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BudjarnLambeth

Joined 22 July 2022
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I am a 23 year old man from regional New South Wales, Australia.
This is the user page of '''Budjarn Lambeth''', the wiki contributor and amateur music theorist.


I have a casual interest in xenharmonic/microtonal music. My favourite artists are Brendan Byrnes, Sevish and Greystar. I am nervous, timid, and care a lot about what other people think of me, but I want to be as helpful as I can be.
Not to be confused with ''[[lambeth chords]]'' nor ''[[1573/1568]] (the lambeth comma)''. Those are unrelated to me.


Frontiers have always fascinated me: The unexplored depths of the Earth's ancient history, lost to deep time. The unexplored far reaches of the solar system, the galaxy and the universe. And, the unexplored depths of the infinite pitch spectrum, an infinite expanse, hiding in plain sight between the keys of the piano!
== Personal information ==
* Location: New South Wales, Australia
* Born: 1999
* Pronouns: he/him/his or she/her/hers
* Contactable at: https://www.facebook.com/budjarnlambeth/ or on my [[User talk:BudjarnLambeth|talk page]]
<br><br>


I am prone to making careless mistakes, especially when calculating things with numbers, so apologies in advance for any of those. Please correct them if you see them.
== Music ==
My favourite tracks I have made :)
# [https://m.youtube.com/watch?v=scCuGXnj5IY 33edo track Feb 2024] (bright, lush, mellow and colourful synthwave)
# [https://www.youtube.com/watch?v=_NepcrTf9ng Recording in my "Rocket temperament"] (melancholic, wistful dungeon synth; loosely inspired by [[Greystar]])
# [https://www.youtube.com/watch?v=6N_8QM2UK5I Compressed 8ve 80edo track Aug 2025] (contemporary classical improv on synthesizer)
# [https://www.youtube.com/watch?v=tIwfO1lZWAc 21edo track May 2025] (dark dungeon synth; loosely inspired by Indonesian [[gamelan]] and Japanese music)
# [https://www.youtube.com/watch?v=iZI9x2Fto-A 60afdo track Dec 2024] (bright, spacious, tropical dungeon synth; loosely inspired by Greystar)


=== Music I've made ===
https://www.youtube.com/playlist?list=PLVHnByvMeRTohfmDPkc0EfOByWaX4xXAF


https://budjarnlambeth.bandcamp.com/
YouTube discography:  


=== Contact information ===
https://youtube.com/playlist?list=PLVHnByvMeRTohfmDPkc0EfOByWaX4xXAF
https://www.facebook.com/budjarnlambeth/


=== Families of scales and temperaments ===
This is a personal tool to help me navigate the wiki.           


==== Just intonation scales ====
Bandcamp discography:
* [[Just intonation|Just intonation scales]]
**[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]]
**[[Chord cubes]]
**[[Crystal balls]]
**[[Highschool scales]]
**[[Homothetic just intonation|Homothetic JI scales]]
**[[Tritriadic scale|Tritriadic scales]]
**[[Tonality diamond|Tonality diamonds]]
***[[Breed diamonds]]
***[[Diaconv scales]]
**[[Combination product sets]]
***[[Dekany|Dekanies]]
***[[Eikosany|Eikosanies]]
***[[Hexany|Hexanies]]
***[[Pentadekany|Pentadekanies]]
***[[Pentany|Pentanies]]
**[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]]
***Modes of the [[oddharmonic series]]
***Modes of the [[prime harmonic series]]
***[[Primodality|Primodal scales]]
***[[Neji|NEJI scales]]
***Modes of the [[triangulharmonic series]]


==== Tempered scales ====
https://budjarnlambeth.bandcamp.com/
*[[Temperament|Temperaments]]
**[[Clippers]]
**[[Elves]]
**[[List of essentially tempered scales|Essentially tempered scales]]
**[[Lesfip scales]]
**[[Well temperament|Well temperaments]]
***[[Kartvelian scales]]
**[[Dwarves]]
***[[Especially tempered dwarves]]
***[[Marvelous dwarves]]
**[[Hobbits]]
***[[MOS scale|Moment of symmetry scales]]
****[[MOS Cradle|MOS cradles]]
**[[Regular temperament|Regular temperaments]]
***[[Rank-4 temperament|Rank-4 temperaments]]
****[[Keenanismic temperaments]]
****[[Werckismic temperaments]]
****[[Swetismic temperaments]]
****[[Lehmerismic temperaments]]
****[[Kalismic temperaments]]
*** [[Rank-3 temperament|Rank-3 temperaments]]
**** Families defined by a 2.3.5 comma
*****''see [[Tour of regular temperaments]]''
**** Families defined by a 2.3.7 comma
*****''see [[Tour of regular temperaments]]''
**** Families defined by a 2.3.5.7 comma
*****''see [[Tour of regular temperaments]]''
**** Temperament groups defined by an 11-limit comma
*****''see [[Tour of regular temperaments]]''
*** [[Rank-2 temperament|Rank-2 temperaments]] ([[Map of rank-2 temperaments|map]])
****[[Map of linear temperaments|Linear temperaments]]
****[[Linear temperament|Moment of symmetry scales]]
*****[[MOS Cradle|MOS cradles]]
****Families defined by a 2.3 comma
*****''see [[Tour of regular temperaments]]''
****Families defined by a 2.3.5 comma
*****''see [[Tour of regular temperaments]]''
****Clans defined by a 2.3.7 comma
*****''see [[Tour of regular temperaments]]''
****Clans defined by a 2.3.11 comma
*****''see [[Tour of regular temperaments]]''
****Clans defined by a 2.3.13 comma
*****''see [[Tour of regular temperaments]]''
****Clans defined by a 2.5.7 comma
*****''see [[Tour of regular temperaments]]''
****Clans defined by a 3.5.7 comma
*****''see [[Tour of regular temperaments]]''
****Temperament groups defined by a 2.3.5.7 comma
*****''see [[Tour of regular temperaments]]''
*** [[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]]
****Equal multiplications
*****[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]]
*****[[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]]
****Equal divisions
*****[[EDO|Equal divisions of the octave (EDOs or ED2s)]]
*****[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]]
*****[[Edonoi|Edonois]]
******[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]]
******[[Ed4|Equal divisions of the fourth harmonic (ED4s)]]
******[[Ed5|Equal divisions of the fifth harmonic (ED5s)]]
******[[Ed6|Equal divisions of the sixth harmonic (ED6s)]]
******[[Ed7|Equal divisions of the seventh harmonic (ED7s)]]
******[[Ed8|Equal divisions of the eighth harmonic (ED8s)]]
******[[Ed9|Equal divisions of the ninth harmonic (ED9s)]]
******[[Ed10|Equal divisions of the tenth harmonic (ED10s)]]
******[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]]
******[[:Category:Edonoi|...]]
******[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]]
******[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]]
******[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]]
******[[Ed5/4|Equal divisions of the major third (ED5/4s)]]
******[[:Category:Edonoi|...]]
******[[Ed5/2|Equal divisions of 5/2 (EDXs or ED5/2s)]]
******[[Ed7/2|Equal divisions of 7/2 (ED7/2s)]]
******[[:Category:Edonoi|...]]
******[[Ed7/3|Equal divisions of 7/3 (ED7/3s)]]
******[[Ed8/3|Equal divisions of 8/3 (ED8/3s)]]
******[[Ed10/3|Equal divisions of 10/3 (ED10/3s)]]
******[[:Category:Edonoi|...]]
******[[Ed9/4|Equal divisions of 9/4 (EDIXs or ED9/4s)]]
******[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]]
******[[Edφ|Equal divisions of Phi (Edφs)]]
******[[CET|''n''-cent equal tunings (''n''-cETs)]]
 
==== Fokker blocks ====
 
* [[Fokker block|Fokker blocks]]
**[[Linear temperament|Moment of symmetry scales]]
***[[MOS Cradle|MOS cradles]]
**[[Gallery of wakalixes|Superwakalixes]]
**[[Gallery of wakalixes|Wakalixes]]
***r-wakalixes
****Triple wakalixes
****Quadruple wakalixes
****Pentuple wakalixes
****...
 
