which don't match any of the nine simple step ratios. ''Hypohard'' could be used for tunings that are harder than basic but not as hard as the 3:1 tuning; similarly, ''hyposoft'' can be used for the range between soft and basic. Note that the soft-of-basic range is always strictly proper while the hard-of-basic range is often improper but is always proper in the case that there is 1 small step per period in the mos pattern.

By default, all ranges include their endpoints. For example, a hard tuning is considered a quasihard tuning. To exclude endpoints, the modifier ''strict'' can be used, for example ''strict hyposoft''.
{| class="wikitable"
|+Intermediate ranges
!TAMNAMS Name
!Range
|-
|Hyposoft
|3:2 ≤ L:s ≤ 2:1
|-
|Ultrasoft
|1:1 ≤ L:s ≤ 4:3
|-
|Parasoft
|4:3 ≤ L:s ≤ 3:2
|-
|Quasisoft
|3:2 ≤ L:s ≤ 5:3
|-
|Minisoft
|5:3 ≤ L:s ≤ 2:1
|-
|Minihard
|2:1 ≤ L:s ≤ 5:2
|-
|Quasihard
|5:2 ≤ L:s ≤ 3:1
|-
|Parahard
|3:1 ≤ L:s ≤ 4:1
|-
|Ultrahard
|4:1 ≤ L:s ≤ 1:0
|-
|Hypohard
|2:1 ≤ L:s ≤ 3:1
|}

=== Central spectrum ===
'''Equalized''': L/s = 1/1 (trivial/pathological)

::: ('''Ultrasoft''' range here, may also be called ''pseudoequalized'' if especially close to equalized.)

:: '''Supersoft''': L/s = 4/3

::: ('''Parasoft''' range here.)

: '''Soft''': L/s = 3/2

::: (Beginning of '''hyposoft''' range here.)

::: ('''Quasisoft''' range here.)

:: '''Semisoft''': L/s = 5/3

::: ('''Minisoft''' range here.)

::: (End of '''hyposoft''' range here.)

'''Quintesssential''': L/s = 2/1

::: (Beginning of '''hypohard''' range here.)

::: ('''Minihard''' range here.)

:: '''Semihard''': L/s = 5/2

::: ('''Quasihard''' range here.)

::: (End of '''hypohard''' range here.)

: '''Hard''': L/s = 3/1

::: ('''Parahard''' range here.)

:: '''Superhard''': L/s = 4/1

::: ('''Ultrahard''' range here, may also be called ''pseudocollapsed'' if especially close to collapsed.)

'''Collapsed''': L/s = 1/0 = infinity (trivial/pathological)

== Naming mos intervals ==
To denote interval classes within the mos, TAMNAMS uses the generic prefix ''mos-'', or the specific prefixes and abbreviations listed under ''mos pattern names''. One might be tempted to
generalize diatonic 1-indexed ordinal names: ''In 31edo's ultrasoft [[mosh]] scale, the perfect mosthird (aka Pmosh3rd) is a neutral third and the major mosfifth (aka Lmosh5th) is a perfect fifth.''

The way intervals are named above (and in 12edo theory) has a problem. An interval that's n steps wide is named ''(n+1)th''. This means that adding two intervals is more complicated than it should be. Stacking two fifths makes a ninth, when naively it would make a tenth. We're used to this for the diatonic scale, but when dealing with unfamiliar scale structures, it can be very confusing.

Thus TAMNAMS uses a 0-indexed name system for non-diatonic mos intervals: First, use the term ''mosstep'' for steps of the mos, large or small. From there, an interval which is k mossteps wide is a ''k-mosstep'', short for ''k-mosstep interval''. Major, minor, perfect, etc would apply as established. The names ''mosoctave'' (or ''mosequave'' for nonoctave mosses) and ''mosunison'' could still be used, interchangeably with ''n-mosstep'' (for an n-tone mos) and ''0-mosstep'' respectively. This change makes the arithmetic needed to understand mos intervals much smoother.

In contexts where it doesn't cause ambiguity, ''k-mosstep'' can be shortened to ''k-step''. ''k-step'' is also generalizable to non-mos scale types such as 3-step-size scales; see below for naming in scales with 3 step sizes.

(The ordinal names could still be suggestive for e.g. (tunings of) heptatonic mosses where the ordinal names tend to match up well with diatonic ordinal categories.)
{| class="wikitable"
|+Example: 3L4s
!Interval name
!Abbreviation
!10edo Size
!Gens up
|-
|Perfect mosunison
|P0ms
|0\10
|0
|-
|Minor mosstep (or small mosstep)
|m1ms
|1\10
| -3
|-
|Major mosstep (or large mosstep)
|M1ms
|2\10
|4
|-
|Diminished 2-mosstep
|d2ms
|2\10
| -6
|-
|Perfect 2-mosstep
|P2ms
|3\10
|1
|-
|Minor 3-mosstep
|m3ms
|4\10
| -2
|-
|Major 3-mosstep
|M3ms
|5\10
|5
|-
|Minor 4-mosstep
|m4ms
|5\10
| -5
|-
|Major 4-mosstep
|M4ms
|6\10
|2
|-
|Perfect 5-mosstep
|P5ms
|7\10
| -1
|-
|Augmented 5-mosstep
|A5ms
|8\10
|6
|-
|Minor 6-mosstep
|m6ms
|8\10
| -4
|-
|Major 6-mosstep
|M6ms
|9\10
|3
|-
|Perfect mosoctave
|P7ms
|10\10
|0
|}

TAMNAMS uses the following modifiers to denote different interval sizes within a mos interval class:
* For multiples of the period plus or minus 0 or 1 generators: ''perfect''. (Diatonic examples: perfect mos4th (Pmos4th), perfect mos5th (Pmos5th), perfect mos8th (Pmos8th), perfect mos12th (Pmos12th), etc.)
* For generic interval classes with 2 specific sizes of intervals therein (which are therefore separated by a chroma of c = L - s), ''major'' and ''minor'' are used to distinguish the larger (L) and smaller (s) intervals. Note that the generator, its period-equivalents, and the generator's period-complement and its period-equivalents are the only intervals excluded from this rule due to their inclusion in the previous rule. Diatonic examples: major mos2nd (abbreviated Lmos2nd), minor mos3rd (abbreviated smos3rd), major mos3rd (Lmos3rd), etc.)
* For nL ns scales, there's an exception to the above two rules. Only multiples of the period (1\n) are called ''perfect''. Other intervals are called major or minor, despite being period-equivalent to a generator. The reason for this exception is that otherwise all intervals would be called ''perfect'', leading to ambiguity.
* If you subtract a chroma from a perfect (Pmos) or minor (smos) interval, it becomes ''diminished'' (d; dmos). If you subtract two chromas instead, it becomes ''doubly diminished'' (dd; ddmos). (Diatonic examples: diminished mos3rd (dmos3rd), diminished mos4th (dmos4th), doubly diminished mos5th (ddmos5th), etc.)
** When modifying unisons or octave multiples, ''mosdiminished'' and ''mosaugmented'' could be used (e.g. ''mosdiminished octave'' instead of ''diminished mosoctave''), because the unison and the octave don't change depending on the mos pattern, but the meanings of ''augmented'' and ''diminished''.
* If you add a chroma to a perfect (Pmos) or major (Lmos) interval, it becomes ''augmented'' (A; Amos). If you add two chromas instead, it becomes ''doubly augmented'' (AA; AAmos). (Diatonic examples: augmented mos2nd (Amos2nd), augmented mos4th (Amos4th), doubly augmented mos5th (AAmos5th).)
* The pattern continues, ddd for triply diminished and AAA for triply augmented. Note that applying this operation more than 3 times is an unlikely usecase, and a shorthand notaton of d^3 and A^3 or an alternative notation or terminology entirely would likely be preferable in such circumstances, hence repetition of the corresponding letter is a sufficient system.

Other interval names:
* ''moschroma'' or ''chroma'': L − s
* ''mosdiesis'': |chroma − s| = |L − 2s|

== Naming mos degrees ==
To denote degrees in a given mos (or altered mos) mode, we use the term ''k-mosdegree'', abbreviated as kmd (or ''k-degree'' and kd if context allows). Just like for mos interval names, we use 0-indexing, so the perfect 0-mosdegree is the tonic. The modifiers ''perfect'', ''minor'', ''major'', ''augmented'' and ''diminished'' can be used just like for mos interval names: for example, ''minor 3-mosdegree'' (m3md) denotes the degree that lies a minor 3-mosstep above the tonic. Modifiers can be omitted when clear from context.

To denote a chord or a mode on a given degree, write the chord or the mode in parentheses after the degree symbol. The most explicit option is to write out the chord in cents, edosteps or mossteps (e.g. in [[13edo]] [[5L 3s]], the 0-369-646 chord can be written 0-4-7\13, P0ms-M2ms-M4ms or 7|0 0-2-4ms) and to write the mode. To save space, you can use whatever names or abbreviations for the chord or mode you have defined for the reader. For example, in the LsLLsLLs mode of 5L 3s, we have m2md(0-369-646), or the chord 0-369-646 on the 2-mosdegree which is a minor 2-mosstep. The LsLLsLLs mode also has m2md(7|), meaning that we have the 7| (LLsLLsLs) mode on the 2-mosdegree which is a minor 2-mosstep in LsLLsLLs (see [[TAMNAMS#Proposal: Naming mos modes|below]] for the convention we have used to name the mode).

== Mos pattern names ==
NOTE: Names are finalized, prefixes and abbreviations are still open to change.

TAMNAMS suggests the following names for selected small mosses. These names are optional; interval size names and step ratio names can be combined with conventional ''xL ys'' names. For example: ''21edo is the soft [[5L 3s]] tuning and its major mosthird is a neutral third of size 342.9 cents.''

Some of the names come from older temperament-agnostic mos names, such as names (such as ''mosh'') from [[Graham Breed]]'s [[mos naming#Graham_Breed.27s_naming_scheme|mos names]]. These names have been coined so that mosses can be discussed more independently of RTT temperaments. Sometimes the prefix has a different source than the scale name for euphonic reasons.

1L ns names are named with the an- prefix if they are generalised names and anti- prefix if the name for the corresponding nL1s scale assumed a period of an octave.

