11edt: Difference between revisions
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== Intervals == | |||
{| class="wikitable center-all" | |||
! # | |||
! Cents | |||
! Hekts | |||
! Approximate ratios | |||
! [[Arcturus]] nonatonic notation | |||
|- | |||
| colspan = "3" | 0 | |||
| [[1/1]] | |||
| H | |||
|- | |||
| 1 | |||
| 172.9 | |||
| 118.1 | |||
| [[11/10]], [[10/9]] | |||
| H#, Ib | |||
|- | |||
| 2 | |||
| 345.8 | |||
| 236.2 | |||
| [[11/9]] | |||
| I | |||
|- | |||
| 3 | |||
| 518.7 | |||
| 354.3 | |||
| [[4/3]], [[27/20]] | |||
| J | |||
|- | |||
| 4 | |||
| 691.6 | |||
| 472.4 | |||
| K | |||
|- | |||
| 5 | |||
| 864.5 | |||
| 590.5 | |||
| L | |||
|- | |||
| 6 | |||
| 1037.4 | |||
| L#, Mb | |||
|- | |||
| 7 | |||
| 1210.3 | |||
| 826.7 | |||
| M | |||
|- | |||
| 8 | |||
| 1383.2 | |||
| 944.8 | |||
| N | |||
|- | |||
| 9 | |||
| 1556.1 | |||
| 1062.9 | |||
| O | |||
|- | |||
| 10 | |||
| 1729 | |||
| 1181 | |||
| P | |||
|- | |||
| 11 | |||
| 1902 | |||
| 1300 | |||
| H | |||
|} | |||
== Pieces == | |||
Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 sonata #11 in A Major K331 in 11 EDT] (using a 11 => 12 key mapping so octaves become tritaves) | Mozart's [http://micro.soonlabel.com/6th-comma-meantone/K331-period/k331-walter-piano-11edt.mp3 sonata #11 in A Major K331 in 11 EDT] (using a 11 => 12 key mapping so octaves become tritaves) | ||
Revision as of 23:02, 18 February 2023
| ← 10edt | 11edt | 12edt → |
(semiconvergent)
11edt means the division of 3, the tritave, into 11 equal parts of 175.905 cents each, corresponding to 6.940 edo. It can therefore be seen as a very stretched version of 7edo, with octaves sharpened by ten and a third cents. The octave stretching makes the fifth in better tune, and of course the twelfth is the pure 3/1 tritave.
From a no-two point of view, it tempers out 49/45 and 15625/15309 in the 7-limit and 35/33 and 77/75 in the 11-limit.
Tuning in scala format is as follows:
! E:\cakewalk\scales\11_of_tritave.scl
!
11 in tritave
!
172.90500
345.81000
518.71500
691.62000
864.52500
1037.43000
1210.33500
1383.24000
1556.14500
1729.05000
3/1
Intervals
| # | Cents | Hekts | Approximate ratios | Arcturus nonatonic notation |
|---|---|---|---|---|
| 0 | 1/1 | H | ||
| 1 | 172.9 | 118.1 | 11/10, 10/9 | H#, Ib |
| 2 | 345.8 | 236.2 | 11/9 | I |
| 3 | 518.7 | 354.3 | 4/3, 27/20 | J |
| 4 | 691.6 | 472.4 | K | |
| 5 | 864.5 | 590.5 | L | |
| 6 | 1037.4 | L#, Mb | ||
| 7 | 1210.3 | 826.7 | M | |
| 8 | 1383.2 | 944.8 | N | |
| 9 | 1556.1 | 1062.9 | O | |
| 10 | 1729 | 1181 | P | |
| 11 | 1902 | 1300 | H | |
Pieces
Mozart's sonata #11 in A Major K331 in 11 EDT (using a 11 => 12 key mapping so octaves become tritaves)
Frozen Time Occupies Wall Street by Chris Vaisvil =>information about the piece
Molly's Playground by Chris Vaisvil => information about the piece