==== Metascales ====
* [[Metascales]]
**[[Compound scale|Compound scales]]
** [[Scale products and scale powers]]
** [[MOS Cradle|MOS cradles]]
** [[Muddle|MOS muddles]]
** [[Polymicrotonality|Polysystemic scales / Polymicrotonal scales]]
 
==== Periodic scales ====
* [[Periodic scale|Periodic scales]]
**[[Generator-offset property|Generator-offset scales]]
**[[Maximal harmony epimorphic scales]]
**[[SN scale|Step-nested scales]]
***[[Linear temperament|Moment of symmetry scales]]
****[[MOS Cradle|MOS cradles]]
**[[Harmonotonic tuning|Harmonotonic / step-monotonic tunings]]
***[[Xenharmonic series]]
****[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]]
****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]]
****[[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]]
****[[Powharmonic series]]
****Modes of the [[prime harmonic series]]
****[[Logharmonic series]]
****Modes of the [[metallic harmonic series]]
****Modes of the [[oddharmonic series]]
****[[Powharmonic series|Subpowharmonic series]]
****[[Logharmonic series|Sublogharmonic series]]
****Modes of the [[triangulharmonic series]]
***Non-arithmetic harmonotonic tunings
****[[Powharmonic series]]
****[[Logharmonic series]]
****[[Powharmonic series|Subpowharmonic series]]
****[[Logharmonic series|Sublogharmonic series]]
***[[Arithmetic tuning|Arithmetic tunings]]
****Equal length step tunings
*****[[Subharmonic series|Aliquot scales (modes of the subharmonic series)]] / [[EDL|EDLs]]
****Equal frequency step tunings
*****[[Overtone scale|Overtone scales (modes of the harmonic series)]] / [[AFDO|AFDOs]]
******Modes of the [[oddharmonic series]]
******Modes of the [[prime harmonic series]]
******[[Primodality|Primodal scales]]
******[[Neji|NEJI scales]]
******Modes of the [[triangulharmonic series]]
****Equal pitch step tunings
*****[[Equal-step tuning|Rank-1 temperaments / Equal-step tunings]]
******Equal multiplications
*******[[Ambitonal sequence|Ambitonal sequences (AS) / Equal multiplications of a rational interval]]
*******[[Arithmetic pitch sequence|Arithmetic pitch sequences (APS) / Equal multiplications of an irrational interval]]
******Equal divisions
*******[[EDO|Equal divisions of the octave (EDOs or ED2s)]]
*******[[The Riemann zeta function and tuning|Zeta-stretched equal divisions]]
*******[[Edonoi|Edonois]]
********[[EDT|Equal divisions of the third harmonic (EDTs or ED3s)]]
********[[Ed4|Equal divisions of the fourth harmonic (ED4s)]]
********[[Ed5|Equal divisions of the fifth harmonic (ED5s)]]
********[[Ed6|Equal divisions of the sixth harmonic (ED6s)]]
********[[Ed7|Equal divisions of the seventh harmonic (ED7s)]]
********[[Ed8|Equal divisions of the eighth harmonic (ED8s)]]
********[[Ed9|Equal divisions of the ninth harmonic (ED9s)]]
********[[Ed10|Equal divisions of the tenth harmonic (ED10s)]]
********[[Ed11|Equal divisions of the eleventh harmonic (ED11s)]]
********[[:Category:Edonoi|...]]
********[[Ed3/2|Equal divisions of the perfect fifth (EDFs or ED3/2s)]]
********[[Ed4/3|Equal divisions of the perfect fourth (ED4/3s)]]
********[[Ed5/3|Equal divisions of the major sixth (ED5/3s)]]
********[[Ed5/4|Equal divisions of the major third (ED5/4s)]]
********[[:Category:Edonoi|...]]
********[[Ed5/2|Equal divisions of 5/2 (EDXs or ED5/2s)]]
********[[Ed7/2|Equal divisions of 7/2 (ED7/2s)]]
********[[:Category:Edonoi|...]]
********[[Ed7/3|Equal divisions of 7/3 (ED7/3s)]]
********[[Ed8/3|Equal divisions of 8/3 (ED8/3s)]]
********[[Ed10/3|Equal divisions of 10/3 (ED10/3s)]]
********[[:Category:Edonoi|...]]
********[[Ed9/4|Equal divisions of 9/4 (EDIXs or ED9/4s)]]
********[[Ed11/5|Equal divisions of 11/5 (ED11/5s)]]
********[[Edφ|Equal divisions of Phi (Edφs)]]
********[[CET|Cent equal temperaments (cETs)]]
 
==== Miscellaneous scale structures ====
*[[Cartesian scale|Cartesian scales]]
*[[Euler-Fokker genus|Euler-Fokker genera]]
*[[Omniconsonant scale|Omniconsonant scales]]
*[[Yantras]]
 
=== My favourite scales ===
==== [[5- to 8-tone scales from the modes of the harmonic series|Overtone scales]]====
Dozenal Cliffedge
 
14/12
 
16/12
 
18/12
 
23/12
 
24/12
 
Dozenal Dungeon
 
15/12
 
16/12
 
18/12
 
19/12
 
24/12
 
Dozenal Freeway
 
14/12
 
16/12
 
18/12
 
20/12
 
22/12
 
24/12
 
Dozenal Geode
 
14/12
 
16/12
 
18/12
 
22/12
 
24/12
 
Spectral Mechanical
 
19/16
 
20/16
 
24/16
 
28/16
 
32/16
 
Spectral Mirage
 
18/16
 
21/16
 
24/16
 
25/16
 
30/16
 
32/16
 
Spectral Moonbeam


18/16


19/16
''Most tracks on Bandcamp have not yet been uploaded to YouTube and vice versa.''
<br><br><br><br>


24/16
==My favourite microtonal composers==
*'''[[Brendan Byrnes]]'''
*[[Greystar]]
*[[JUMBLE]]
*[[Benyamind]]
*[[Sevish]]
<br><br><br>


30/16
==Wiki contributions==
===Discoveries===
====Invented approaches to constructing tunings ====
These are the same category of thing as “equal temperaments”.


32/16
''Procedural approaches'':
* [[Basal subgroup]]s
* [[Half-prime subgroup|Half-basis, third-basis, quarter-basis, etc. subgroups]]
* [[Equalizer subgroup]]s
* [[Sin(x) tuning#Generalizations|Function(x) tuning]]s
* [[Polytriadic]] tunings
* [[Substitute harmonic]]s
* [[Tritavesque]] intervals
* [[Sin(x) tuning#Generalizations|Waveform(x) tuning]]s
* [[Ed255/128|Equal divisions of 255/128]]
* [[Ed257/128|Equal divisions of 257/128]]


Spectral Springwater
''Sculptural approaches'':
* [[Breuddwyd scale]]s
* [[Breuddwyd scale|Sonhar tuning]]s
* [[Sooty fox scale]]s
* [[Breuddwyd scale|Wijzerplaat scale⁠]]s
* [[Gallery of arithmetic pitch sequences|APS#farab scales]]
* [[Gallery of arithmetic pitch sequences|APS#gene scales]]
* [[Gallery of arithmetic pitch sequences|APS#hekt scales]]
* [[Gallery of arithmetic pitch sequences|APS#jot scales]]
* [[Gallery of arithmetic pitch sequences|APS#méride scales]]
* [[Gallery of arithmetic pitch sequences|APS#tina scales]]


