11edt: Difference between revisions
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CompactStar (talk | contribs) Changing H = 1/1 to J = 1/1 as it seems to be more common |
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| Line 11: | Line 11: | ||
! Hekts | ! Hekts | ||
! Approximate ratios | ! Approximate ratios | ||
! [[Arcturus]] nonatonic notation | ! [[Arcturus]] nonatonic notation (J = 1/1) | ||
|- | |- | ||
| colspan = "3" | 0 | | colspan = "3" | 0 | ||
| [[1/1]] | | [[1/1]] | ||
| | | J | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 21: | Line 21: | ||
| 118.1 | | 118.1 | ||
| [[11/10]], [[10/9]] | | [[11/10]], [[10/9]] | ||
| | | J#, Kb | ||
|- | |- | ||
| 2 | | 2 | ||
| Line 27: | Line 27: | ||
| 236.2 | | 236.2 | ||
| [[11/9]] | | [[11/9]] | ||
| | | K | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 33: | Line 33: | ||
| 354.3 | | 354.3 | ||
| [[4/3]], [[27/20]] | | [[4/3]], [[27/20]] | ||
| | | L | ||
|- | |- | ||
| 4 | | 4 | ||
| Line 39: | Line 39: | ||
| 472.4 | | 472.4 | ||
| [[3/2]], [[40/27]] | | [[3/2]], [[40/27]] | ||
| | | M | ||
|- | |- | ||
| 5 | | 5 | ||
| Line 45: | Line 45: | ||
| 590.5 | | 590.5 | ||
| [[5/3]], [[28/17]], [[105/64]] | | [[5/3]], [[28/17]], [[105/64]] | ||
| | | N | ||
|- | |- | ||
| 6 | | 6 | ||
| Line 51: | Line 51: | ||
| 708.6 | | 708.6 | ||
| [[29/16]], [[20/11]], [[64/35]] | | [[29/16]], [[20/11]], [[64/35]] | ||
| | | N#, Ob | ||
|- | |- | ||
| 7 | | 7 | ||
| Line 57: | Line 57: | ||
| 826.7 | | 826.7 | ||
| [[2/1]] | | [[2/1]] | ||
| | | O | ||
|- | |- | ||
| 8 | | 8 | ||
| Line 63: | Line 63: | ||
| 944.8 | | 944.8 | ||
| | | | ||
| | | P | ||
|- | |- | ||
| 9 | | 9 | ||
| Line 69: | Line 69: | ||
| 1062.9 | | 1062.9 | ||
| | | | ||
| | | Q | ||
|- | |- | ||
| 10 | | 10 | ||
| Line 75: | Line 75: | ||
| 1181 | | 1181 | ||
| | | | ||
| | | R | ||
|- | |- | ||
| 11 | | 11 | ||
| Line 81: | Line 81: | ||
| 1300 | | 1300 | ||
| | | | ||
| | | J | ||
|} | |} | ||
Revision as of 03:47, 1 March 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.
Intervals
| # | Cents | Hekts | Approximate ratios | Arcturus nonatonic notation (J = 1/1) |
|---|---|---|---|---|
| 0 | 1/1 | J | ||
| 1 | 172.9 | 118.1 | 11/10, 10/9 | J#, Kb |
| 2 | 345.8 | 236.2 | 11/9 | K |
| 3 | 518.7 | 354.3 | 4/3, 27/20 | L |
| 4 | 691.6 | 472.4 | 3/2, 40/27 | M |
| 5 | 864.5 | 590.5 | 5/3, 28/17, 105/64 | N |
| 6 | 1037.4 | 708.6 | 29/16, 20/11, 64/35 | N#, Ob |
| 7 | 1210.3 | 826.7 | 2/1 | O |
| 8 | 1383.2 | 944.8 | P | |
| 9 | 1556.1 | 1062.9 | Q | |
| 10 | 1729 | 1181 | R | |
| 11 | 1902 | 1300 | J | |
Scala file
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
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