This list is maintained by [[User:Inthar]] and [[User:Godtone]].
{| class="wikitable center-all"
|+ TAMNAMS moss names
!colspan=6| 2-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix>used in interval, degree and mode names, e.g. ''perfect 3-oneirostep, perfect 3-oneirodegree, oneiro-3-up''</ref> !! Abbreviation<ref name="abbr">written abbreviations of prefixes, e.g. ''P3neiros, P3neirod, on-3|''</ref> !! Allows non-octave tunings?<ref name="general">whether the name can be used for mosses with no octaves; lightly tempered octaves are allowed; names for mosses with more than 5 notes do not admit nonoctave tunings because the names are specific to the corresponding valid tuning range</ref> !! Etymology
|-
| [[1L 1s]] || trivial || triv- || trv || Yes; can have any period || the simplest valid mos pattern
|-
| [[1L 1s]] || monowood || monowd- || wood || No; must have octave period || blackwood[10] & whitewood[14] generalized to n-wood for nL ns
|-
!colspan=6| 3-note mosses (non-octave<ref name=general/>)
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! (Non-octave periods allowed)<ref name=general/> !! Etymology
|-
| [[1L 2s]] || antrial || atri- || atri || Yes; can have any period || broader range than trial so named w.r.t. it (anti-trial; antial; antrial)
|-
| [[2L 1s]] || trial || tri- || tri || Yes; can have any period || from tri- for 3
|-
!colspan=6| 4-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Allows non-octave tunings?<ref name=general/> !! Etymology
|-
| [[1L 3s]] || antetric || atetra- || att || Yes; can have any period || broader range than tetric so named w.r.t. it (anti-tetric; antetric)
|-
| [[2L 2s]] || biwood || biwd- || bw || No; two periods must be an octave || from 2-wood
|-
| [[3L 1s]] || tetric || tetra- || tt || Yes; can have any period || from tetra- for 4
|-
!colspan=6| 5-note mosses (non-octave<ref name=general/>)
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! (Non-octave periods allowed)<ref name=general/> !! Etymology
|-
| [[1L 4s]] || pedal || ped- || ped || || [[#Pedal (1L 4s)|one big toe and four small toes]]
|-
| [[2L 3s]] || pentic || pent- || pt || || common pentatonic; from penta- for 5
|-
| [[3L 2s]] || antipentic || apent- || apt || || opposite pattern of common pentatonic mos
|-
| [[4L 1s]] || manual || manu- || manu || || one thumb and four longer fingers
|-
!colspan=6| 6-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Notes on tuning<ref name=general/> !! Etymology
|-
| [[1L 5s]] || antimachinoid || amech- || amech || || opposite pattern of machinoid
|-
| [[2L 4s]] || malic || mal- || mal || antrial mos with 2 periods per octave || apples have two concave ends, lemons have two pointy ends.
|-
| [[3L 3s]] || triwood || triwud- || trw || trivial mos with 3 periods per octave || from 3-wood
|-
| [[4L 2s]] || citric || citro- || cit || trial mos with 2 periods per octave || parent mos of lemon and lime
|-
| [[5L 1s]] || machinoid || mech- || mech || || from [[machine]] temperament
|-
!colspan=6| 7-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! (Octave periods only.)<ref name=general/> !! Etymology
|-
| [[1L 6s]] || onyx || on- || on || || [[#Onyx (1L 6s)|from a ''lot'' of naming puns]]
|-
| [[2L 5s]] || antidiatonic || pel- || pel || || pel- is from pelog
|-
| [[3L 4s]] || mosh || mosh- || mosh || || Graham Breed's name; from "mohajira-ish"
|-
| [[4L 3s]] || smitonic || smi- || smi || || from "sharp minor third"
|-
| [[5L 2s]] || diatonic || ''none'' || ''none'' || ||
|-
| [[6L 1s]] || arch(a)eotonic || arch- || arch || || originally a name for 13edo's 6L 1s
|-
!colspan=6| 8-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Notes on tuning<ref name=general/> !! Etymology
|-
| [[1L 7s]] || antipine || apine- || apine || || opposite pattern of pine
|-
| [[2L 6s]] || subaric || subar- || subar || antetric mos with 2 periods per octave || largest subset mos of jaric and taric
|-
| [[3L 5s]] || checkertonic || check- || chk || || from the [[Kite Giedraitis's Categorizations of 41edo Scales|Kite guitar checkerboard scale]]
|-
| [[4L 4s]] || tetrawood; diminished || tetwud- || ttw || trivial mos with 4 periods per octave || from 4-wood
|-
| [[5L 3s]] || oneirotonic || oneiro- || onei || || originally a name for 13edo's 5L 3s
|-
| [[6L 2s]] || ekic || ek- || ek || tetric mos with 2 periods per octave || from temperaments [[echidna]] and [[hedgehog]]
|-
| [[7L 1s]] || pine || pine- || pine || || from [[porcupine]] temperament
|-
!colspan=6| 9-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Notes on tuning<ref name=general/> !! Etymology
|-
| [[1L 8s]] || antisubneutralic || ablu- || ablu || || opposite pattern of subneutralic
|-
| [[2L 7s]] || balzano || bal- /bæl/ || bal || || from Balzano scale in 20edo which is 2L 7s
|-
| [[3L 6s]] || tcherepnin || cher- || ch || antrial mos with 3 periods per octave || common name
|-
| [[4L 5s]] || gramitonic || gram- || gram || ||from "grave minor third"
|-
| [[5L 4s]] || semiquartal || cthon- || cth || || from "half fourth" and "chthonic"
|-
| [[6L 3s]] || hyrulic || hyru- || hyru || trial mos with 3 periods per octave || allusion to [[triforce]] temperament
|-
| [[7L 2s]] || superdiatonic || arm- || arm || || common name, arm- is from [[Armodue]]
|-
| [[8L 1s]] || subneutralic || blu- || blu || || blu- is from [[bleu]] temperament
|-
!colspan=6| 10-note mosses
|-
! Pattern !! Name !! Prefix<ref name=prefix/> !! Abbreviation<ref name=abbr/> !! Notes on tuning<ref name=general/> !! Etymology
|-
| [[1L 9s]] || antisinatonic || asina- || asi || || opposite pattern of sinatonic
|-
| [[2L 8s]] || jaric || jara- || jar || pedal mos with 2 periods per octave || from temperaments [[pajara]], [[injera]] and [[diaschismic]]
|-
| [[3L 7s]] || sephiroid || seph- || seph || || from [[sephiroth]] temperament
|-
| [[4L 6s]] || lime || lime- || lime || pentic mos with 2 periods per octave || limes/4L 6s's steps tend to be smaller than lemons/6L 4s's steps
|-
| [[5L 5s]] || pentawood || penwud- || pw || trivial mos with 5 periods per octave || from 5-wood
|-
| [[6L 4s]] || lemon || lem- || lem || anpentic mos with 2 periods per octave || from [[lemba]] temperament
|-
| [[7L 3s]] || dicoid /'daɪˌkɔɪd/ or zaltertic || dico- or zal- || dico or zal || || from exotemperaments [[Dicot family#Dichotic|dichotic]] and [[dicot]] (dicoid), from "central Zalzalian third" for neutral third (zaltertic)
|-
| [[8L 2s]] || taric || tara- || tar || manual mos with 2 periods per octave || from Hindi ''aṭhārah'' '[[#Taric (8L 2s)|18]]'
|-
| [[9L 1s]] || sinatonic || sina- || si || || from [[sinaic]]
|}
<references/>
=== Reasoning for the names ===
The goal of TAMNAMS mos names is to choose memorable but aesthetically neutral names.

All names ending in -oid refer to an exotemperament which, when including extreme tunings, covers the entire range of the corresponding octave-period mos, such that many edos with simple step ratios for that mos will correspond to valid tunings, if not by patent val, then with a small number of warts.

All names for mosses with five or less notes - excluding (mono)wood and biwood (which like all n-wood mosses are specific to octave tuning) - require that some small integer multiple of the period is equal to an octave, under the reasoning that mosses with five or less notes are common and broad in tuning enough that they are much more likely to find interest in non-octave contexts. Because of this, their names were chosen to be extremely general, both to avoid bias/being too flavorful and (correspondingly) so that the terms could validly be reused for any mos for which the period is not equal to a (potentially tempered) octave.

Any multiperiod mos with more than five notes was given a name that wasn't reliant on the name of a mos with five or less notes as such names were based on those mos names formerly requiring an octave tuning (which is to say some small integer multiple of their period must be equal to a (potentially slightly tempered) octave).

Former names like "orwelloid" and "sensoid" were abandoned because the names were too temperament-specific in the sense that even considering extreme tunings didnt cover the whole range of the mos. The remaining temperament-based names have been abstracted or altered heavily, namely "pine", "hyrulic", "jaric", "ekic" and "lemon".

The inclusion of mos names for "multiperiod" mosses was from a desire to have all ten-note-and-under mosses named for completeness, which is also what prompted some of the reconsiderations mentioned earlier. Similarly, the inclusion of mosses of the form 1L ns using the "anti-" prefix (or an- for less-than-six-note mosses) was also for a practical consideration; although the tuning range is very unhelpful for knowing what such a mos will sound, it is nonetheless useful for describing structure in situations where one does not want to use the mathematical name, especially given that in such situations the tuning will likely be specified somewhere already. Jaric and taric specifically were chosen over bipedal and bimanual because of this, and to a lesser extent, lemon and lime were chosen over antibipentic and bipentic respectively (and for consistency with that their parent MOSS, 4L2s, is named citric).

The distinction between using the prefixes "anti-" vs "an-" for reversing the number of large vs. small steps is also not as trivial as it may sound. In the case of mosses with six or more notes, as the period is always an octave, there is a very large tuning range for the 1L ns mosses (hence the original reason for omitting such mosses), but the "anti-" prefix shows that what is significant is that it has the opposite structure to the corresponding nL 1s mos while pointing out the resulting ambiguity of range. In the case of mosses with five or less notes, as the period is not known and therefore could be very small, this is not as much of a concern as fuller specification is likely required anyway, especially in the case of larger periods, so the name should not be tediously long as the name refers to a very simple mos pattern, and for related reasons, the name shouldn't give as much of a sense of one 'orientation' of the structure being more 'primary' than the other, while with mosses with more than five notes, this suggestion of sense is very much intended, because it will almost always make more sense to talk about the (n+1)L 1s child mos of whatever 1L ns mos you want to speak of.

=== Name-specific reasonings ===
==== Pedal (1L 4s) ====
Pedals are operated with feet, which have one large toe and four small toes. Also comes from words like "bipedal", where in TAMNAMS, "bipedal" would literally mean a pedal scale with a period equal to half of some chosen interval, although such a scale would have either two right feet or two left feet depending on orientation chosen. If you think "car"/"vehicle" when you think "pedal" and don't think (or want to think) much about feet then you can think about "[[beep]]ing" (as [[beep]] is the 7-limit 4&5 exotemperament). Because this name relies so heavily and fundamentally on there being 1 large and 4 small steps per period, it is appropriate to generalise for any size of period you would want. In that regard, same goes for manual, pentic and anpentic.
==== Malic (2L 4s) and citric (4L 2s) ====
Malic derives from Latin ''malus'' 'apple'. An apple has two concave ends, and large steps in a scale with more small steps are hole-like, hence the two large steps in malic. Citric (4L 2s) is named after the child mosses of citric, namely lemon (6L 4s) and lime (4L 6s). Unlike apples, lemons have two convex pointy ends, and small steps in a scale with more large steps are pointy, hence the two small steps. Malic and citric acids are both ubiquitous in food and biology, thus justifying their use for fairly small mos scales.

==== Machinoid (5L 1s) ====
[[Machine]] is the 5&6 temperament in the 2.9.7.11 subgroup with a comma list of 64/63 and 99/98.

Its list of EDO tunings is {{ val list | 5, 6, (5+5=10e,) 11, 12, 16, 17, (5+10e+12=21be,) 22, 23, (5+5+5+5+6=26qe,) 27, 28, 33 }} with non-patent val EDOs in brackets but included for demonstrating virtual completeness of the tuning range and the unusually large [[33edo]] tuning being to show [[11edo]]'s strength as a tuning.

==== Onyx (1L 6s) ====
"1Ln-ic's" and "nL1-ic's (like, the -ic suffix applied to MOSS names, collectivised for 1Lns and nL1s) sounds like "one-el-en-ics" or "en-el-one-ics" which abbreviated sort of sounds like "one-ics" => "onyx". Then "onyx" sounds sort of like "one-six". Furthermore the onyx mineral comes in many colours and types, which seems fitting given this is the parent scale for a wide variety of MOSSes; specifically of interest being 7L 1s (pine), 8L 1s (subneutralic) and 9L 1s (sinatonic). Finally, the name "onyx" is also supposed to be vaguely reminiscent of "anti-archaeotonic" as "chi" (the greek letter) is written like an "x" (this is related to why "christmas" is abbreviated sometimes as "X-mas") and other than that, the letters "o" and "n" and their sounds are also present in "archaeotonic", and "x" is vaguely reminiscent of negation and multiplication. There is also something like a "y" sound in "archaeotonic" in the "aeo" part (depending partially on your pronounciation).
==== Subaric (2L 6s) ====
This name alludes to the fact that 2L 6s is the largest proper '''sub'''set mos of both j'''aric''' (2L 8s) and t'''aric''' (8L 2s).
==== Jaric (2L 8s) ====
This name alludes to a few highly notable and generally inaccurate (with the exception of diaschismic) temperaments that exist in the tuning range of this MOSS. Specifically, notice how the letters and sound of "jaric" has (or is intended to have) a lot of overlap with [[pajara]], [[diaschismic]] and [[injera]] (listed in order of increasingly sharp fourths; note that diatonic fourths and 4-jarasteps are equated in jaric, a notable property).
==== Taric (8L 2s) ====
Taric was named based on it being the only octave-tuned TAMNAMS pattern with a [[#Simple step ratios|basic]] tuning of [[18edo]] (because [[5L 6s]] has more than 10 notes so is out of the scope of TAMNAMS, although not necessarily out of the scope of extensions) and it was also named based on rhyming with jaric (as they share the parent mos [[2L 6s]]).
==== Sephiroid (3L 7s) ====
[[Sephiroth]] is the 3&10 temperament in the 2.5.7.11.13.17.21 subgroup with commas including 65/64, 85/84, 221/220, 105/104, 169/168, 170/169, 221/220, 273/272, 275/273.