18/16
====Invented approaches to classifying tunings ====
These are the same category of thing as “pentatonic scales”.
* [[the Riemann zeta function and tuning#Non-record edos|Anti-zeta EDOs]]
* [[the Riemann zeta function and tuning#Non-record edos|Indecisive EDOs]]
* [[the Riemann zeta function and tuning#Non-record edos|Local zeta EDOs]]
* [[the Riemann zeta function and tuning#''k''-ary peak EDOs|Parker EDOs]]
* [[Human EDO size categorization]] (HUECAT)
* [[Metascale]]s
* [[Runoff]] scales
* [[Structural beating]]


20/16
====Invented tunings (scales)====
These are the same category of thing as “the chromatic scale”.
* The [[Shoal17#Scales|algal bloom]] scale
* The [[25edo#Scales|amulet]] scale
* The [[anisopteran scale]]
* The [[antipental blues]] scale
* The [[14afdo#Scales|apex]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|apple mint]] scale
* The [[Gallery of arithmetic pitch sequences#APS of tinas|Argentina]] scale
* The [[30edo#Scales|bathypelagic]] scale
* The [[breuddwyd inverse]] scale
* The [[breuddwyd6|breuddwyd-6]] scale
* The [[blackened skies]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|bubblegum]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|candycorn]] scale
* The [[30edo#Scales|carousel]] scale
* The [[9edf#Scales|cloudscape]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|cola]] scale
* The [[9edf#Scales|corrugated]] scale
* The [[32afdo#Scales|cosmic]] scale
* The [[dalmatian scale]]
** The Dante, Da Vinci, Dawkins, Deepak, Deja Vu, Delgado, Dolly, Dylan, Fergus & Hansel [[101afdo#Scales|scales]]
* The [[30edo#Scales|dewdrops]] scale
* The [[Shoal17#Scales|diffractive scale]]
* The [[Shoal17#Scales|diffractive tetrad]]
* The [[27edo#Scales|direct sunlight]] scale
* The [[Shoal17#Scales|driftwood]] scale
* The [[Peppermint-24#Salt and pepper scale and its subsets|evacuated planet]] scale
* The [[firedance]] scale
* The [[5- to 10-tone scales in 60edo|fossa tetratonic]] scale
* The [[5- to 10-tone scales in 60edo|fossa pentatonic]] scale
* The [[56edo#Scales|frankincense]] scale
* The [[goldfish]] scale
* The [[27edo#Scales|hypersakura]] scale
* The [[Peppermint-24#Ketchup and mustard scale and its subsets|ketchup and mustard]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|lemonade]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|liquorice]] scale
* The [[9edf#Scales|livewire]] scale
* The [[lost spirit]] scale
* The [[magnetosphere scale]]
* The [[16afdo#Scales|mechanical]] scale
* The [[9edf#Scales|molten pelog]] scale
* The [[9edf#Scales|molten slendro]] scale
* The [[5- to 10-tone scales in 47zpi|monsoon]] scale
* The [[16afdo#Scales|moonbeam]] scale
* The [[30edo#Scales|nightdrive]] scale
* The [[oclock]] scale
* The [[User:BudjarnLambeth/Over the Hedge|Over the Hedge]] scale
** The H.ammy, H.eather, O.zzie, R.J, S.tella, T.iger & V.erne [[User:BudjarnLambeth/Over the Hedge|scales]]
* The [[29edo#Scales|palace]] scale
* The [[30edo#Scales|pelagic]] scale
* The [[Peppermint-24#Salt_and_pepper_scale_and_its_subsets|pepperbass]] scale
* The [[9edf#Scales|purgatory]] scale
* The [[9edf#Scales|pylon]] scale
* The [[47edo#Scales|quasi-equiheptatonic minor pentatonic]] scale
* The [[9edf#Scales|quest]] scale
* The [[Shoal17#Scales|refractive scale]]
* The [[Shoal17#Scales|refractive tetrad]]
* The [[5- to 10-tone scales in 47zpi|rockpool]] scale
* The [[47edo#Scales|sabertooth hexatonic]] scale
* The [[47edo#Scales|sabertooth neutral]] scale
* The [[47edo#Scales|sabertooth pentatonic]] scale
* The [[Peppermint-24#Salt and pepper scale and its subsets|salt and pepper]] scale
* The [[Shoal17#Scales|shoal17 over-9 tetrad]]
* The [[breuddwyd6|snow braid]] scale
* The [[9edf#Scales|snowcone]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|sourgummy]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|spearmint]] scale
* The [[spectral blues]] scale
* The [[9edf#Scales|swan]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|trailmix]] scale
* The [[Batch 89 temperaments#Example inflected MOS scale: UFO scale|UFO scale]]
* The [[breuddwyd inverse|vinyl braid]] scale
* The [[16afdo#Scales|volcanic]] scale
* The [[5- to 10-tone scales from the modes of the harmonic series#Macrotonal NEJI edos|whitechocolate]] scale
* The [[26ed5#13ed5plus|13ed5plus]] scale
* The [[80edo#Scales|16-tone 5&16edo scale]]
* The [[80edo#Scales|12-tone 5&16edo scale]]
* The [[80edo#Scales|14-tone 8&10edo scale]]
* The [[80edo#Scales|12-tone 8&10edo scale]]
* The [[80edo#Scales|14-tone 8&20edo scale]]
* The [[80edo#Scales|12-tone 8&20edo scale]]
* [[1ed148.5c|APS148.5¢]]
* [[1ed237.8c|APS237.8¢]]
* [[Gallery of arithmetic pitch sequences#APS of farabs|APS3.21farab]]
* [[Gallery of arithmetic pitch sequences#APS of hekts|APS7hekt]]
* [[1ed28.5c|APS715jot]]
* [[1ed28.7c|APS720jot]]
* [[Gallery of arithmetic pitch sequences#APS of mérides|APS4/5méride]]
* [[Gallery of arithmetic pitch sequences#APS of mérides|APS5/8méride]]
* [[Gallery of arithmetic pitch sequences#APS of mérides|APS7/12méride]]
* [[Gallery of arithmetic pitch sequences#APS of tinas|APS70tina]]


