8edo: Difference between revisions
m →Temperaments: this isn't an edo join |
→Music: Add Anne Veinberg's ''8 vs 16 vs 32 Notes Per Octave — The 96-Tone Piano in Its Subdivision Glory'' (2026) |
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| Line 35: | Line 35: | ||
! rowspan="2" | Steps | ! rowspan="2" | Steps | ||
! rowspan="2" | Cents | ! rowspan="2" | Cents | ||
! colspan=" | ! colspan="4" | JI approximation | ||
!Other | !Other | ||
|- | |- | ||
| Line 41: | Line 41: | ||
! 2.5/3.11/3.13/5* | ! 2.5/3.11/3.13/5* | ||
! 10:11:12:13:14* | ! 10:11:12:13:14* | ||
!val 8d** | |||
!Patent val ⟨8 13 19] | !Patent val ⟨8 13 19] | ||
|- | |- | ||
| Line 48: | Line 49: | ||
| 1/1 | | 1/1 | ||
| 1/1 | | 1/1 | ||
|1/1 | |||
|1/1, 16/15 | |1/1, 16/15 | ||
|- | |- | ||
| Line 55: | Line 57: | ||
| 12/11 | | 12/11 | ||
| 12/11, 11/10 | | 12/11, 11/10 | ||
|14/13, 13/12, 12/11, 11/10 | |||
|10/9, 25/24 | |10/9, 25/24 | ||
|- | |- | ||
| Line 62: | Line 65: | ||
| 6/5 | | 6/5 | ||
| 6/5 | | 6/5 | ||
|13/11, 6/5 | |||
|6/5, 9/8 | |6/5, 9/8 | ||
|- | |- | ||
| Line 69: | Line 73: | ||
| 13/10 | | 13/10 | ||
| 13/10 | | 13/10 | ||
|9/7, 13/10 | |||
|4/3, 5/4 | |4/3, 5/4 | ||
|- | |- | ||
| Line 76: | Line 81: | ||
| | | | ||
| 7/5, 10/7 | | 7/5, 10/7 | ||
|7/5, 10/7 | |||
|27/20, 25/18, 36/25 | |27/20, 25/18, 36/25 | ||
|- | |- | ||
| Line 83: | Line 89: | ||
| 20/13 | | 20/13 | ||
| 20/13 | | 20/13 | ||
|14/9 | |||
|3/2, 8/5 | |3/2, 8/5 | ||
|- | |- | ||
| Line 90: | Line 97: | ||
| 5/3 | | 5/3 | ||
| 5/3 | | 5/3 | ||
|5/3 | |||
|5/3, 16/9 | |5/3, 16/9 | ||
|- | |- | ||
| Line 97: | Line 105: | ||
| 11/6 | | 11/6 | ||
| 20/11, 11/6 | | 20/11, 11/6 | ||
|11/6, 13/7 | |||
|9/5, 48/50 | |9/5, 48/50 | ||
|- | |- | ||
| Line 104: | Line 113: | ||
| 2/1 | | 2/1 | ||
| 2/1 | | 2/1 | ||
|2/1 | |||
|2/1, 15/8 | |2/1, 15/8 | ||
|} | |} | ||
<nowiki />* Allows [[inversion]] by 2/1; other interpretations also possible | <nowiki />* Allows [[inversion]] by 2/1; other interpretations also possible | ||
<nowiki />** 16 integer limit, relative error < 15 % | |||
== Notation == | == Notation == | ||
| Line 560: | Line 572: | ||
; [[Aaron Andrew Hunt]] | ; [[Aaron Andrew Hunt]] | ||
* [https://aaronandrewhunt.bandcamp.com/track/fantasia-fugue-a4-in-8et "Fantasia & Fugue a4 in 8ET"], from [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard ''The Equal-Tempered Keyboard''] (1999-2022) | * [https://aaronandrewhunt.bandcamp.com/track/fantasia-fugue-a4-in-8et "Fantasia & Fugue a4 in 8ET"], from [https://aaronandrewhunt.bandcamp.com/album/the-equal-tempered-keyboard ''The Equal-Tempered Keyboard''] (1999-2022) | ||
; [[User:Fitzgerald_Lee|Fitzgerald Lee]] | |||
* [https://youtu.be/zwRDfjLzXkU Jonky Jazz] (2025) | |||
; [[NullPointerException Music]] | ; [[NullPointerException Music]] | ||
| Line 580: | Line 595: | ||
; [[Ron Sword]] | ; [[Ron Sword]] | ||
* [http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3 ''Acoustic Improvisation in 8EDO'']{{dead link}} | * [http://www.ronsword.com/sounds/ronsword_8edo_improv.mp3 ''Acoustic Improvisation in 8EDO'']{{dead link}} | ||
; [[Anne Veinberg]] | |||
* [https://www.youtube.com/watch?v=fm32IYUtITU ''8 vs 16 vs 32 Notes Per Octave — The 96-Tone Piano in Its Subdivision Glory''] (2026, performed on a digital recreation of [[Julián Carrillo]]'s 96-tone metamorphoser piano, using subsets 8edo, [[16edo]], [[32edo]], and then glissandos in full [[96edo]]) | |||
; [[Stephen Weigel]] | ; [[Stephen Weigel]] | ||
| Line 586: | Line 604: | ||
; [[Randy Winchester]] | ; [[Randy Winchester]] | ||
* [https://archive.org/details/jamendo-005173/07.mp3 "7. 8 / octave"], from ''[[Comets Over Flatland]]'' (2007) | * [https://archive.org/details/jamendo-005173/07.mp3 "7. 8 / octave"], from ''[[Comets Over Flatland]]'' (2007) | ||
== Ear training == | == Ear training == | ||