Its list of patent val EDO tunings is {{ val list | 3, 10, 13, 16, 23, 26 }} with non-patent val tunings including 6eg, 7e*, 19eg, 20e, 29g, 32egq, 33ce, 36c.

* Extreme tunings even occasionally go outside of this range like with 7e, but this would never be considered a good tuning.

(Note that ''q'' in the above is a placeholder symbol meaning that the generator 21 is warted.)

Note therefore how practically a full range of tunings is covered both in breadth and depth.
==== Dicoid/Zaltertic (7L 3s) ====
[[Dicot family#Dichotic|Dichotic]] is the 7&10 temerament in the 11-limit with commas including 25/24, 45/44, 55/54, 56/55, 64/63 and is an extension of the 5-limit exotemperament [[dicot]] which tempers 25/24, equating 5/4 and 6/5 into a neutral third sized interval, which is the generator. To help justify using these temperament for inspiration for the name, note that:

Its list of patent val EDO tunings is {{ val list | 7, 10, 17 }} with non-patent val tunings including 14cd(=7+7), 20e(=10+10), 24cd(=17+7), 27ce(=17+10).

Note there are many more warted tunings than this with even more extreme tunings, which makes it reasonable to associate the exotemperament with the range of vaguely saner tunings.
==== On the term ''diatonic'' ====
In TAMNAMS, ''diatonic'' exclusively refers to 5L 2s. Other diatonic-based scales (specifically with 3 step sizes or more), such as [[Zarlino]], [[blackdye]] and [[diasem]], are called ''[[Detempering|detempered]]'' (if the philosophy is [[RTT]]-based) or ''deregularized/detuned'' (RTT-agnostic) ''diatonic scales''. The adjectives ''diatonic-like'' or ''diatonic-based'' may also be used to refer to diatonic-based scales, depending on what's contextually the most appropriate.

(The choice of how to define ''diatonic'' isn't bound by history, since many other terms have different meanings depending on the historical musical system referred to, for example the ''enharmonic scale'' may refer to a chain-of-fifths-based scale with 12edo enharmonics not equated, or to an ancient Greek genus.)

== Proposal: Naming mos modes ==
For any mos pattern, TAMNAMS allows one to use a modified version of [[UDP notation]] to name a given mos's mode. We use "xL ys k|" to denote the mode of the mos xL ys that has k generators above the tonic and n − 1 − k generators below the tonic. For example, "5L 3s 5|" for LsLLsLLs, read "5 ell 3 ess 5 pipe". We skip the number of chroma-positive generators down and the number of periods, which are redundant though these are required by standard UDP notation. The | symbol is read "pipe" instead of "up", because "up" here may be interpreted as part of the accidental alteration modifier (see below).

For an altered mode we can use any accidental alteration whose meaning is clear. For non-diatonic mosses, the degree modified is indicated using TAMNAMS's 0-indexing convention. For example, LsLsLLLs can be written "5L 3s 5| @4d" (read "5L 3s 5 pipe at-4-degree"), using the @ accidental from [[diamond-mos notation]]. Using this convention, any mode of any mos can be referred to without introducing new mode names to memorize.

For a mos pattern given a name in TAMNAMS, there is also the option of using the prefix for the pattern instead of saying "xL ys": the 5L 3s mode LsLLsLLs can be called "oneiro-5-pipe" and written "onei-5|".

== Proposal: Extensions for Descendent MOSes ==
{{see also| TAMNAMS Extension}}
{{see also| User:Frostburn/TAMNAMS Extension}}

There is currently a proposal for a series of systematic extensions to this system for naming MOSes descended from the main ones listed here, as well as a few others. These extensions are currently being worked on mainly by [[User:Frostburn|Frostburn]].

== Non-mos scales ==
=== Intervals in arbitrary scales ===
Zero-indexed interval names are also used for arbitrary scales, so we can still call a k-step interval a ''k-step'' and the corresponding degree the ''k-degree''. But instead of ''k-mosstep'' and ''k-mosdegree'', we use ''k-scalestep'' and ''k-scaledegree'' for arbitrary scales.

=== Proposal: Naming 3-step-size scales' step ratios ===
Analogously to 2-step-size scales including mosses, scales with three step sizes L > M > S, including [[MV3]] scales, can also be defined by their L:M:S ratios. Here TAMNAMS names the L/M ratio and then the M/S ratio as if these were mos step ratios: for example, [[21edo]] [[diasem]] (5L 2M 2s, LMLSLMLSL or its inverse) has a step ratio of L:M:S = 3:2:1, so we name it ''soft-basic diasem''.

For step ratios where one ratio is unspecified:
* x:y:z (where x:y is known but y:z is not) is called ''(hardness term for x/y)-any''. x:x:1 is called ''equalized-any'' or ''LM-equalized''.
* x:y:z (where y:z is known but x:y is not) is called ''any-(hardness term for y/z)''. x:1:1 is called ''any-equalized'' or ''MS-equalized''.

=== 3-step scale pattern names ===

=== Naming MV3 intervals ===
[[MV3]] scales, such as [[diasem]], have at most 3 sizes for each interval class. For every interval class that occurs in exactly 3 sizes, we use ''large'', ''medium'' and ''small k-step''. For every interval class that occurs in 2 sizes, we use ''large k-step'' and ''small k-step''. If an interval class only has one size, then we call it ''perfect k-step''.

== Appendix ==

=== Derivation of the step ratio names ===
The idea is to start with the simplest ratios (L/s = 1/0 and L/s = 1/1) and derive more complex ratios through repeated application of the [[mediant]] (aka Farey addition) to adjacent fractions.

* Applying the mediant to the starting intervals 1/0 and 1/1 gives (1+1)/(1+0) = 2/1, and as this is the simplest possible ratio where the large and small step are distinguished and nonzero, it is called the ''quintessential'' (''quintess.'' or ''essential'' for short) or ''basic'' tuning. (Note that if applying the mediant to 1/0 seems confusing, think of it as equivalent to applying the mediant to 0/1 and 1/1 and the ratios as flipped, thus representing s/L rather than L/s when written this way.)

* As L/s = 1/1 represents L and s being equal in size, it is called ''equalized''.

* As L/s = 1/0 represents s = 0, it is called ''collapsed'', as the small scale steps collapse to zero cents and disappear.

* The mediant of 1/1 and 2/1 is 3/2, thus making the scale sound mellower/softer, and as this is the simplest (in the sense of lowest [[Odd limit#Relationship_to_other_limits|integer limit]]) ratio to represent such a property, it is simply called the ''soft'' tuning.

* Analogously, the mediant of 2/1 and 1/0, 3/1, is called the ''hard'' tuning. Thus you can say that a step ratio tuning is ''hard of'' or ''soft of'' another step ratio tuning.

* To get something between soft and basic we take the mediant again and get 5/3 for ''semisoft'', and analogously 5/2 for ''semihard''. To get something more extreme we take the mediant of 1/0 with 3/1 for a harder-than-hard tuning, giving us 4/1 for ''superhard'' and analogously 4/3 for ''supersoft''.

There are also tertiary names beyond the above:

* Anything softer than supersoft is ''ultrasoft,'' and anything harder than superhard is ''ultrahard''. Something between soft and supersoft is ''parasoft'', as ''para-'' means both ''beyond'' and ''next to''. Something between hard and superhard is ''parahard''.

* Something between soft and basic is ''hyposoft'' as it is less soft than soft. Something between hard and basic is ''hypohard'' for the same reason. Between semisoft and quintessential is ''minisoft'' and between semihard and quintessential is ''minihard''.

* Finally, between soft and semisoft is ''quasisoft'' as such scales may potentially be mistaken for soft or semisoft while not being either - hence the use of the prefix ''quasi-'', and between hard and semihard is ''quasihard'' for the same reason.

The reasoning for the ''para- super- ultra-'' progression (note that ''super-'' is the odd one out as it refers to an exact ratio) is it mirrors naming for shades of musical intervals and because ''parapythagorean'' is between ''pythagorean'' and ''superpythagorean''.

This results in the ''central spectrum'' - an elegant system which names all exact L/s ratios in the 5-integer-limit excepting only 5/1 and 5/4 which are disincluded intentionally for a variety of reasons: to keep the maximum corresponding notes per period in an [[EPD|equal pitch division]] low, because it keeps the 'tree' of mediants complete to a certain number of layers, and because their disinclusion gives a roughly-equally-spaced set of ratios, with the regions between 4/3 and 1/1 and between 4/1 and 1/0 being the only exceptions - corresponding to extreme tunings. Note that filling in those extreme regions is the purpose of the extended spectrum.
=== Extending the spectrum's edges ===
Extending the spectrum builds on the central spectrum and relies on a few key observations. Firstly, as periods and mosses come in wildly different shapes and sizes, and as we want to represent a somewhat representative variety of ''simple'' tunings for the step ratio for a given mos pattern and period, the notion of ''simple'' used will correspond to the number of equally-spaced tones per period required. This is expressed as [number of large steps in pattern]*L + [number of small steps in pattern]*s, where L and s are from the step ratio itself, L/s, and are assumed to be coprime. Then, in order to not introduce bias to mos patterns with more L's or more s's, we should assume that both are equally likely and thus weight both equally, which means that the resulting minimum number of tones per period for a ratio L/s is L+s. The next observation is that the large values of L/s can be a lot more consequential than the ones close to 1/1 due to the fact that small steps are guaranteed to be smaller than large steps and that we don't know how many small steps there are compared to large steps, and therefore the ''hard'' end of the spectrum is more vast, and analogously, L/s values close to 1/1 will tend to be inconsequential and for very close values likely impractical to distinguish - in the extremes only serving small tuning adjustments rather than melodic properties. This leads to another observation: mos patterns with periods tuned to step ratios, while related to temperaments, ''are not'' temperaments - instead forming a sort of amalgamative superset of temperaments if you want to force a temperament interpretation, and thus their main function is in melodic structure, with temperaments informing potential harmonies and microtunings. Thus, the spectrum should be kept minimal and simple so that it is both generally hearable and not too specific.

The most obvious adjustment to the edges is to draw a distinction between ''ultrasoft'' and ''pseudoequalized'' by adding a step ratio corresponding to ''semiequalized'', and between ''ultrahard'' and ''pseudocollapsed'' by adding a step ratio corresponding to ''semicollapsed''. Thus:

'''Ultrasoft''' is between '''supersoft''' and '''semiequalized''' and '''pseudoequalized''' is between '''semiequalized''' and '''equalized'''.

'''Ultrahard''' is between '''superhard''' and '''semicollapsed''', and '''pseudocollapsed''' is between '''semicollapsed''' and '''collapsed'''.