24/16
====Invented tunings (regular temperaments)====
These are the same category of thing as “quarter-comma meantone temperament”.
* [[7921/7776|Attic]] temperament
* [[979/972|Basement]] temperament
* [[Subgroup temperaments#Blacktetra|Blacktetra]] temperament
* [[1000/979|Canine]] temperament
* [[Substitute harmonic#Daggerminished|Daggerminished]] temperament
* [[Substitute harmonic#Narrowed compton|Dotcom]] temperament
* [[Vavoom family|Doubloon]] temperaments
* [[Meantone family#Dreamtone|Dreamtone]] temperament
* [[Equalizer subgroup|Ectophotia]] temperament
* [[Equalizer subgroup|Fifigeist]] temperament
* [[Batch 89 temperaments#Floor|Floor]] temperament
* [[No-twos subgroup temperaments#Fomalhaut|Fomalhaut]] temperament
* [[Subgroup temperaments#Fourwar|Fourwar]] temperament
* [[Substitute harmonic#Narrowed compton|Glycome]] temperament
* [[No-sevens subgroup temperaments#Hypnotone|Hypnotone]] temperament
* [[8000/7921|Incisor]] temperament
* [[Substitute harmonic#Narrowed compton|Income]] temperament
* [[Substitute harmonic#Narrowed compton|Intercom]] temperament
* [[Vavoom family|Kaboom]] temperament
* [[Equalizer subgroup|Lieerie]] temperament
* [[Lightyear comma|Lightyear]] temperament
* [[2883/2848|Lilac]] temperament
* [[8277/8192|Lilly pilly]] temperament
* [[7936/7921|Lily]] temperament
* [[No-fives subgroup temperaments#Lipsett|Lipsett]] temperament
* [[Batch 89 temperaments#Lylla|Lylla]] temperament
* [[Substitute harmonic#Narrowed compton|Minicom]] temperament
* [[Molar comma|Molar]] temperament
* [[Substitute harmonic#Narrowed compton|Newcome]] temperament
* [[Nimona]] temperament
* [[Substitute harmonic#Narrowed compton|Outcome]] temperament
* [[729/712|Oxidizer]] temperament
* [[Substitute harmonic#Pajaraxe|Pajaraxe]] temperament
* [[Equalizer subgroup|Phantadecimal]] temperament
* [[Equalizer subgroup|Phantasrutal]] temperament
* [[Equalizer subgroup|Poltercompton]] temperament
* [[Batch 89 temperaments#Rocket|Rocket]] temperament
* [[Substitute harmonic#Narrowed compton|Romcom]] temperament
* [[Substitute harmonic#Sahara|Sahara]] temperament
* [[Substitute harmonic#Narrowed compton|Satcom]] temperament
* [[Equalizer subgroup|Semihaunt]] temperament
* [[Equalizer subgroup|Shadecimal]] temperament
* [[Equalizer subgroup|Shrutarnatural]] temperament
* [[Substitute harmonic#Narrowed compton|Sitcom]] temperament
* [[Subgroup temperaments#Sixscared|Sixscared]] temperament
* [[Equalizer subgroup|Spectrephore]] temperament
* [[89/88|Tailwind]] temperament
* [[Batch 89 temperaments#Teefs|Teefs]] temperament
* [[Substitute harmonic#Narrowed compton|Telecom]] temperament
* [[Subgroup temperaments#Tetramagic|Tetramagic]] temperament
* [[Vavoom family#Vacuum|Vacuum]] temperament
* [[Vavoom family#Void|Void]] temperament
* [[Vavoom family#Vortex|Vortex]] temperament
* [[Equalizer subgroup|Werecatler]] temperament
<br><br>


28/16
===Improvements===
====Significant page creations====
* Authored the [[survey of efficient temperaments by subgroup]] to help people navigate quickly to their favourite temperament pages
* Authored the [[Gallery of arithmetic pitch sequences]] & [[Gallery of combination product sets]] pages to help people find musical [[scale]]s
* Authored the pages about [[equipentatonic]] and [[equiheptatonic]] scales
* Created the [[Xenharmonic Wiki:Cross-platform dialogue]] page to aid collaboration between editors who are mostly active on Facebook and those who are mostly active on Discord
* Authored pages answering the [[FAQ]] questions:
** “[[What are this wiki's strengths and weaknesses?]] (How does it compare to other resources?)”
** “[[I'm a new editor, what is everything I can do to help?]]”
** “[[Systematic comma names explained|How do I decode those strange looking comma names?]]”
* Authored dozens of wanted pages about [[:Category:Composers|composers]]
* Authored several extensive [[:Category:Lists of scales|lists of scales]]


32/16
====Bulk page improvements====
* Constructed the 5-, 6-, 7-, 8-, 9-, 10-, 11- and 12-period tables on the [[map of rank-2 temperaments]]
* Heavily added to the 2-, 3- and 4-period tables on the [[map of rank-2 temperaments]]
* Added dozens of sources and inline citations to the [[historical temperaments]] page
* Added [[Template:Temp gallery]] to all '[[User:BudjarnLambeth/Prominent temperament gallery pages|very highly prominent temperament gallery pages]]'
* Added [[Template:Temp gallery]] to all '[[User:BudjarnLambeth/Prominent temperament gallery pages|highly prominent temperament gallery pages]]'
* Added [[Template:Temp gallery]] to all '[[User:BudjarnLambeth/Prominent temperament gallery pages|moderately prominent temperament gallery pages]]'
* Added [[Template:Temp gallery]] to all '[[User:BudjarnLambeth/Prominent temperament gallery pages|less prominent temperament]] families and clans'
* Merged “useful tools” & “software” into [[Software|one unified page]]
* Added infobox, intro, intervals, modes, subheadings & todo categories to dozens of previously close-to-empty [[MOS scale]] pages
* Added intro, intervals table and harmonics table to several hundred [[equal-step tuning]] pages (which used to just be blank pages with a single infobox)


Spectral Volcanic
====Structural wiki improvements====
* Added categories & formatting tags to several hundred [[:Category:Pages with Scala files|pages with Scala files]]
* Added links around the wiki to over 150 previously [[Special:LonelyPages|orphaned pages]], bringing the number down from above 250 to below 70 (as of 4 Dec 2024)
* Created [[Template:Navbox Lumatone]] with very extensive help from [[User:ArrowHead294]]
** With ArrowHead294’s extensive help, incorporated the template into over 50 pages for [[:Category:Lumatone mappings]]
* Ran a survey of editors, created the [[Xenharmonic Wiki:Optional guidelines for interval page todo categories]] (XW:IntTodo) from the results, and ensured all interval pages were categorized in line with XW:IntTodo


17/16
===== • List and table creations=====
Constructed:
* [[List of taxicab-2 intervals]]
* [[User:BudjarnLambeth/Table of n-comma meantone generators]]
* [[Harmonic entropy of just intervals]]
* [[Table of zeta-stretched edos]]


20/16
===== • Comma documentation and organisation=====
* Added all missing commas from “[[:Category:Large commas]]” to the table on the page “[[Large commas]]”
* Added all missing commas from “[[:Category:Medium commas]]” to the table on the page “[[Medium commas]]”
* Added all missing commas from “[[:Category:Small commas]]” to the table on the page “[[Small comma]]”
* Added all missing commas from “[[:Category:Unnoticeable commas]]” to the table on the page “[[Unnoticeable commas]]”
* Constructed “[[:Category:Commas by name]]” and its many subcategories
* Categorised all 5, 7, 11, 13, 17, 19, 23 and >23 limit large commas into ’Commas by name’ subcategories
* Categorised all 5, 7, 11, 13, 17, 19, 23 and >23 limit medium commas into ’Commas by name’ subcategories
* Categorised all 5, 7, 11, 13, 17, 19, 23 and >23 limit small commas into ’Commas by name’ subcategories
* Categorised all 5, 7, 11, 13, 17, 19, 23 and >23 limit unnoticeable commas into ’Commas by name’ subcategories
* Conducted the [[User:BudjarnLambeth/Survey of named and unnamed commas]]


