11edt
| ← 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 | |
Prime harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +10.3 | +0.0 | +20.7 | -19.8 | +10.3 | -83.6 | +31.0 | +0.0 | -9.5 | -1.6 | +20.7 |
| Relative (%) | +6.0 | +0.0 | +12.0 | -11.5 | +6.0 | -48.4 | +17.9 | +0.0 | -5.5 | -0.9 | +12.0 | |
| Steps (reduced) |
7 (7) |
11 (0) |
14 (3) |
16 (5) |
18 (7) |
19 (8) |
21 (10) |
22 (0) |
23 (1) |
24 (2) |
25 (3) | |
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