Then all that's left is to decide what the step ratios for semicollapsed and semiequalized should be. In order to keep the spacing (of the s/L ratios when graphed, or to a lesser extent the L/s ratios if you see the roughly gradual increase in spacing in that form) roughly consistent with all the other ratios, '''semiequalized''' should be L/s = 6/5 rather than L/s = 5/4. Then note the complexity of L/s = 6/5 is 6+5=11, so to find the corresponding complexity for '''semicollapsed''' we use L/s = 10/1 as 10+1=11 too. Then finally, to preserve some of the symmetry, we include L/s = 6/1 as '''extrahard'''. Although L/s = 10/1 for '''semicollapsed''' may seem a little extreme of a boundary, L/s = 12/1 would actually be what is the most ''equally spaced'' continuing on from 6/1 for the same reason that L/s = 6/5 is the most ''equally spaced''. Note that while the range from '''superhard''' to '''semicollapsed''' is '''ultrahard''', the region may be split into two sub-ranges:

'''superhard''' (L/s=4/1) to '''extrahard''' (L/s=6/1) is '''hyperhard''' (4 < L/s < 6).

'''extrahard''' (L/s=6/1) to '''semicollapsed''' (L/s=10/1) is '''clustered''' (6 < L/s < 10).

With the inclusion of these 3 new L/s ratios nearer the edges of the spectrum and names for the range divisions they create, we get the extended spectrum, summarised and detailed above, just for the regions affected to avoid repetition.

=== Extended spectrum ===
'''Equalized''': L/s = 1/1 (trivial/pathological)

::: ('''Pseudoequalized''' range here.)

:: '''Semiequalized''': L/s = 6/5

::: ('''Ultrasoft''' range here.)

:: '''Supersoft''': L/s = 4/3

(4/3 < L/s < 4/1 range here, called the '''nonextreme''' range, detailed by central spectrum.)

:: '''Superhard''': L/s = 4/1

::: (Beginning of '''ultrahard''' range here.)

::: ('''Hyperhard''' range here.)

:: '''Extrahard''': L/s = 6/1

::: ('''Clustered''' range here.)

::: (End of '''ultrahard''' range here.)

::'''Semicollapsed''': L/s = 10/1

::: ('''Pseudocollapsed''' range here.)

'''Collapsed''': L/s = 1/0 = infinity (trivial/pathological)
=== Terminology and final notes ===
A ratio of L/s = k/1 can be called ''k-hard'' and a ratio of L/s = k/(k-1) can analogously be called ''k-soft'', so the simplest ultrasoft tuning is 5-soft or ''pentasoft'', the simplest hyperhard tuning is 5-hard or ''pentahard'', the simplest clustered tuning is 7-hard or ''heptahard'', 8-hard is ''octahard'', 9-hard is ''nonahard'', and finally, the characteristic simple ultrahard tuning is 6-hard or ''extrahard'', as previously discussed, which can be seen to be similar to ''hexahard'' - hopefully helping with memorisation.

A perhaps useful (or otherwise mildly amusing) mnemonic is ''2-soft is too soft to be hard and 2-hard is too hard to be soft'', representing that 2-soft = 2-hard = 2/1 = '''basic'''.

Note that often the central spectrum will be sufficient for exploring a mos pattern-period combination, and the extended spectrum is intended more for (literally) edge cases where it may be useful. Often if a temperament interpretation doesn't seem to show up for a mos pattern-period combination, it just means the temperament needs a more complex mos pattern to narrow down the generator range. An example of this phenomena is the highly complex mos pattern of [[12L 17s]] represents near-Pythagorean tunings well due to having a generator of a fourth or a fifth bounded between those of [[12edo]] and those of [[29edo]], which are roughly equally off but in opposite directions, and many important near-Pythagorean systems show up in just the ratios of the central spectrum alone.

[[Category:MOS]]

User talk:Arseniiv/Timbres

2022-11-13T23:46:23Z

Xenwolf: /* Sound examples */ (re to )update(s)

== Sound examples ==

Hi Arseniiv, 
Your timbres ''read'' interesting, but have you got any sound examples? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:32, 15 October 2020 (UTC)

: Hi Xenwolf! Not yet. I’m curious too, and I plan to test with some chords later. I’ll definitely attach something but I don’t know how soon. --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 12:59, 15 October 2020 (UTC)

:: What tools are you planning to use for sounds? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 15:01, 15 October 2020 (UTC)

::: Python 3 or Wolfram Mathematica, whichever I’ll find more comfortable. --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 23:06, 15 October 2020 (UTC)

:::: Xenwolf, in case you watch this page, I can say hopefully the examples would come soon. I just finished upgrading my OS and sorting out various programs and issues and made myself almost as comfortable as before that, so I can continue with the tools and also hopefully share them as I plan to refactor my experimenting to a small Jupyter notebook and a module with functions which it uses (right now it’s all a big notebook). --[[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 19:00, 31 October 2020 (UTC)

::::: Nice to see you active again, hope you are doing well. I listened to some samples today (including the DropBox ones) and some are very impressive, for example I didn't realize until now how good 28:33:42 sounds. You might be interested to know that there have been some efforts for in-browser sound generation, see [[User:Plumtree/Sound]] for more. (I just see that I had apparently overlooked your meanwhile updates regarding the sound examples.) --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 23:46, 13 November 2022 (UTC)

== Why Pseudographics? ==

You can download a SVG file totally suitable for your purposes and reference it on your page. — [[User:SAKryukov|SA]] 07:54, 27 November 2020 (UTC)

: Hi! Welll, it was easier for me that time to draw in this style than make an SVG, though this is a good idea of course. [[User:Arseniiv|Arseniiv]] ([[User talk:Arseniiv|talk]]) 22:16, 9 October 2021 (UTC)

3L 2s

2022-11-12T15:48:59Z

Xenwolf: /* Name */ improve wording

: ''For the 3/2-equivalent 3L 2s pattern, see [[3L 2s (fifth-equivalent)]].''

{{Infobox MOS
| Name = antipentic
| Periods = 1
| nLargeSteps = 3
| nSmallSteps = 2
| Equalized = 3
| Collapsed = 2
| Pattern = LLsLs
}}

'''3L 2s''' or '''antipentic''' is a 5-tone scale. The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[Sensipent_family|sensi]], in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.

== Name ==
The TAMNAMS system applies the name ''antipentic'' as the scale utilizes opposite step sizes to the “classic” pentatonic scale ([[2L 3s]]).

== Modes ==
* 4|0 LLsLs
* 3|1 LsLLs
* 2|2 LsLsL
* 1|3 sLLsL
* 0|4 sLsLL

== Scale tree ==
Generator ranges:
* Chroma-positive generator: 720 cents (3\5) to 800 cents (2\3)
* Chroma-negative generator: 400 cents (1\3) to 480 cents (2\5)

{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 3\5 || || || || || || 720.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 17\28 || 728.571 || 6 || 5 || 1.200 ||
|-
| || || || || 14\23 || || 730.435 || 5 || 4 || 1.250 ||
|-
| || || || || || 25\41 || 731.707 || 9 || 7 || 1.286 ||
|-
| || || || 11\18 || || || 733.333 || 4 || 3 || 1.333 ||
|-
| || || || || || 30\49 || 734.694 || 11 || 8 || 1.375 || [[Semisept]]
|-
| || || || || 19\31 || || 735.484 || 7 || 5 || 1.400 ||
|-
| || || || || || 27\44 || 736.364 || 10 || 7 || 1.429 ||
|-
| || || 8\13 || || || || 738.462 || 3 || 2 || 1.500 ||
|-
| || || || || || 29\47 || 740.426 || 11 || 7 || 1.571 ||
|-
| || || || || 21\34 || || 741.176 || 8 || 5 || 1.600 ||
|-
| || || || || || 34\55 || 741.818 || 13 || 8 || 1.625 || Golden [[father]]/[[petritri]]/[[aurora]] (741.6408¢)
|-
| || || || 13\21 || || || 742.857 || 5 || 3 || 1.667 ||
|-
| || || || || || 31\50 || 744.000 || 12 || 7 || 1.714 ||
|-
| || || || || 18\29 || || 744.828 || 7 || 4 || 1.750 ||
|-
| || || || || || 23\37 || 745.946 || 9 || 5 || 1.800 ||
|-
| || 5\8 || || || || || 750.000 || 2 || 1 || 2.000 || Basic antipentic (Generators smaller than this are proper)
|-
| || || || || || 22\35 || 754.286 || 9 || 4 || 2.250 ||
|-
| || || || || 17\27 || || 755.556 || 7 || 3 || 2.333 ||
|-
| || || || || || 29\46 || 756.522 || 12 || 5 || 2.400 || [[Sensi]]
|-
| || || || 12\19 || || || 757.895 || 5 || 2 || 2.500 ||
|-
| || || || || || 31\49 || 759.184 || 13 || 5 || 2.600 || Golden [[sentry]] (759.4078¢)
|-
| || || || || 19\30 || || 760.000 || 8 || 3 || 2.667 ||
|-
| || || || || || 26\41 || 760.976 || 11 || 4 || 2.750 ||
|-
| || || 7\11 || || || || 763.636 || 3 || 1 || 3.000 ||
|-
| || || || || || 23\36 || 766.667 || 10 || 3 || 3.333 ||
|-
| || || || || 16\25 || || 768.000 || 7 || 2 || 3.500 ||
|-
| || || || || || 25\39 || 769.231 || 11 || 3 || 3.667 ||
|-
| || || || 9\14 || || || 771.429 || 4 || 1 || 4.000 ||
|-
| || || || || || 20\31 || 774.194 || 9 || 2 || 4.500 || [[Squares]]/[[skwares]]
|-
| || || || || 11\17 || || 776.471 || 5 || 1 || 5.000 ||
|-
| || || || || || 13\20 || 780.000 || 6 || 1 || 6.000 ||
|-
| 2\3 || || || || || || 800.000 || 1 || 0 || → inf ||
|}

[[Category:Antipentic]]
[[Category:5-tone scales]]

Talk:19edo modes

2022-11-12T15:35:42Z

Xenwolf: /* Error in 5-tone modes */ new section

== Error in 5-tone modes ==

The files [[:File:Minor 2 Pentatonic (19-EDO).mp3]] (<code>53533, 4|0</code>) and [[:File:Minor Pentatonic (19-EDO).mp3]] (<code>53353, 3|1</code>) don't sound correct to me. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 15:35, 12 November 2022 (UTC)

3L 2s

2022-11-12T14:26:21Z

Xenwolf: Intro with main and alias lemma in bold. I wouldn't say that 3L 2s is really a name

: ''For the 3/2-equivalent 3L 2s pattern, see [[3L 2s (fifth-equivalent)]].''

{{Infobox MOS
| Name = antipentic
| Periods = 1
| nLargeSteps = 3
| nSmallSteps = 2
| Equalized = 3
| Collapsed = 2
| Pattern = LLsLs
}}

'''3L 2s''' or '''antipentic''' is a 5-tone scale. The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[Sensipent_family|sensi]], in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.

== Name ==
The TAMNAMS system uses the name antipentic as it uses opposite step sizes to the “classic” pentatonic scale ([[2L 3s]]).