24/16
====Name changes I was involved in====
* There was an old temperament that pre-dated my participation in the wiki. Its old, original name was “septimal temperament”. When I discovered the name, I disliked it because of its potential for confusion with other uses of the term “septimal”. I decided I wanted to change it. Many people on [[Discord]], the Wiki Workgroup on [[XA Facebook]], and the wiki talk page agreed. I coined the new name “'''[[7th-octave temperaments#Austinpowers|austinpowers temperament]]'''” which has now replaced it.
* There was an old temperament that pre-dated my participation in the wiki. Its old, original name was “catcall temperament”. When I discovered the name, I disliked it because it was demeaning to women. I decided I wanted to change it. Many people on [[Discord]] and on the wiki talk page agreed. I coined the new name “'''[[catnip|catnip temperament]]'''” which has now replaced it.
* There was an old temperament that pre-dated my participation in the wiki. Its old, original name was “decades temperament”. Some people on the XA Discord said that they disliked it due to its convoluted etymology. I coined the new name “'''[[gamelstearn|gamelstearn temperament]]'''” based on its two defining commas. After a few days, not many people commented or reacted to the proposal, but all were in favour and none were against, so the name "gamelstearn" was adopted.
* There was an old comma that pre-dated my participation in the wiki. Its old, original name was “the Buddhisma”. There was nothing wrong with that name in and of itself, the problem is that it was explicitly stated to be named after the sectarian group the 969 Movement, and the comma number was 969/968. I thought this was inappropriate, so I proposed a few replacement names on [[Discord]]. Of the names I coined “'''[[969/968|the kingfisher comma]]'''” was the clear favourite, so I renamed the comma to the kingfisher comma.
* There used to be two temperaments named “semidim temperament”. To resolve the confusion, after discussion on the XA Discord, myself and [[Lériendil]] came up with new names for each of the two temperaments. Lériendil coined “[[ammon|ammon temperament]]” for the first, and I coined “'''[[octonion|octonion temperament]]'''” for the second.
* There was an old comma that pre-dated my participation in the wiki. Its old, original name was “the erogluisma”. Its original namer posted on [[Discord]] that he no longer liked it, and would like someone to please rename it. I coined the new name “'''[[1682/1681|the shaftesburisma]]'''” which has now replaced it.
* Someone else described a new comma and named it “the shikanokonokonokokoshitantanma”. This name was kept, but it was too long for some use cases, so I invented an alternate short version - “'''[[nokotan|the nokotan]]'''” - for use cases where a shorter name is needed.
* The comma “68630377364883 / 68630356164608” was too long to be referred to by its number alone, it needed a name instead. So I named it “'''[[zudilisma|the zudilisma]]'''”.
<br><br>


28/16
=== Full list of contributions ===
* [[Special:Contributions/BudjarnLambeth]]
<br><br>


32/16
=== (To-do) ===
Things I [[Wikifuture|plan to do]] on the wiki in the near future. Feel free to go ahead and do these any of these things first if you’re interested in doing so. I feel overwhelmed by the sheer amount of things I want to do and am very happy for any help I receive getting through it all :)


Subharm Starship
==== Structural wiki improvements ====
* Make “Undertone scales” page that exists in mutually supportive conversation with “[[IFDO]]” in a similar way how “[[Overtone scale]]” does with “[[AFDO]]”
* Add “[[:Category:Temperaments]]” to all temperament [[special:ListRedirects|redirects]]


42/40
==== Construct diagrams or lists ====
* For every temperament on the page [[Survey of efficient temperaments by subgroup]], generate a [[Scala]] file of whichever of its MOS scales is closest to (2 x its [[graham complexity]]). List all the Scala files in a wiki page along the lines of “Scala files for efficient subgroup temperaments” or something like that and link it from the Survey page
* Make all the wanted tables listed in [[:Category:Todo:add rank 2 temperaments table]]
* Make manual, curated tables of [[interval]]s for:<small>
** [[8ed5/4]] to 9ed5/4
** [[4ed4/3]] to 8ed4/3
** [[4ed5/3]] to 6ed5/3
** [[11ed5/3]]
** [[5ed7/4]] to 12ed7/4
** [[5ed9/5]] to 7ed9/5
** [[9ed11/5]]
** [[11ed9/4]]
** [[5ed7/3]]
** [[8ed7/3]]
** [[5ed5/2]] to 6ed5/2
** [[8ed5/2]]
** [[12edt]]
** [[3ed4]] to 6ed4
** [[8ed4]] to 15ed4
** [[3ed5]] to 5ed5
** [[4ed6]]</small>
* Make all the wanted mappings listed in [[:Category:Todo:add lumatone mapping]]
* Construct a table of the sharpness or flatness of every prime harmonic in every edo up to 53.
** Each edo will be a row, and the columns will be from -60%, -55%, -50%… -5%, 0, +5%… +50%, +55%, +60%. And I will list each prime in whichever bin it is closest too (so if prime 7/1 had +23.9% error in Nedo, it goes in column +25% in that edo’s row).
** Make a separate absolute error table in cents for EDOs 1 to 30, and relative error table for all EDOs 1 to 53 with the possibility of expanding both to higher edos later.
* Construct a version of an “[[odd limit]]” but for each “[[equalizer subgroup]]” and document them on the equalizer subgroup page
* Construct a [[tonality diamond]] or something like one for each “[[equalizer subgroup]]” and document them on the equalizer subgroup page


42/34
==== Improve pages I made ====
* On my page [[5- to 10-tone scales in 60edo]], change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format
* On my page [[5- to 10-tone scales in 72edo]], change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format
* On my page [[5- to 10-tone scales in 84edo]], change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format
* On my page [[5- to 10-tone scales in 91edo]], change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format
* On my page [[5- to 10-tone scales in 96edo]], change the scales to be in the more compact format that is used on edo pages instead of a ‘Scala-like’ format


42/32
==== Explore, discover, document ====
 
* Find nice 5 to 7 tone subsets of [[Shaka10]], [[Starling12]], [[Thrush12]] and document them under a “subsets” heading on those scales’ pages
42/28
* Find more unique scales in [[Catnip]][36] in [[60edo]] that can’t be replicated in [[Compton]][36] and document them on [[5- to 10-tone scales in 60edo]]
 
* Find 4 to 7 tone subsets for every 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 or 19-tone scale page
42/24
 
42/21
====[[5- to 8-tone scales in zeta stretched 15edo|15edo]]====
Atoll
 
79.716
 
398.578
 
478.294
 
717.441
 
956.588
 
1195.735
 
Augmented
 
318.863
 
398.578
 
717.441
 
797.157
 
1116.020
 
1195.735
 
Equipentatonic
 
239.147
 
478.294
 
717.441
 
956.5881
 
1195.735
 
Firedance
 
239.147
 
558.010
 
717.441
 
956.588
 
1195.735
 
Monsoon
 
239.147
 
478.294
 
717.441
 
1036.304
 
1195.735
 
Rainbow
 
398.578
 
558.010
 
717.441
 
876.872
 
1036.304
 
1195.735
 
Rockpool
 
398.578
 
478.294
 
717.441
 
956.588
 
1195.735
====[[21edo]]====
Pelog Lima
 
114.28571428571429
 
285.7142857142857
 
685.7142857142858
 
800.


==== Approximate x in y ====
* Approximate the following scales in modes 34 to 101 of the harmonic series and document the results in “[[5- to 10-tone scales from the modes of the harmonic series]]”:
<pre>
Tobago6
101.53846
350.76923
600.
701.53846
950.76923
1200.
1200.
====[[22edo modes|22edo]]====
Manohari
272.72727272727275
490.90909090909093
709.0909090909091
927.2727272727273


981.8181818181819
Zeus1
157.57576
387.87879
545.45455
703.03030
1042.42424
2/1


Oceanfront5
227.82
486.09
713.91
972.18
1200.
1200.


Shailaja
Oceanfront Ionian Pent.
 
455.64
272.72727272727275
486.09
 
713.91
709.0909090909091
1169.55
 
763.6363636363636
 
981.8181818181819
 
1200.
1200.


Subminor Hexatonic
Oceanfront Minor Harmonic Pent.
 
258.27
218.1818181818182
486.09
 
713.91
272.72727272727275
1169.55
 
490.90909090909093
 
709.0909090909091
 
981.8181818181819
 
1200.
1200.


Subminor Pentatonic
Oceanfront Mixolydian Pent.
 
455.64
272.72727272727275
486.09
 
713.91
490.90909090909093
972.18
 
709.0909090909091
 
981.8181818181819
 
1200.
1200.
====[[5- to 8-tone scales in 43edo|43edo]]====
Blues Aeolian Hexatonic
306.9767441860465
502.3255813953488
613.953488372093
697.6744186046511
809.3023255813954
1200.
Blues Aeolian Pentatonic I
306.9767441860465
502.3255813953488
697.6744186046511
809.3023255813954


Oceanfront Adrift Pent.
197.37
258.27
683.46
713.91
1200.
1200.
</pre>


Blues Aeolian Pentatonic II
* Approximate the following scales in modes 102 to 200 of the harmonic series and document the results in “[[5- to 10-tone scales from the modes of the harmonic series]]”:
<pre>
5edo
1\5
2\5
3\5
4\5
5\5


306.9767441860465
6edo
1\6
2\6
3\6
4\6
5\6
6\6


697.6744186046511
7edo
 
1\7
809.3023255813954
2\7
 
3\7
1004.6511627906976
4\7
5\7
6\7


Slendric6
233.68421
467.36842
701.05263
934.73684
966.31579
1200.
1200.


