36edo: Difference between revisions
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
→21st century: Add Norokusi's ''Hiroki Naito - Symphony: Moratorium for Large Orchestra in a 36EDO Subset'' (2025 - 2026) |
||
| (12 intermediate revisions by 5 users not shown) | |||
| Line 197: | Line 197: | ||
| 17 | | 17 | ||
| 566.7 | | 566.7 | ||
| | | [[112/81]] | ||
| [[18/13]] | | [[18/13]] | ||
| [[7/5]] | | [[7/5]] | ||
| Line 206: | Line 206: | ||
| 18 | | 18 | ||
| 600.0 | | 600.0 | ||
| | | [[729/512]], [[1024/729]] | ||
| [[17/12]], [[24/17]] | | [[17/12]], [[24/17]] | ||
| [[45/32]], [[64/45]] | | [[45/32]], [[64/45]] | ||
| Line 215: | Line 215: | ||
| 19 | | 19 | ||
| 633.3 | | 633.3 | ||
| | | 81/56 | ||
| [[13/9]] | | [[13/9]] | ||
| [[10/7]] | | [[10/7]] | ||
| Line 380: | Line 380: | ||
== Notation == | == Notation == | ||
=== | === Stein–Zimmermann–Gould notation === | ||
[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows: | |||
{{Sharpness-sharp3-szg|36}} | |||
If the arrows are taken to have their own layer of enharmonic spellings, then in some cases notes may be best denoted using double arrows. | |||
=== | === Kite's ups and downs notation === | ||
Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud. | Spoken as up, downsharp, sharp, upsharp, etc. Note that downsharp can be respelled as dup (double-up), and upflat as dud. | ||
{{Ups and downs sharpness}} | {{Ups and downs sharpness}} | ||
=== Colored notes === | |||
One way of notating 36edo (at least for people who are not colorblind) is to use colors. For example, {{colored note|blue|A}} is 33{{frac|3}}{{c}} below {{colored note|A}} and {{colored note|red|A}} is 33{{frac|3}} cents above {{colored note|A}}. Or, the colors could be written out (red A, blue C♯, etc.) or abbreviated as rA, bC♯, etc. This use of red and blue is consistent with [[Kite's_color_notation|color notation]] (ru and zo). | |||
=== Sagittal notation === | === Sagittal notation === | ||
This notation uses the same sagittal sequence as [[43edo#Sagittal notation| | This notation uses the same sagittal sequence as [[43edo #Sagittal notation|43edo]], is a subset of the notation for [[72edo #Sagittal notation|72edo]], and is a superset of the notations for edos [[18edo #Sagittal notation|18]], [[12edo #Sagittal notation|12]], and [[6edo #Sagittal notation|6]]. | ||
==== Evo flavor ==== | ==== Evo flavor ==== | ||
| Line 1,061: | Line 1,062: | ||
== Scales == | == Scales == | ||
''See also: [[List of MOS scales in 36edo]]'' | ''See also: [[List of MOS scales in 36edo]]'' | ||
{{Idiosyncratic terms}} | {{Idiosyncratic terms|[[Budjarn Lambeth]] coined and is so far the only known user of the "N&M-tone scale"-type names, the names of the catnip subsets, and the name "baobab".}} | ||
; [[Polymicrotonal]] scales | ; [[Polymicrotonal]] scales | ||
| Line 1,147: | Line 1,148: | ||
* Niner[18] MOS: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 (''9/18 keys have a 3/2, 0/18 keys have both a 4/3 and a 3/2'') | * Niner[18] MOS: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 (''9/18 keys have a 3/2, 0/18 keys have both a 4/3 and a 3/2'') | ||
* Niner[18] [[modmos]]: 1 1 3 1 3 5 1 1 1 3 1 3 1 1 3 1 3 3 (''11/18 keys have a 3/2, 6/18 keys have both a 4/3 and a 3/2'') | * Niner[18] [[modmos]]: 1 1 3 1 3 5 1 1 1 3 1 3 1 1 3 1 3 3 (''11/18 keys have a 3/2, 6/18 keys have both a 4/3 and a 3/2'') | ||
* Baobab: 9 6 6 6 4 5 (''approximated from [[30afdo]]'') | |||
== Tuning by ear == | == Tuning by ear == | ||
| Line 1,157: | Line 1,159: | ||
36edo can also be played using three instruments tuned to 12edo with different root notes (that is, a sixth-tone apart). | 36edo can also be played using three instruments tuned to 12edo with different root notes (that is, a sixth-tone apart). | ||