== Modes ==
* 4|0 LLsLs
* 3|1 LsLLs
* 2|2 LsLsL
* 1|3 sLLsL
* 0|4 sLsLL

== Scale tree ==
Generator ranges:
* Chroma-positive generator: 720 cents (3\5) to 800 cents (2\3)
* Chroma-negative generator: 400 cents (1\3) to 480 cents (2\5)

{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 3\5 || || || || || || 720.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 17\28 || 728.571 || 6 || 5 || 1.200 ||
|-
| || || || || 14\23 || || 730.435 || 5 || 4 || 1.250 ||
|-
| || || || || || 25\41 || 731.707 || 9 || 7 || 1.286 ||
|-
| || || || 11\18 || || || 733.333 || 4 || 3 || 1.333 ||
|-
| || || || || || 30\49 || 734.694 || 11 || 8 || 1.375 || [[Semisept]]
|-
| || || || || 19\31 || || 735.484 || 7 || 5 || 1.400 ||
|-
| || || || || || 27\44 || 736.364 || 10 || 7 || 1.429 ||
|-
| || || 8\13 || || || || 738.462 || 3 || 2 || 1.500 ||
|-
| || || || || || 29\47 || 740.426 || 11 || 7 || 1.571 ||
|-
| || || || || 21\34 || || 741.176 || 8 || 5 || 1.600 ||
|-
| || || || || || 34\55 || 741.818 || 13 || 8 || 1.625 || Golden [[father]]/[[petritri]]/[[aurora]] (741.6408¢)
|-
| || || || 13\21 || || || 742.857 || 5 || 3 || 1.667 ||
|-
| || || || || || 31\50 || 744.000 || 12 || 7 || 1.714 ||
|-
| || || || || 18\29 || || 744.828 || 7 || 4 || 1.750 ||
|-
| || || || || || 23\37 || 745.946 || 9 || 5 || 1.800 ||
|-
| || 5\8 || || || || || 750.000 || 2 || 1 || 2.000 || Basic antipentic (Generators smaller than this are proper)
|-
| || || || || || 22\35 || 754.286 || 9 || 4 || 2.250 ||
|-
| || || || || 17\27 || || 755.556 || 7 || 3 || 2.333 ||
|-
| || || || || || 29\46 || 756.522 || 12 || 5 || 2.400 || [[Sensi]]
|-
| || || || 12\19 || || || 757.895 || 5 || 2 || 2.500 ||
|-
| || || || || || 31\49 || 759.184 || 13 || 5 || 2.600 || Golden [[sentry]] (759.4078¢)
|-
| || || || || 19\30 || || 760.000 || 8 || 3 || 2.667 ||
|-
| || || || || || 26\41 || 760.976 || 11 || 4 || 2.750 ||
|-
| || || 7\11 || || || || 763.636 || 3 || 1 || 3.000 ||
|-
| || || || || || 23\36 || 766.667 || 10 || 3 || 3.333 ||
|-
| || || || || 16\25 || || 768.000 || 7 || 2 || 3.500 ||
|-
| || || || || || 25\39 || 769.231 || 11 || 3 || 3.667 ||
|-
| || || || 9\14 || || || 771.429 || 4 || 1 || 4.000 ||
|-
| || || || || || 20\31 || 774.194 || 9 || 2 || 4.500 || [[Squares]]/[[skwares]]
|-
| || || || || 11\17 || || 776.471 || 5 || 1 || 5.000 ||
|-
| || || || || || 13\20 || 780.000 || 6 || 1 || 6.000 ||
|-
| 2\3 || || || || || || 800.000 || 1 || 0 || → inf ||
|}

[[Category:Antipentic]]
[[Category:5-tone scales]]

3L 2s

2022-11-12T14:23:01Z

Xenwolf: /* Names */ link related scale

: ''For the 3/2-equivalent 3L 2s pattern, see [[3L 2s (fifth-equivalent)]].''

{{Infobox MOS
| Name = antipentic
| Periods = 1
| nLargeSteps = 3
| nSmallSteps = 2
| Equalized = 3
| Collapsed = 2
| Pattern = LLsLs
}}

The only notable low-harmonic-entropy scale for this [[MOSScales|MOS]] pattern is [[Sensipent_family|sensi]], in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.

== Names ==
The TAMNAMS system uses the name '''antipentic''' as it uses opposite step sizes to the “classic” pentatonic scale ([[2L 3s]]).

== Modes ==
* 4|0 LLsLs
* 3|1 LsLLs
* 2|2 LsLsL
* 1|3 sLLsL
* 0|4 sLsLL

== Scale tree ==
Generator ranges:
* Chroma-positive generator: 720 cents (3\5) to 800 cents (2\3)
* Chroma-negative generator: 400 cents (1\3) to 480 cents (2\5)

{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 3\5 || || || || || || 720.000 || 1 || 1 || 1.000 ||
|-
| || || || || || 17\28 || 728.571 || 6 || 5 || 1.200 ||
|-
| || || || || 14\23 || || 730.435 || 5 || 4 || 1.250 ||
|-
| || || || || || 25\41 || 731.707 || 9 || 7 || 1.286 ||
|-
| || || || 11\18 || || || 733.333 || 4 || 3 || 1.333 ||
|-
| || || || || || 30\49 || 734.694 || 11 || 8 || 1.375 || [[Semisept]]
|-
| || || || || 19\31 || || 735.484 || 7 || 5 || 1.400 ||
|-
| || || || || || 27\44 || 736.364 || 10 || 7 || 1.429 ||
|-
| || || 8\13 || || || || 738.462 || 3 || 2 || 1.500 ||
|-
| || || || || || 29\47 || 740.426 || 11 || 7 || 1.571 ||
|-
| || || || || 21\34 || || 741.176 || 8 || 5 || 1.600 ||
|-
| || || || || || 34\55 || 741.818 || 13 || 8 || 1.625 || Golden [[father]]/[[petritri]]/[[aurora]] (741.6408¢)
|-
| || || || 13\21 || || || 742.857 || 5 || 3 || 1.667 ||
|-
| || || || || || 31\50 || 744.000 || 12 || 7 || 1.714 ||
|-
| || || || || 18\29 || || 744.828 || 7 || 4 || 1.750 ||
|-
| || || || || || 23\37 || 745.946 || 9 || 5 || 1.800 ||
|-
| || 5\8 || || || || || 750.000 || 2 || 1 || 2.000 || Basic antipentic (Generators smaller than this are proper)
|-
| || || || || || 22\35 || 754.286 || 9 || 4 || 2.250 ||
|-
| || || || || 17\27 || || 755.556 || 7 || 3 || 2.333 ||
|-
| || || || || || 29\46 || 756.522 || 12 || 5 || 2.400 || [[Sensi]]
|-
| || || || 12\19 || || || 757.895 || 5 || 2 || 2.500 ||
|-
| || || || || || 31\49 || 759.184 || 13 || 5 || 2.600 || Golden [[sentry]] (759.4078¢)
|-
| || || || || 19\30 || || 760.000 || 8 || 3 || 2.667 ||
|-
| || || || || || 26\41 || 760.976 || 11 || 4 || 2.750 ||
|-
| || || 7\11 || || || || 763.636 || 3 || 1 || 3.000 ||
|-
| || || || || || 23\36 || 766.667 || 10 || 3 || 3.333 ||
|-
| || || || || 16\25 || || 768.000 || 7 || 2 || 3.500 ||
|-
| || || || || || 25\39 || 769.231 || 11 || 3 || 3.667 ||
|-
| || || || 9\14 || || || 771.429 || 4 || 1 || 4.000 ||
|-
| || || || || || 20\31 || 774.194 || 9 || 2 || 4.500 || [[Squares]]/[[skwares]]
|-
| || || || || 11\17 || || 776.471 || 5 || 1 || 5.000 ||
|-
| || || || || || 13\20 || 780.000 || 6 || 1 || 6.000 ||
|-
| 2\3 || || || || || || 800.000 || 1 || 0 || → inf ||
|}

[[Category:Antipentic]]
[[Category:5-tone scales]]

2L 5s

2022-11-12T11:30:19Z

Xenwolf: bold redirect lemma

{{Infobox MOS
| Name = antidiatonic
| Periods = 1
| nLargeSteps = 2
| nSmallSteps = 5
| Equalized = 3
| Collapsed = 1
| Pattern = LssLsss
| Neutral = 4L 3s
}}

'''2L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 3\7 (3 degrees of [[7edo]] = 514.29¢) to 1\2 (one degree of [[2edo]] = 600¢). In the case of 7edo, L and s are the same size; in the case of 2edo, s becomes so small it disappears (and all that remains are the two equal L's).

While '''antidiatonic''' is closely associated with [[mavila temperament]] and [[7L 2s]], not every 2L 5s scale is an instance of "mavila", since some of them extend to [[2L 7s]] scales (like the 2L 5s generated by 11edo's 6\11 = 656.5657¢), not 7L 2s mavila superdiatonic scales. (In particular, between 13\29 and 14\31, and centered on 9\20, is the albitonic scale for the 2.7.11.13 subgroup temperament [[Chromatic pairs #Score|score]], which is not intended to be treated as having any kind of fifth, flat or otherwise.)

In terms of harmonic entropy, the most significant minimum is at [[Meantone family #Liese|Liese]]/Triton, in which the generator is about 7/5 and three of them make a 3/1.

== Names ==
It is often called '''antidiatonic''', because it has the step pattern of diatonic ([[5L 2s]]), but with the large and small steps switched. [[TAMNAMS]] uses this name as well.

== Notation ==
We'll use the convention DEFGABCD (D Antidorian, sLsssLs); D = 293.665 Hz, &/@ = raise and lower by one chroma. The chain of mavila fifths becomes … E& B& F C G D A E B F@ C@ … Note that 7 fifths up ''flattens'' a note by a chroma, rather than sharpening it as in diatonic ([[5L 2s]]).

== Intervals ==
Note: In TAMNAMS, a k-step interval class in antidiatonic may be called a "k-step", "k-mosstep", or "k-pelstep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.

== Modes ==
* 6|0 LssLsss (anti-locrian)
* 5|1 LsssLss (anti-phrygian)
* 4|2 sLssLss (anti-aeolian)
* 3|3 sLsssLs (anti-dorian)
* 2|4 ssLssLs (anti-mixolydian)
* 1|5 ssLsssL (anti-ionian)
* 0|6 sssLssL (anti-lydian)

== Scale tree ==
Generator ranges:
* Chroma-positive generator: 514.2857 cents (3\7) to 600 cents (1\2)
* Chroma-negative generator: 600 cents (1\2) to 685.7143 cents (4\7)

{| class="wikitable center-all"
! colspan="6" | Generator
! Cents
! L
! s
! L/s
! Comments
|-
| 3\7 || || || || || || 514.286 || 1 || 1 || 1.000 ||
|-
| || || || || || 16\37 || 518.919 || 6 || 5 || 1.200 || [[Gravity]]↑
|-
| || || || || 13\30 || || 520.000 || 5 || 4 || 1.250 ||
|-
| || || || || || 23\53 || 520.755 || 9 || 7 || 1.286 ||
|-
| || || || 10\23 || || || 521.739 || 4 || 3 || 1.333 ||
|-
| || || || || || 27\62 || 522.581 || 11 || 8 || 1.375 ||
|-
| || || || || 17\39 || || 523.077 || 7 || 5 || 1.400 ||
|-
| || || || || || 24\55 || 523.636 || 10 || 7 || 1.428 ||
|-
| || || 7\16 || || || || 525.000 || 3 || 2 || 1.500 || [[Mavila]] is in this region
|-
| || || || || || 25\57 || 526.316 || 11 || 7 || 1.571 ||
|-
| || || || || 18\41 || || 526.829 || 8 || 5 || 1.600 ||
|-
| || || || || || 29\66 || 527.273 || 13 || 8 || 1.625 || Golden mavila (527.1497¢)
|-
| || || || 11\25 || || || 528.000 || 5 || 3 || 1.667 ||
|-
| || || || || || 26\59 || 528.814 || 12 || 7 || 1.714 ||
|-
| || || || || 15\34 || || 529.412 || 7 || 4 || 1.750 ||
|-
| || || || || || 19\43 || 530.233 || 9 || 5 || 1.800 || [[Mabila]] / [[Amavil]]
|-
| || 4\9 || || || || || 533.333 || 2 || 1 || 2.000 || Basic antidiatonic (Generators smaller than this are proper)
|-
| || || || || || 17\38 || 536.842 || 9 || 4 || 2.250 ||
|-
| || || || || 13\29 || || 537.931 || 7 || 3 || 2.333 ||
|-
| || || || || || 22\49 || 538.776 || 12 || 5 || 2.400 ||
|-
| || || || 9\20 || || || 540.000 || 5 || 2 || 2.500 || Score
|-
| || || || || || 23\51 || 541.176 || 13 || 5 || 2.600 || Unnamed golden tuning (541.3837¢)
|-
| || || || || 14\31 || || 541.935 || 8 || 3 || 2.667 || [[Casablanca]] is around here
|-
| || || || || || 19\42 || 542.857 || 11 || 4 || 2.750 ||
|-
| || || 5\11 || || || || 545.455 || 3 || 1 || 3.000 ||
|-
| || || || || || 16\35 || 548.571 || 10 || 3 || 3.333 ||
|-
| || || || || 11\24 || || 550.000 || 7 || 2 || 3.500 ||
|-
| || || || || || 17\37 || 551.351 || 11 || 3 || 3.667 || [[Freivald]] / [[emka]]
|-
| || || || 6\13 || || || 553.846 || 4 || 1 || 4.000 ||
|-
| || || || || || 13\28 || 557.143 || 9 || 2 || 4.500 ||
|-
| || || || || 7\15 || || 560.000 || 5 || 1 || 5.000 || [[Thuja]] is around here
|-
| || || || || || 8\17 || 564.706 || 6 || 1 || 6.000 || [[Liese]]↓, [[triton]]↓
|-
| 1\2 || || || || || || 600.000 || 1 || 0 || → inf ||
|}

[[Category:7-tone scales]]
[[Category:Antidiatonic| ]]

User talk:Xenwolf

2022-11-12T10:03:21Z

Xenwolf: /* Thank you for reconstructing my diagram on 10648/10647 */ re

User talk:Mschulter1325

2022-11-10T13:10:49Z

Xenwolf: /* Typographic hint */ new section

== Welcome ==
And as a tip, feel free to write casually in your user page. Gene created a separate page about you containing some objective information in third-person tone, which you might also like to work on. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 19:24, 14 September 2022 (UTC)

== Typographic hint ==

Hi Margo, welcome to the wiki.