Blues Bright Double Harmonic
Tobago6
 
101.53846
111.62790697674419
350.76923
 
600.
390.69767441860466
701.53846
 
950.76923
502.3255813953488
 
697.6744186046511
 
809.3023255813954
 
1004.6511627906976
 
1088.3720930232557
 
1200.
 
Blues Dark Double Harmonic
 
195.34883720930233
 
306.9767441860465
 
502.3255813953488
 
613.953488372093
 
697.6744186046511
 
809.3023255813954
 
1088.3720930232557
 
1200.
1200.


Blues Dorian Hexatonic
Zeus1
 
157.57576
306.9767441860465
387.87879
 
545.45455
502.3255813953488
703.03030
 
1042.42424
697.6744186046511
 
893.0232558139535
 
1004.6511627906976
 
1200.
1200.


Blues Dorian Pentatonic
Oceanfront5
 
227.82
306.9767441860465
486.09
 
713.91
697.6744186046511
972.18
 
893.0232558139535
 
1004.6511627906976
 
1200.
1200.


Blues Dorian Septatonic
Oceanfront Ionian Pent.
 
455.64
306.9767441860465
486.09
 
713.91
502.3255813953488
1169.55
 
613.953488372093
 
697.6744186046511
 
893.0232558139535
 
1004.6511627906976
 
1200.
1200.


Blues Harmonic Hexatonic
Oceanfront Minor Harmonic Pent.
 
258.27
195.34883720930233
486.09
 
713.91
306.9767441860465
1169.55
 
502.3255813953488
 
697.6744186046511
 
1088.3720930232557
 
1200.
1200.


Blues Harmonic Septatonic
Oceanfront Mixolydian Pent.
 
455.64
306.9767441860465
486.09
 
713.91
502.3255813953488
972.18
 
613.953488372093
 
697.6744186046511
 
809.3023255813954
 
1088.3720930232557
 
1200.
1200.


Blues Leading
Oceanfront Adrift Pent.
 
197.37
306.9767441860465
258.27
 
683.46
502.3255813953488
713.91
 
613.953488372093
 
697.6744186046511
 
1004.6511627906976
 
1088.3720930232557
 
1200.
1200.
</pre>


Blues Minor
* Approximate the following scales in BOTH prime modes 75-100 of the harmonic series AND sqfr semiprm modes 75-100 and document the results in “[[5- to 10-tone scales from the modes of the harmonic series]]”:
 
<pre>
306.9767441860465
Antipental Blues
 
7/6
502.3255813953488
4/3
 
11/8
613.953488372093
3/2
 
7/4
697.6744186046511
2/1
 
1004.6511627906976
 
1200.
 
Blues Minor Maj7
 
306.9767441860465
 
502.3255813953488
 
613.953488372093
 
697.6744186046511
 
1088.3720930232557
 
1200.
 
Blues Pentachordal
 
195.34883720930233
 
306.9767441860465
 
502.3255813953488
 
613.953488372093
 
697.6744186046511
 
1200.
 
Dominant Pentatonic
 
195.34883720930233
 
390.69767441860466
 
697.6744186046511
 
1004.6511627906976
 
1200.
 
Dorian
 
195.34883720930233
 
306.9767441860465
 
502.3255813953488
 
697.6744186046511
 
893.0232558139535
 
1004.6511627906976
 
1200.
 
Double Harmonic
 
111.62790697674419
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
809.3023255813954
 
1088.3720930232557
 
1200.
 
Hirajoshi
 
195.34883720930233
 
306.9767441860465
 
697.6744186046511
 
809.3023255813954
 
1200.
 
Ionian Pentatonic
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
1088.3720930232557
 
1200.
 
Javanese Pentachordal
 
111.62790697674419
 
306.9767441860465
 
613.953488372093
 
697.6744186046511
 
1200.
 
Kokin-Joshi
 
195.34883720930233
 
306.9767441860465
 
697.6744186046511
 
893.0232558139535
 
1200.
 
Locrian
 
111.62790697674419
 
306.9767441860465
 
502.3255813953488
 
613.953488372093
 
809.3023255813954
 
1004.6511627906976
 
1200.
 
Lydian
 
195.34883720930233
 
390.69767441860466
 
613.953488372093
 
697.6744186046511
 
893.0232558139535
 
1088.3720930232557
 
1200.
 
Major
 
195.34883720930233
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
893.0232558139535
 
1088.3720930232557
 
1200.
 
Major Pentatonic
 
195.34883720930233
 
390.69767441860466
 
697.6744186046511
 
893.0232558139535
 
1200.
 
Minor
 
195.34883720930233
 
306.9767441860465
 
502.3255813953488
 
697.6744186046511
 
809.3023255813954
 
1004.6511627906976
 
1200.
 
Minor Harmonic
 
195.34883720930233
 
306.9767441860465
 
502.3255813953488
 
697.6744186046511
 
809.3023255813954
 
1088.3720930232557
 
1200.
 
Minor Harmonic Pentatonic
 
195.34883720930233
 
306.9767441860465
 
697.6744186046511
 
1088.3720930232557
 
1200.
 
Minor Hexatonic
 
195.34883720930233
 
306.9767441860465
 
502.3255813953488
 
697.6744186046511
 
1004.6511627906976
 
1200.
 
Minor Melodic
 
195.34883720930233
 
306.9767441860465
 
502.3255813953488
 
697.6744186046511
 
893.0232558139535
 
1088.3720930232557
 
1200.
 
Minor Pentatonic
 
306.9767441860465
 
502.3255813953488
 
697.6744186046511
 
1004.6511627906976
 
1200.
 
Mixolydian
 
195.34883720930233
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
893.0232558139535
 
1004.6511627906976
 
1200.
 
Mixolydian Harmonic
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
809.3023255813954
 
1004.6511627906976
 
1200.
 
Mixolydian Pentatonic
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
1004.6511627906976
 
1200.
 
Phrygian
 
111.62790697674419
 
306.9767441860465
 
502.3255813953488
 
697.6744186046511
 
809.3023255813954
 
1004.6511627906976
 
1200.
 
Phrygian Dominant
 
111.62790697674419
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
809.3023255813954
 
1004.6511627906976
 
1200.
 
Phrygian Dominant Hexatonic
 
111.62790697674419
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
1004.6511627906976
 
1200.
 
Phrygian Dominant Pentatonic
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
809.3023255813954
 
1200.
 
Phrygian Pentatonic
 
111.62790697674419
 
306.9767441860465
 
697.6744186046511
 
809.3023255813954
 
1200.
 
Picardy Hexatonic
 
195.34883720930233
 
390.69767441860466
 
502.3255813953488
 
697.6744186046511
 
809.3023255813954
 
1200.
 
Picardy Pentatonic
 
195.34883720930233
 
390.69767441860466
 
697.6744186046511
 
809.3023255813954
 
1200.
====[[5- to 8-tone scales in 53edo|53edo]]====
Dozenal Blues
 
271.6981132075472
 
498.1132075471698
 
611.3207547169811
 
701.8867924528302
 
1200.
 
Dozenal Cliffedge
 
271.6981132075472
 
498.1132075471698
 
701.8867924528302
 
1132.0754716981132
 
1200.
 