At least one 36edo harmonium has been built (the "sixth-tone harmonium" used by 20th century Czech microtonal composer {{W|Alois Habá}}), having effectively two quasi-Halberstadt keyboards (but with the bottom one duplicated at the top), each having 18 notes per octave organized in 6 groups of 2 natural-position notes and 1 flat/sharp-position note — see the Music section below for a video demonstration. | |||
== Music == | == Music == | ||
=== 20th century === | |||
; [[Alois Hába]] | |||
* ''Six compositions for sixth-tone harmonium, op. 37'' (1928) | |||
** [https://www.youtube.com/watch?v=UJwLdLMvdu8 String quartet version] — performed by Stamitz Quartet (unknown recording date) (currently the video title erroneously says this is for sixteenth-tone harmonium) | |||
** [https://www.youtube.com/watch?v=-Ktbo7EfhEA Sixth-tone harmonium version] — performed by Miroslav Beinhauer ([https://miroslavbeinhauer.com/?page_id=139&lang=en site]) (2019, with much of the video showing keyboard views of the sixth-tone harmonium being played) | |||
; {{W|Henri Pousseur}} | |||
* [https://www.youtube.com/watch?v=tiWbbbU6ZPw ''Prospection''] (1952-1953) – for three pianos detuned by a sixth-tone from each other | |||
=== 21st century === | |||
; [[Ambient Esoterica]] | ; [[Ambient Esoterica]] | ||
* [https://www.youtube.com/watch?v=nadDPD1m-1Y ''A Trip to PRS with a Circle of Augmented 5ths''] (2024) | * [https://www.youtube.com/watch?v=nadDPD1m-1Y ''A Trip to PRS with a Circle of Augmented 5ths''] (2024) | ||
| Line 1,176: | Line 1,190: | ||
* [https://www.youtube.com/shorts/3la1W-_-ceA ''36edo cowbell''] (2025) | * [https://www.youtube.com/shorts/3la1W-_-ceA ''36edo cowbell''] (2025) | ||
* [https://www.youtube.com/shorts/MjUdMnUA-2k ''18 tone unequal improv''] (2026) (this is tuned as two rings of [[9edo]] offset by 35{{c}}, to make a good approximation of [[3/2]] available, for a tuning that is an 18 note subset of a well-tempered derivative of 36edo) | * [https://www.youtube.com/shorts/MjUdMnUA-2k ''18 tone unequal improv''] (2026) (this is tuned as two rings of [[9edo]] offset by 35{{c}}, to make a good approximation of [[3/2]] available, for a tuning that is an 18 note subset of a well-tempered derivative of 36edo) | ||
* [https://www.youtube.com/shorts/KCtEYSkEK8U ''36edo improv''] (2026) | |||
; [[E8 Heterotic]] | ; [[E8 Heterotic]] | ||
| Line 1,197: | Line 1,212: | ||
; [[Joseph Monzo]] | ; [[Joseph Monzo]] | ||
* [https://m.youtube.com/watch?v=7t79lBI_4_s ''African Rhythms in 36-ET''] (2005) | * [https://m.youtube.com/watch?v=7t79lBI_4_s ''African Rhythms in 36-ET''] (2005) | ||
; [[Norokusi]] | |||
* [https://www.youtube.com/watch?v=JPpjYzddGSg&t=495s ''Symphony for String Orchestra''] (2024) | |||
** [https://www.youtube.com/watch?v=l5SQOI1kTHc ''Arranged for orchestra''] (2026) | |||
* [https://www.youtube.com/watch?v=_DQKj0afWwE ''Hiroki Naito - Symphony: Moratorium for Large Orchestra in a 36EDO Subset''] (2025 - 2026) (also has a [[24edo]] vibraphone part) | |||
; [[NullPointerException Music]] | ; [[NullPointerException Music]] | ||
| Line 1,206: | Line 1,226: | ||
; [[Chris Orphal]] | ; [[Chris Orphal]] | ||
* [https://www.youtube.com/watch?v=qbOOzC4360M ''Vademecum - Vadetecum (36-EDO) - Perf. New Music New Mexico''] (2023) (Saxophone: Edwin Anthony; Horn: Samuel Lutz; Trumpet: Doug Falk; Guitar: Carlos Arellano; Guitar tuned -31¢: Chris Orphal; Piano: Axel Retif) | * [https://www.youtube.com/watch?v=qbOOzC4360M ''Vademecum - Vadetecum (36-EDO) - Perf. New Music New Mexico''] (2023) (Saxophone: Edwin Anthony; Horn: Samuel Lutz; Trumpet: Doug Falk; Guitar: Carlos Arellano; Guitar tuned -31¢: Chris Orphal; Piano: Axel Retif) | ||
; [[Chris Vaisvil]] | ; [[Chris Vaisvil]] | ||