I think diagrams like the one you abandoned as hopeless in the [[10648/10647]] article are indeed possible in this wiki, see the [[Talk:10648/10647#Diagram in monospace font|corresponding section on the discussion page]]. I didn't put the diagram directly into the article, because it will surely need some rewriting again.

With kind regards
--[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 13:10, 10 November 2022 (UTC)

Talk:Harmonisma

2022-11-10T13:10:34Z

Xenwolf: /* Diagram in monospace font */ another minor rewrite -- Please excuse the many attempts!

__TOC__
== Name ==

Why are we calling this the "harmonisma"? Such a generic name seems to suggest it's "the comma of harmony", which is very misleading because there's hundreds of other commas that have an equally good claim to such a description. Who named it and why? —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 19:34, 16 June 2021 (UTC)

: Maybe open a thread in the Facebook group? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:43, 18 June 2021 (UTC)

The harmonisma is named in honor of the harmoniai of Kathleen Schlesinger, since these have many superparticular steps of 14:13 and 13:12 and 12:11, and many intervals of 13:11 and 14:11. The context in which I came upon the harmonisma was, in 2002, when designing a just tuning called JOT-17 (Just Octachord Tuning) that modified an arithmetic series 28:27:26:25:24:23:22:21, a division of a 4:3 fourth typical of Schlesinger's approach and also of the diaphonic tunings of Erv Wilson, John Chalmers, and Kraig Grady, to 1/1-28/27-14/13-44/39-7/6-28/23-14/11-4/3, with 14:11 resulting from two near-equal tones at 44:39 and 273:242, which differ by the harmonisma (note that this division has seven adjacent steps or eight notes, thus the octachord of the Just Octachord Tuning or JOT).

The harmonisma is tempered out in parapyth, along with 352/351 and 364/363, of which it is the difference, and also the product of 352/351 and 364/363, 896/891.
[[User:Mschulter1325|Mschulter1325]] 03:17, 9 November 2022 (UTC)

== Diagram in monospace font ==

In this wiki, monospace blocks can be added by starting each line with one white space. So the diagram Margo Schulter planned to add to the [[10648/10647]] article would probably look like this:

62.961c. 58.019c. 58.036c. 53.273c
28/27--------------121/117-----91/88--------------33/32
| 352/351. 10648/10647. 364/363. |
| 4.925. 0.163c. 4.763c. |
|--------------------- 896/891 -------------------|
9.688c

Another option is to enclose the preformatted text in <code><pre></code> tags.
-- [[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:51, 10 November 2022 (UTC)

Talk:Harmonisma

2022-11-10T12:59:04Z

Xenwolf: add toc

__TOC__
== Name ==

Why are we calling this the "harmonisma"? Such a generic name seems to suggest it's "the comma of harmony", which is very misleading because there's hundreds of other commas that have an equally good claim to such a description. Who named it and why? —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 19:34, 16 June 2021 (UTC)

: Maybe open a thread in the Facebook group? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:43, 18 June 2021 (UTC)

The harmonisma is named in honor of the harmoniai of Kathleen Schlesinger, since these have many superparticular steps of 14:13 and 13:12 and 12:11, and many intervals of 13:11 and 14:11. The context in which I came upon the harmonisma was, in 2002, when designing a just tuning called JOT-17 (Just Octachord Tuning) that modified an arithmetic series 28:27:26:25:24:23:22:21, a division of a 4:3 fourth typical of Schlesinger's approach and also of the diaphonic tunings of Erv Wilson, John Chalmers, and Kraig Grady, to 1/1-28/27-14/13-44/39-7/6-28/23-14/11-4/3, with 14:11 resulting from two near-equal tones at 44:39 and 273:242, which differ by the harmonisma (note that this division has seven adjacent steps or eight notes, thus the octachord of the Just Octachord Tuning or JOT).

The harmonisma is tempered out in parapyth, along with 352/351 and 364/363, of which it is the difference, and also the product of 352/351 and 364/363, 896/891.
[[User:Mschulter1325|Mschulter1325]] 03:17, 9 November 2022 (UTC)

== Diagram in monospace font ==

In this wiki, monospace blocks can be added by starting each line with one white space. So the diagram [https://en.xen.wiki/index.php?title=10648%2F10647&type=revision&diff=98937&oldid=98934 Margo Schulter wished to] add to the [[10648/10647]] article would most probably look like this:

62.961c. 58.019c. 58.036c. 53.273c
28/27--------------121/117-----91/88--------------33/32
| 352/351. 10648/10647. 364/363. |
| 4.925. 0.163c. 4.763c. |
|--------------------- 896/891 -------------------|
9.688c

Another option is to enclose the preformatted text in <code><pre></code> tags.
-- [[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:51, 10 November 2022 (UTC)

Talk:Harmonisma

2022-11-10T12:58:37Z

Xenwolf: /* Diagram in monospace font */ minor fix

== Name ==

Why are we calling this the "harmonisma"? Such a generic name seems to suggest it's "the comma of harmony", which is very misleading because there's hundreds of other commas that have an equally good claim to such a description. Who named it and why? —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 19:34, 16 June 2021 (UTC)

: Maybe open a thread in the Facebook group? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:43, 18 June 2021 (UTC)

The harmonisma is named in honor of the harmoniai of Kathleen Schlesinger, since these have many superparticular steps of 14:13 and 13:12 and 12:11, and many intervals of 13:11 and 14:11. The context in which I came upon the harmonisma was, in 2002, when designing a just tuning called JOT-17 (Just Octachord Tuning) that modified an arithmetic series 28:27:26:25:24:23:22:21, a division of a 4:3 fourth typical of Schlesinger's approach and also of the diaphonic tunings of Erv Wilson, John Chalmers, and Kraig Grady, to 1/1-28/27-14/13-44/39-7/6-28/23-14/11-4/3, with 14:11 resulting from two near-equal tones at 44:39 and 273:242, which differ by the harmonisma (note that this division has seven adjacent steps or eight notes, thus the octachord of the Just Octachord Tuning or JOT).

The harmonisma is tempered out in parapyth, along with 352/351 and 364/363, of which it is the difference, and also the product of 352/351 and 364/363, 896/891.
[[User:Mschulter1325|Mschulter1325]] 03:17, 9 November 2022 (UTC)

== Diagram in monospace font ==

In this wiki, monospace blocks can be added by starting each line with one white space. So the diagram [https://en.xen.wiki/index.php?title=10648%2F10647&type=revision&diff=98937&oldid=98934 Margo Schulter wished to] add to the [[10648/10647]] article would most probably look like this:

62.961c. 58.019c. 58.036c. 53.273c
28/27--------------121/117-----91/88--------------33/32
| 352/351. 10648/10647. 364/363. |
| 4.925. 0.163c. 4.763c. |
|--------------------- 896/891 -------------------|
9.688c

Another option is to enclose the preformatted text in <code><pre></code> tags.
-- [[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:51, 10 November 2022 (UTC)

Talk:Harmonisma

2022-11-10T12:56:42Z

Xenwolf: /* Diagram in monospace font */ add reference to edits and article

== Name ==

Why are we calling this the "harmonisma"? Such a generic name seems to suggest it's "the comma of harmony", which is very misleading because there's hundreds of other commas that have an equally good claim to such a description. Who named it and why? —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 19:34, 16 June 2021 (UTC)

: Maybe open a thread in the Facebook group? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:43, 18 June 2021 (UTC)

The harmonisma is named in honor of the harmoniai of Kathleen Schlesinger, since these have many superparticular steps of 14:13 and 13:12 and 12:11, and many intervals of 13:11 and 14:11. The context in which I came upon the harmonisma was, in 2002, when designing a just tuning called JOT-17 (Just Octachord Tuning) that modified an arithmetic series 28:27:26:25:24:23:22:21, a division of a 4:3 fourth typical of Schlesinger's approach and also of the diaphonic tunings of Erv Wilson, John Chalmers, and Kraig Grady, to 1/1-28/27-14/13-44/39-7/6-28/23-14/11-4/3, with 14:11 resulting from two near-equal tones at 44:39 and 273:242, which differ by the harmonisma (note that this division has seven adjacent steps or eight notes, thus the octachord of the Just Octachord Tuning or JOT).

The harmonisma is tempered out in parapyth, along with 352/351 and 364/363, of which it is the difference, and also the product of 352/351 and 364/363, 896/891.
[[User:Mschulter1325|Mschulter1325]] 03:17, 9 November 2022 (UTC)

== Diagram in monospace font ==

In this wiki, monospace blocks can be added by starting each line with one white space. So the diagram [https://en.xen.wiki/index.php?title=10648%2F10647&type=revision&diff=98937&oldid=98934 Margo Schulter wished to] add to the [[10648/10647]] article would most probably look like this:

62.961c. 58.019c. 58.036c. 53.273c
28/27--------------121/117-----91/88--------------33/32
| 352/351. 10648/10647. 364/363. |
| 4.925. 0.163c. 4.763c. |
|--------------------- 896/891 -------------------|
9.688c

... another option is to enclose the preformatted text in <code><pre></code> tags.
-- [[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:51, 10 November 2022 (UTC)

Talk:Harmonisma

2022-11-10T12:53:02Z

Xenwolf: /* Diagram in monotype font */ correct wording

== Name ==

Why are we calling this the "harmonisma"? Such a generic name seems to suggest it's "the comma of harmony", which is very misleading because there's hundreds of other commas that have an equally good claim to such a description. Who named it and why? —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 19:34, 16 June 2021 (UTC)

: Maybe open a thread in the Facebook group? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:43, 18 June 2021 (UTC)

The harmonisma is named in honor of the harmoniai of Kathleen Schlesinger, since these have many superparticular steps of 14:13 and 13:12 and 12:11, and many intervals of 13:11 and 14:11. The context in which I came upon the harmonisma was, in 2002, when designing a just tuning called JOT-17 (Just Octachord Tuning) that modified an arithmetic series 28:27:26:25:24:23:22:21, a division of a 4:3 fourth typical of Schlesinger's approach and also of the diaphonic tunings of Erv Wilson, John Chalmers, and Kraig Grady, to 1/1-28/27-14/13-44/39-7/6-28/23-14/11-4/3, with 14:11 resulting from two near-equal tones at 44:39 and 273:242, which differ by the harmonisma (note that this division has seven adjacent steps or eight notes, thus the octachord of the Just Octachord Tuning or JOT).