Dozenal Dungeon
 
384.90566037735846
 
498.1132075471698
 
701.8867924528302
 
792.4528301886792
 
1200.
 
Dozenal Geode
 
271.6981132075472
 
498.1132075471698
 
701.8867924528302
 
1041.509433962264
 
1200.
 
Spectral Arcade
 
384.90566037735846
 
475.47169811320754
 
701.8867924528302
 
973.5849056603773
 
1200.
 
Spectral Mechanical
 
294.33962264150944
 
384.90566037735846
 
701.8867924528302
 
973.5849056603773
 
1200.
 
Spectral Moonbeam
 
203.77358490566036
 
294.33962264150944
 
701.8867924528302
 
1086.7924528301887
 
1200.
 
Spectral Springwater
 
203.77358490566036
 
384.90566037735846
 
701.8867924528302
 
973.5849056603773
 
1200.
 
Spectral Starship
 
90.56603773584905
 
384.90566037735846
 
475.47169811320754
 
701.8867924528302
 
973.5849056603773
 
1200.
 
Spectral Volcanic
 
113.2075471698113
 
384.90566037735846
 
701.8867924528302
 
973.5849056603773
 
1200.
====[[Dalmatian scale]]====
Blues Aeolian Hexatonic
 
120/101
 
135/101
 
143/101
 
151/101
 
160/101
 
202/101
 
Blues Aeolian Pentatonic I
 
120/101
 
135/101
 
151/101
 
160/101
 
202/101
 
Blues Aeolian Pentatonic II
 
120/101
 
151/101
 
160/101
 
180/101
 
202/101
 
Blues Bright Double Harmonic
 
107/101
 
127/101
 
135/101
 
151/101
 
160/101
 
180/101
 
191/101
 
202/101
 
Blues Dark Double Harmonic
 
113/101
 
120/101
 
135/101
 
143/101
 
151/101
 
160/101
 
191/101
 
202/101
 
Blues Dorian Hexatonic
 
120/101
 
135/101
 
151/101
 
170/101
 
180/101
 
202/101
 
Blues Dorian Pentatonic
 
120/101
 
151/101
 
170/101
 
180/101
 
202/101
 
Blues Dorian Septatonic
 
120/101
 
135/101
 
143/101
 
151/101
 
170/101
 
180/101
 
202/101
 
Blues Harmonic Hexatonic
 
113/101
 
120/101
 
135/101
 
151/101
 
191/101
 
202/101
 
Blues Harmonic Septatonic
 
120/101
 
135/101
 
143/101
 
151/101
 
160/101
 
191/101
 
202/101
 
Blues Leading
 
120/101
 
135/101
 
143/101
 
151/101
 
180/101
 
191/101
 
202/101
 
Blues Minor
 
120/101
 
135/101
 
143/101
 
151/101
 
180/101
 
202/101
 
Blues Minor Maj7
 
120/101
 
135/101
 
143/101
 
151/101
 
191/101
 
202/101
 
Blues Pentachordal
 
113/101
 
120/101
 
135/101
 
143/101
 
151/101
 
202/101
 
Dominant Pentatonic
 
113/101
 
127/101
 
151/101
 
180/101
 
202/101
 
Dorian
 
113/101
 
120/101
 
135/101
 
151/101
 
170/101
 
180/101
 
202/101
 
Double Harmonic
 
107/101
 
127/101
 
135/101
 
151/101
 
160/101
 
191/101
 
202/101
 
Hirajoshi
 
113/101
 
120/101
 
151/101
 
160/101
 
202/101
 
Ionian Pentatonic
 
127/101
 
135/101
 
151/101
 
191/101
 
202/101
 
Javanese Pentachordal
 
107/101
 
120/101
 
143/101
 
151/101
 
202/101
 
Kokin-Joshi
 
113/101
 
120/101
 
151/101
 
170/101
 
202/101
 
Locrian
 
107/101
 
120/101
 
135/101
 
143/101
 
160/101
 
180/101
 
202/101
 
Lydian
 
113/101
 
127/101
 
143/101
 
151/101
 
170/101
 
191/101
 
202/101
 
Major
 
113/101
 
127/101
 
135/101
 
151/101
 
170/101
 
191/101
 
202/101
 
Major Pentatonic
 
113/101
 
127/101
 
151/101
 
170/101
 
202/101
 
Minor
 
113/101
 
120/101
 
135/101
 
151/101
 
160/101
 
180/101
 
202/101
 
Minor Harmonic
 
113/101
 
120/101
 
135/101
 
151/101
 
160/101
 
191/101
 
202/101
 
Minor Harmonic Pentatonic
 
113/101
 
120/101
 
151/101
 
191/101
 
202/101
 
Minor Hexatonic
 
113/101
 
120/101
 
135/101
 
151/101
 
180/101
 
202/101
 
Minor Melodic
 
113/101
 
120/101
 
135/101
 
151/101
 
170/101
 
191/101
 
202/101
 
Minor Pentatonic
 
120/101
 
135/101
 
151/101
 
180/101
 
202/101
 
Mixolydian
 
113/101
 
127/101
 
135/101
 
151/101
 
170/101
 
180/101
 
202/101
 
Mixolydian Harmonic
 
127/101
 
135/101
 
151/101
 
160/101
 
180/101
 
202/101
 
Mixolydian Pentatonic
 
127/101
 
135/101
 
151/101
 
180/101
 
202/101
 
Phrygian
 
107/101
 
120/101
 
135/101
 
151/101
 
160/101
 
180/101
 
202/101
 
Phrygian Dominant
 
107/101
 
127/101
 
135/101
 
151/101
 
160/101
 
180/101
 
202/101
 
Phrygian Dominant Hexatonic


107/101
Evened Minor Hexatonic
187.500
312.500
500.000
700.000
987.500
1200.000


127/101
Evened Phrygian Dominant Hexatonic
112.500
387.500
500.000
712.500
987.500
1200.000


135/101
Flattened Blues Aeolian Pentatonic
287.500
487.500
687.500
787.500
1200.000


151/101
Flattened Blues Minor Maj7
287.500
500.000
600.000
700.000
1100.000
1200.000


180/101
Roughened Blues Dorian Pentatonic
300.000
700.000
912.500
987.500
1200.000


202/101
Sharpened Blues Aeolian Pentatonic
312.500
712.500
800.000
1000.000
1200.000


Phrygian Dominant Pentatonic
Sharpened Blues Dorian Hexatonic
312.500
512.500
712.500
900.000
1012.500
1200.000


127/101
Sharpened Blues Harmonic Septatonic
312.500
512.500
612.500
712.500
812.500
1112.500
1200.000


135/101
Sharpened Dorian Harmonic
212.500
312.500
612.500
712.500
912.500
1012.500
1200.000


151/101
Sharpened Hirajoshi
200.000
312.500
700.000
812.500
1200.000


160/101
Sharpened Kokin-Joshi
200.000
312.500
700.000
900.000
1200.000


202/101
Sharpened Minor Pentatonic
312.500
500.000
700.000
1012.500
1200.000
</pre>


Phrygian Pentatonic
==== Xenharmonify 12edo scales ====
Approximate [[12edo]] subsets with these tunings, test them by noodling, and list all good-sounding ones in a big page:
* [[August]] in EDOs: ................. {{EDOs|21, 33, 45, 58, 69}}
* [[Augene]] in EDOs: ................. {{EDOs|15, 27, 39, 66}}
* [[Bidia]] in EDOs: ................. {{EDOs|56, 68, 80}}
* [[Diaschismic]] in EDOs: ................. {{EDOs|46, 58, 104}}
* [[Dimcomp]] in EDOs: ................. {{EDOs|44, 48, 56, 60, 68, 72}}
* [[Diminished]] in EDOs: ................. {{EDOs|20, 28, 32, 44}}
* [[Grackle]] in EDOs: ................. {{EDOs|53, 65, 77, 89}}
* [[Helenus]]/[[Photia]] in EDOs: ................. {{EDOs|41, 53, 65, 118}}
* [[Hexe]] in EDOs: ................. {{EDOs|30, 42}}
* [[Injera]] in EDOs: ................. {{EDOs|14, 26, 38, 40, 90, 102}}
* [[Misty]] in EDOs: ................. {{EDOs|39, 51, 63, 75, 87, 99}}
* [[Nickel]] in EDOs: ................. {{EDOs|16, 21, 28}}
* [[Pajara]] in EDOs: ................. {{EDOs|22, 34, 56}}
* [[Pajarous]] in EDOs: ................. {{EDOs|22, 32, 54, 76, 120}}
* [[Passion]] in EDOs: ................. {{EDOs|25, 37, 49, 61, 73, 110}}
* [[Ripple]] in EDOs: ................. {{EDOs|71, 83, 95, 107, 119}}
* [[Semimeantone]] in EDOs: ................. {{EDOs|38, 50, 62}}
* [[Srutal]]/[[Srutal archagall]] in EDOs: ................. {{EDOs|22, 34, 46, 80, 114, 126}}
* [[Wronecki]] in EDOs: ................. {{EDOs|66, 78, 90, 102, 114, 126}}
<br><br>


107/101
==Random stuff I’d like to share==


120/101
===List of equal divisions including novelties===
* [[User:BudjarnLambeth/List of equal divisions including novelties]]
<br>


151/101
===Hot takes===
'''Everything in this section is opinion, not facts!'''


160/101
'''Do not give any of it too much weight.'''


202/101
* '''Silliness:''' We should take ourselves less seriously: we should have more fun, we should be more silly 🎉
* '''Arbitrary numbers:''' It’s fine to explore the 2.3.5.101 [[subgroup]] if you want to. It doesn’t matter that it’s less [[concordant]] than 2.3.5.7. Explore it anyway and see what happens. Do some stuff with [[:Category:Novelties|arbitrary numbers]] that don’t make logical sense and just see what comes of it. That’s where the fun is! (Though do keep a “2.3” or “3.5” in there just to smooth over the gnarliest edges, heehee.)
* '''Importance of common names:''' I would prefer to use a temperament [[Temperament naming|named]] something fun like “waterslide” or “jinglebells” even if it has lots of error, over one named something dry and bland like “countertrihexakleismatic” even if it’s super [[damage|accurate]] and [[badness|technically better]] - a bland name can kill a temperament’s appeal, a fun name can create appeal out of nothing.
* '''My opinion on zeta peak indexes:''' My view on to what degree [[zeta peak index]]es are useful or not.


Picardy Hexatonic
::: [[User:BudjarnLambeth/My opinion on zeta peak indexes]]
* '''Misrepresentation of traditions:''' A cheeky little opinion piece I wrote criticising the negative and celebrating the positive ways Western tuning theory has borrowed from the world’s traditions:


113/101
::: [[User:BudjarnLambeth/Cultural appropriation-o-meter]]
* '''Comma naming debate brainstorm:''' A futile attempt I made to try to begin resolving one of the big behind the scenes debates among wiki editors:


127/101
::: [[User:BudjarnLambeth/Brainstorming mostly bad ideas to solve the comma naming debate]]
<br><br>


135/101
===Approximations of gamelan scales in edos up to 60===
* [[User:BudjarnLambeth/Edo approximations of gamelan scales]]
<br><br>


151/101
===Eagle JI subsets===
* [[User:BudjarnLambeth/Eagle JI subsets]]
<br><br>


160/101
===12edo interpreted as a 2.3.5.17.19 subgroup temperament===
* [[User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning]]
<br><br>


202/101
===Tunings for each subgroup===
* [[User:BudjarnLambeth/Tunings for each subgroup]]
<br><br>


Picardy Pentatonic
===Gallery of xenharmonic word painting (you can contribute!)===
* [[User:BudjarnLambeth/Gallery of xenharmonic word painting]]
<br><br>


113/101
===What I look for in a good xenharmonic piece===
The tuning sounds consonant, all the combinations of intervals you used sound within the same range of consonant-ness as all the combinations available in 12edo. There are more dissonant and less dissonant sections, but none that sound more dissonant than the maximum limit of dissonance I'm willing to tolerate (ie, the maximum amount of dissonance achievable with 12edo). All that is a long winded way of saying nothing sounds "out of tune".


127/101
The timbre also sounds good. Despite being midi instruments, the samples used and whatever effects were applied to them (reverb, volume levels, etc.) all come together well into something that is more than the sum of its parts. The timbre works well with the tuning to create a kind of pleasant, warm glow.


151/101
The piece has enough dynamic range, sense of harmonic movement, and interaction between melody lines to hold my interest, to not sound bland, but instead sound captivating.
<br><br><br>


160/101
===Ratios as planets===
The ratios of the octave as celestial bodies of the solar system:
* '''[[2/1]], the sun''', defining the overall structure of the entire octave.
* '''[[3/2]], Jupiter''', the biggest pull aside from the sun itself. Marks out a rough middle of the solar system.
* '''[[4/3]], Saturn''', a kind of echo of Jupiter. Vast and mighty in its own right, similar to Jupiter, but colder and subtler.
* '''[[5/3]], Uranus''', has a strong enough pull to be one of the big guys, but markedly smaller than Jupiter and Saturn. Has a gentle appearance.
* '''[[5/4]], Neptune''', the last of the giant planets, with their huge gravitational pull. Has an energetic, lively surface with the fastest winds in the solar system. Defines the boundary of the Kuiper Belt (like the boundary of major and minor tonality).
* '''[[6/5]], Earth''', a small planet that punches above its weight. It manages to hold an unreasonably large moon, given the small gravitational influence it has. It even developed life and sent probes to explore the other planets. It has far more influence than it seems like it should.
* '''[[7/4]], Venus''', a kind of parallel version of Earth. Its diameter and gravitational pull are almost identical to Earth, but its character is completely different. Home to a completely different temperature, chemical composition and volcanic system.
* '''[[7/5]], Mars''', appears barren and frozen upon first glance, but looking closer reveals a rich and storied history, and potential wonders and microcosms hidden in its underground caves.
* '''[[8/5]], Mercury'''. Caught in a region of the solar system so wild that much of its mass has been stripped away by the solar wind while it was still forming. Still, it holds firm, a foothold in difficult territory.
* '''[[7/6]], the moon'''. Caught in Earth’s orbit, it’s difficult to view separately from the Earth’s influence. If the Earth wasn’t there, it’d be a whole planet in its own right.
* '''[[9/5]], Ceres'''. It doesn’t pull much weight on its own, but in the context of the wider solar system, it demarcates an important in-between point for the other planets. If you want to travel between the different planets, Ceres makes the journey much more pleasant.
* '''[[11/8]], Pluto''', often dismissed outright due to having such a tiny gravitational pull. But it is a whole other type of ‘planet’, the first of a whole new family. When approached on its own terms, it opens up a larger, more diverse solar system than we ever knew existed.
<br><br>


202/101
== Useful links for my own convenience ==
<br>
<big>[[User:BudjarnLambeth/Sandbox]]
<br>
<br>
[[User:BudjarnLambeth/Sandbox2]]
<br>
<br>
[[Gallery of just intervals]]
<br>
<br>
[[Harmonic entropy of just intervals]]
<br>
<br>
[[User:Userminusone/Constructing a comma list using the Averiant]]
<br>
<br>
[[User:Ganaram inukshuk/Catalog of MOS Scales]]
</big>
Retrieved from "https://en.xen.wiki/w/User:BudjarnLambeth"