The harmonisma is tempered out in parapyth, along with 352/351 and 364/363, of which it is the difference, and also the product of 352/351 and 364/363, 896/891.
[[User:Mschulter1325|Mschulter1325]] 03:17, 9 November 2022 (UTC)

== Diagram in monospace font ==

In this wiki, monospace blocks can be added by starting each line with one white space. So the diagram by Margo Schulter would most probably look like this:

62.961c. 58.019c. 58.036c. 53.273c
28/27--------------121/117-----91/88--------------33/32
| 352/351. 10648/10647. 364/363. |
| 4.925. 0.163c. 4.763c. |
|--------------------- 896/891 -------------------|
9.688c

... another option is to enclose the preformatted text in <code><pre></code> tags.
-- [[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:51, 10 November 2022 (UTC)

Talk:Harmonisma

2022-11-10T12:51:40Z

Xenwolf: /* Diagrams in monotype font */ change to singular

== Name ==

Why are we calling this the "harmonisma"? Such a generic name seems to suggest it's "the comma of harmony", which is very misleading because there's hundreds of other commas that have an equally good claim to such a description. Who named it and why? —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 19:34, 16 June 2021 (UTC)

: Maybe open a thread in the Facebook group? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:43, 18 June 2021 (UTC)

The harmonisma is named in honor of the harmoniai of Kathleen Schlesinger, since these have many superparticular steps of 14:13 and 13:12 and 12:11, and many intervals of 13:11 and 14:11. The context in which I came upon the harmonisma was, in 2002, when designing a just tuning called JOT-17 (Just Octachord Tuning) that modified an arithmetic series 28:27:26:25:24:23:22:21, a division of a 4:3 fourth typical of Schlesinger's approach and also of the diaphonic tunings of Erv Wilson, John Chalmers, and Kraig Grady, to 1/1-28/27-14/13-44/39-7/6-28/23-14/11-4/3, with 14:11 resulting from two near-equal tones at 44:39 and 273:242, which differ by the harmonisma (note that this division has seven adjacent steps or eight notes, thus the octachord of the Just Octachord Tuning or JOT).

The harmonisma is tempered out in parapyth, along with 352/351 and 364/363, of which it is the difference, and also the product of 352/351 and 364/363, 896/891.
[[User:Mschulter1325|Mschulter1325]] 03:17, 9 November 2022 (UTC)

== Diagram in monotype font ==

In this wiki, typewrite blocks can be added by starting each line with one white space. So the diagram by Margo Schulter would most probably look like this:

62.961c. 58.019c. 58.036c. 53.273c
28/27--------------121/117-----91/88--------------33/32
| 352/351. 10648/10647. 364/363. |
| 4.925. 0.163c. 4.763c. |
|--------------------- 896/891 -------------------|
9.688c

... another option is to enclose the preformatted text in <code><pre></code> tags.
-- [[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:51, 10 November 2022 (UTC)

Talk:Harmonisma

2022-11-10T12:51:09Z

Xenwolf: /* Diagrams in monotype font */ new section

== Name ==

Why are we calling this the "harmonisma"? Such a generic name seems to suggest it's "the comma of harmony", which is very misleading because there's hundreds of other commas that have an equally good claim to such a description. Who named it and why? —[[User:Keenan Pepper|Keenan Pepper]] ([[User talk:Keenan Pepper|talk]]) 19:34, 16 June 2021 (UTC)

: Maybe open a thread in the Facebook group? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 01:43, 18 June 2021 (UTC)

The harmonisma is named in honor of the harmoniai of Kathleen Schlesinger, since these have many superparticular steps of 14:13 and 13:12 and 12:11, and many intervals of 13:11 and 14:11. The context in which I came upon the harmonisma was, in 2002, when designing a just tuning called JOT-17 (Just Octachord Tuning) that modified an arithmetic series 28:27:26:25:24:23:22:21, a division of a 4:3 fourth typical of Schlesinger's approach and also of the diaphonic tunings of Erv Wilson, John Chalmers, and Kraig Grady, to 1/1-28/27-14/13-44/39-7/6-28/23-14/11-4/3, with 14:11 resulting from two near-equal tones at 44:39 and 273:242, which differ by the harmonisma (note that this division has seven adjacent steps or eight notes, thus the octachord of the Just Octachord Tuning or JOT).

The harmonisma is tempered out in parapyth, along with 352/351 and 364/363, of which it is the difference, and also the product of 352/351 and 364/363, 896/891.
[[User:Mschulter1325|Mschulter1325]] 03:17, 9 November 2022 (UTC)

== Diagrams in monotype font ==

In this wiki, typewrite blocks can be added by starting each line with one white space. So the diagram by Margo Schulter would most probably look like this:

62.961c. 58.019c. 58.036c. 53.273c
28/27--------------121/117-----91/88--------------33/32
| 352/351. 10648/10647. 364/363. |
| 4.925. 0.163c. 4.763c. |
|--------------------- 896/891 -------------------|
9.688c

... another option is to enclose the preformatted text in <code><pre></code> tags.
-- [[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 12:51, 10 November 2022 (UTC)

Chirality

2022-11-07T08:28:51Z

Xenwolf: display WP link on top

{{Wikipedia}}
'''Chirality''' is a property of asymmetry which can be applied to [[periodic scale]]s.

A scale is called ''chiral'' if reversing the order of the steps results in a different scale (which is not a mode of the original scale). The two scales form a ''chiral pair'' and are right/left-handed. Handedness is determined as follows:
# Lexicographically compare all modes of each chirality (i.e. treat scale step size sequences as words to be arranged in "alphabetical order", where this alphabetical order is from bigger step to smaller step). For each chirality, record the mode that comes first (among all the modes of the chirality) according to this alphabetical order. You should end up with two modes M and M'.
# Lexicographically compare M and M'. We choose the convention that if M lexicographically comes before M', then M and all its modes are ''lexicographically right-handed'' (lex-RH), and M' and all its modes are ''lexicographically left-handed'' (lex-LH).

The smallest example of a chiral pair in an [[edo]] is 321/312, with the former being lexicographically right-handed and the latter being lexicographically left-handed. Similarly, the simplest chiral pair for abstract patterns is Lms/Lsm.

Scales for which this property does not hold are called ''achiral''. For example, the [[5L 2s|diatonic scale]] of 12edo is achiral because 2221221 reverses to 1221222, which is identical to the original scale up to cyclical permutation.

== Examples ==
* Odd-sized [[GO]] scales, such as the [[Zarlino]] scale and [[diasem]], are chiral; even-sized GO scales, such as [[blackdye]], are not.
* A [[CPS]] made by choosing n/2 out of n elements (for n even) is achiral. Otherwise it may be chiral (for example, the 1 3 5 7 9 11 [[pentadekany]] is chiral).

== Properties ==
* Chiral scales have at least 3 notes;
* Chiral scales are at least max-variety 3 (they cannot be [[MOS]] or [[DE]])
* Chiral scales have a [http://en.wikipedia.org/wiki/Natural_density density] of 1 (see table below)
* Chiral scales with rational step ratios can only exist in edos larger than [[5edo]]

== Chiral scales in edos up to 20edo ==
{| class="wikitable" style="text-align:right"
! EDO
! Number of Chiral Scales
! Percentage of Chiral Scales
! Corresponding Ratio
|-
| 1
| 0
| 0.0%
| style="text-align:center" | 0/1
|-
| 2
| 0
| 0.0%
| style="text-align:center" | 0/1
|-
| 3
| 0
| 0.0%
| style="text-align:center" | 0/1
|-
| 4
| 0
| 0.0%
| style="text-align:center" | 0/1
|-
| 5
| 0
| 0.0%
| style="text-align:center" | 0/1
|-
| 6
| 2
| 22.2%
| style="text-align:center" | 2/9
|-
| 7
| 4
| 22.2%
| style="text-align:center" | 2/9
|-
| 8
| 12
| 40.0%
| style="text-align:center" | 2/5
|-
| 9
| 28
| 50.0%
| style="text-align:center" | 1/2
|-
| 10
| 60
| 60.6%
| style="text-align:center" | 20/33
|-
| 11
| 124
| 66.7%
| style="text-align:center" | 2/3
|-
| 12
| 254
| 75.8%
| style="text-align:center" | 254/335
|-
| 13
| 504
| 80.0%
| style="text-align:center" | 4/5
|-
| 14
| 986
| 84.9%
| style="text-align:center" | 986/1161
|-
| 15
| 1936
| 88.7%
| style="text-align:center" | 968/1091
|-
| 16
| 3720
| 91.2%
| style="text-align:center" | 31/34
|-
| 17
| 7200
| 93.4%
| style="text-align:center" | 240/257
|-
| 18
| 13804
| 95.0%
| style="text-align:center" | 493/519
|-
| 19
| 26572
| 96.3%
| style="text-align:center" | 26/27
|-
| 20
| 50892
| 97.2%
| style="text-align:center" | 16964/17459
|}

== Chirality in MV3 scales ==
Assume a scale is [[MV3]] and is of the form ax by bz. Additionally assume that the mos ax 2bY that results from equating y and z is not a multimos. Then the scale must be chiral because there are no rotations that will make the two equivalent (each mode of the mos ax 2bY corresponding to two chiral variants).

== External links ==
* [[Wikipedia: Chirality]]

[[Category:Scale]]
[[Category:Terms]]

Porcusmine

2022-11-07T08:27:18Z

Xenwolf: link chiral -> chirality

'''Porcusmine''' is a [[Maximum variety|max-variety-4]] or max-variety-3, [[generator-offset]] scale with step pattern 4L 3M 1s. It is equivalent to the [[porcupine]] ([[7L 1s]]) mos with 4 of the large steps made bigger and the other 3 made smaller, or to the smitonic ([[4L 3s]]) with an extra-small step added. Porcusmine is not [[chiral]]. [[19edo]] is the smallest edo to support a non-degenerate porcusmine.

Porcusmine can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[27/25]], and s represents [[25/24]].

"Porcusmine" is a name given by [[User:CellularAutomaton|cellularAutomaton]], who discovered it as a detempering of porcupine, although the scale has also been [[Kite_Guitar_Translations_by_Kite_Giedraitis#Couples_Therapy_.28Jacob_Barton.2C_microtonal.29|discussed]] by [[Kite Giedraitis]] and possibly others. The name is a portmanteau of "porcupine" and "smitonic", since its step sizes are intermediate between those of the 8-note porcupine and 7-note smitonic mosses.

== Modes ==
Porcusmine has 8 modes. Names are provided based on porcupine (tuning-neutral) and smitonic (for tunings where s is small), as well as a unique portmanteau name. When M and s are close, the scale approaches [[Diminished|diminshed]] ([[4L 4s]]), which has only two distinct modes and is therefore not useful for naming. The porcupine mode names refer to William Lynch's names, and the smitonic mode names refer to [[User:Ayceman|Alexandru Ianu]]'s names. Below are the modes arranged in cyclic order:
{| class="wikitable"
!Modes in cyclic order
|-
|LMLMLMLs
Porcusmine Octopus

Porcusmine Sothic Ascending

Octzothic
|-
|MLMLMLsL
Porcusmine Mantis

Porcusmine Dagothic

Mandagothic
|-
|LMLMLsLM
Porcusmine Dolphin

Porcusmine Lorkhanic

Dolkhanic
|-
|MLMLsLML
Porcusmine Crab

Porcusmine Almalexian

Crablexian
|-
|LMLsLMLM
Porcusmine Tuna

Porcusmine Vivecan

Tunivecan
|-
|MLsLMLML
Porcusmine Salmon

Porcusmine Kagrenacan

Salmenacan
|-
|LsLMLMLM
Porcusmine Starfish

Porcusmine Nerevarine

Starevarine
|-
|sLMLMLML
Porcusmine Whale

Porcusmine Sothic Descending

Whothic
|}

== Tunings ==
Porcusmine is MV3 when L+s=M+M, as reflected in the table below.
{| class="wikitable sortable"
|+Porcusmine tunings
!Tuning
!L:M:s
!Good JI approximations
!Other notes
|-
|JI (5-limit interpretation)
|2.581:1.885:1
|just 3/2, 6/5, 5/4, 9/8, and 10/9
|
|-
|19edo
|3:2:1
|excellent pental thirds, fairly good 3-limit
|MV3
|-
|23edo
|4:2:1
|excellent 6/5 and 9/8, fairly good 7/5
|
|-
|26edo
|4:3:1
|excellent 10/9, 11/8, and 7/4; fairly good 5/4 and 3/2
|
|-
|27edo
|4:3:2
|excellent 10/9, 7/6, 6/5, and 7/5; fairly good 9/7 and 3/2
|MV3
|-
|27edo
|5:2:1
|excellent 5:6:7; fairly good 7/4, 11/9, and 3/2
|
|-
|30edo
|5:3:1
|excellent 15/14, 9/8, 6/5, and 9/7; fairly good 15/8, 7/4, and 11/8
|MV3
|-
|31edo
|5:3:2
|excellent 15/14 or 16/15, 7/6, 5/4, and 7/5; fairly good 6/5, 9/7, 3/2
|meantone fifths
|-
|31edo
|6:2:1
|excellent 7/4, 7/6, 11/9, 5/4, 7/5; fairly good 6/5, 3/2, and 11/8
|single meantone fifth
|-
|33edo
|5:4:1
|excellent 10/9; fairly good 11/6 and 11/8
|
|-
|34edo
|5:4:2
|very close to 5-limit just tuning
|gentle fifths
|-
|34edo
|6:3:1
|excellent 6/5; fairly good 9/8, 11/9, and 14/11
|
|}

[[Category:8-tone scales]]
[[Category:19edo]]
[[Category:23edo]]
[[Category:26edo]]
[[Category:27edo]]
[[Category:31edo]]
[[Category:34edo]]
[[Category:Just intonation scales]]
[[Category:5-limit]]
[[Category:GO scales]]
[[Category:Rank-3 scales]]
[[Category:Scales]]

User:Xenwolf/common.js

2022-11-07T08:20:10Z

Xenwolf: copy from User:Plumtree/common.js

User:Xenwolf/common.css

2022-11-07T08:18:13Z

Xenwolf: copy from User:Plumtree/common.css

Category:User it-2

2022-11-06T12:11:23Z

Xenwolf: Created page with "Category:User it it"

[[Category:User it]]
[[Category:Users by language|it]]

Category:User it

2022-11-06T12:11:21Z

Xenwolf: Created page with "it"

[[Category:Users by language|it]]

Category:User fr-3

2022-11-06T12:10:40Z

Xenwolf: add cats

[[Category:User fr]]
[[Category:Users by language|fr]]

Category:Todo:remove explicit ket notation

2022-10-28T06:36:01Z

Xenwolf: expanded explanation and made the todo character more obvious

This category contains interval pages where parameter <code>Monzo</code>/<code>Ket</code> of [[Template:Infobox Interval|Infobox Interval]] has a value provided in cases when it can be derived from other parameters. Explicit parameters should be removed in the info boxes on top of these pages.

__HIDDENCAT__
[[Category:Todo|remove explicit ket notation]]

Template talk:IoT

2022-10-27T16:10:49Z

Xenwolf: /* Merge categories and deprecate this template? */ delete this as well?

== Merge categories and deprecate this template? ==

I think that [[:Category:Index of temperaments]] and [[:Category:Temperaments]] should be merged. I'd prefer keeping the latter; categories usually don't start with "Index of...", because that's just what categories are: they're indexes of wiki pages.

Right now, both categories are used for the same purpose, but pages are placed in them in different ways: with a template in the first case, and normally ("by hand") in the second case. I'm not convinced by the design choice of using a template for the sole reason of placing pages in a single category. I understand that it acts as a shortcut, but it also means that Cat-a-lot cannot handle the category added by the template; I would need [[Special:ReplaceText|ReplaceText]] to do that, and that requires admin privileges. Of course, I could simply edit the IoT template as needed, but that wouldn't fix the problem I just mentioned, even though it would solve the category merging.

To summarize, I suggest replacing every occurrence of <code><nowiki>{{IoT}}</nowiki></code> with <code><nowiki>[[Category:Temperaments]]</nowiki></code>, using ReplaceText, and then deprecating this template. This would have to be done by an admin. Any thoughts? --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 21:21, 28 February 2022 (UTC)

: I decided to do the categorization via template to change the name of the category later. So take [[:Category:Temperaments]] as the “index of temperaments” and just change the category name within this template. But do whatever you think is right. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 22:37, 28 February 2022 (UTC)

:: I changed the target category for now. I'm still unconvinced by the usage of this template, though. I don't think we'll have to move this category so often, and if we do need to do so, then we can do it with Cat-a-lot very easily. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 23:10, 28 February 2022 (UTC)

::: The template was introduced when the recategorization tool was not yet available, so its value is no longer present.It should also be a performance issue: direct categorization should be cheaper. That's why it should be deprecated. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 07:18, 1 March 2022 (UTC)

::: I will make the mass changes soon (and turn into a "bot" for this). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 11:01, 1 March 2022 (UTC)

:::: As it turned out, [[Special:ReplaceText]] seems kind of broken in this wiki, it produces SQL syntax errors. So one option would be to do it by hand (it's [https://en.xen.wiki/index.php?title=Special%3AWhatLinksHere&limit=500&hideredirs=1&hidelinks=1&target=Template%3AIoT&namespace=0 this list that provides direct ''edit'' links]). We could deprecate it first and make this obvious to people who use the preview function (BTW: the access key is '''p'''). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:46, 1 March 2022 (UTC)

::::: The replacement is now done. @Fredg999 Would you please do the deprecation part? Thanks in advance. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:38, 1 March 2022 (UTC)

:::::: The deprecation part is done. Please let me know if there is anything else we should do here. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 03:53, 2 March 2022 (UTC)

::::::: Maybe this template and talk page should be deleted as well? @Fredg999 do you see anything that would argue against that? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 16:10, 27 October 2022 (UTC)

User talk:Plumtree/Sandbox/Interval

2022-10-26T19:28:34Z

Xenwolf: /* An even better impression */ question answered

== An even better impression ==

I didn't see this before, but this is obviously the most wanted use case of in-browser sound. What exactly is ''Harmonics'' and ''Clear audio''? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:15, 26 October 2022 (UTC)

: Well, I found the answer myself in [[Module:Infobox Interval]]: it's the timbres “violin” and “semisine”. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:28, 26 October 2022 (UTC)

User talk:Plumtree/Sandbox/Interval

2022-10-26T19:15:34Z

Xenwolf: /* An even better impression */ new section

User talk:Plumtree/Sound

2022-10-26T19:09:27Z

Xenwolf: /* First impression */ PS

== First impression ==

It's really great to see that in action, that's what I had in mind when I requested to enable user scripts and CSS for the wiki, but I had never the time (nor the expertise) to get so far…

I briefly looked over the JavaScript, painfully remembering (given your for loops) that <code>let</code> is not available due to an embarrassing bug in MediaWiki (<code>const</code> works, by the way).

What I found that may be added is a way to stop (maybe pause) playing sound. If we are ever dealing with longer sound samples and someone clicks on them rather accidentally, I would estimate the need to quickly stop all output as high.

I'm not sure is this quick review will help you. If you have things in mind I should test, please let me know.

BTW: I'm using the '''Timeless''' skin, which is really great in most aspects. The only downside (and this is a heavy one!) is that I't all to easy to miss the notification when someone changes your user discussion. That's why I read your message only today, despite visiting the wiki nearly every day. If you perhaps know how to make it stand out like in '''Vector''' skin, please let me know.

Best regards --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:07, 26 October 2022 (UTC)

: PS: in case you want top experiment with other skins, you'll find it here: https://en.xen.wiki/w/Special:Preferences#mw-prefsection-rendering --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:09, 26 October 2022 (UTC)

User talk:Plumtree/Sound

2022-10-26T19:07:53Z

Xenwolf: /* First impression */ new section

User:Xenwolf/common.js

2022-10-26T18:28:15Z

Xenwolf: test in-browser sound generation

User:Xenwolf/common.css

2022-10-26T18:28:11Z

Xenwolf: test in-browser sound generation

.sequence-audio-button {
background: #777777;
}
.sequence-audio-button:hover,.sequence-audio-button:active {
cursor: not-allowed;
}

.sequence-audio-button.sequence-audio-valid {
background: #ffffaa;
}
.sequence-audio-button.sequence-audio-valid:hover,.sequence-audio-button.sequence-audio-valid:active {
background: #eeee66;
cursor: pointer;
}

.sequence-audio-button.sequence-audio-playing {
background: #aaffaa;
}
.sequence-audio-button.sequence-audio-playing:hover,.sequence-audio-button.sequence-audio-playing:active {
background: #66ee66;
cursor: wait;
}

.sequence-audio-button.sequence-audio-valid.white-key {
background: #ffffff;
}
.sequence-audio-button.sequence-audio-valid.white-key:hover,.sequence-audio-button.sequence-audio-valid.white-key:active {
background: #ffffaa;
}

.sequence-audio-button.sequence-audio-valid.black-key {
background: #000000;
}
.sequence-audio-button.sequence-audio-valid.black-key:hover,.sequence-audio-button.sequence-audio-valid.black-key:active {
background: #005555;
}

.sequence-audio-button.sequence-audio-invalid {
background: #ffaaaa;
}
.sequence-audio-button.sequence-audio-invalid:hover,.sequence-audio-button.sequence-audio-invalid:active {
background: #ee6666;
cursor: not-allowed;
}

Talk:25/19

2022-10-25T19:59:57Z

Xenwolf: /* Funny coincidence */ new section

== Funny coincidence ==

The cent size of this interval equals its Benedetti height. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 19:59, 25 October 2022 (UTC)

User talk:Plumtree

2022-10-14T10:25:04Z

Xenwolf: /* Welcome */ new section

== Lua modules ==

Hi Plumtree (and welcome to the Xenharmonic Wiki!),

I wanted to thank you for contributing on the Lua modules. As you might have noticed, I am not an experienced programmer, so your improvements are appreciated. And of course I was pleased to see the new functions you have implemented, which follow pretty much what I had in mind when I started working on those.

I also saw that you added documentation for some functions, but not all of them. Since you added them, I guess it would be easier for you to write the documentation, otherwise I'll try to have a look at it eventually.

In any case, the Infobox ET module seems pretty much good to go, but I'll check with a few people on Discord before we deploy it to equal tuning pages. Feel free to join the XA Discord by the way, if you haven't already, link in the left panel!

Thanks again! --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 01:24, 2 October 2022 (UTC)

== Welcome ==

Hi Plumtree, 
the additions you've already made to the wiki are absolutely helpful, and your current sound experiments look very promising to me. I've been thinking for a while if it wouldn't be good if you left a few words on your user page to give the other active users an idea of your ideas and goals (maybe even your background). At least, I personally would be very interested in that. 
Whatever: thank you! --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 10:25, 14 October 2022 (UTC)

User talk:Xenwolf

2022-10-13T21:06:25Z

Xenwolf: /* Maintenance bot */ re

Naming Rank-2 Scales using Mode Numbers

2022-10-08T10:03:24Z

Xenwolf: skip double redirect

#REDIRECT [[Genchain mode numbering]]

Talk:MicrotonalInstruments

2022-10-08T10:02:40Z

Xenwolf: skip double redirect

#REDIRECT [[Talk:Instruments]]

Microguitar

2022-10-08T10:01:48Z

Xenwolf: skip double redirect

#REDIRECT [[Guitar]]