11-odd-limit
The 11-odd-limit is the set of all rational intervals which can be written as 2k(a/b) where a, b ≤ 11 and k is an integer. To the 9-odd-limit, it adds 5 pairs of octave-reduced intervals involving 11.
Below is a list of all octave-reduced intervals in the 11-odd-limit.
- 1/1
- 12/11, 11/6
- 11/10, 20/11
- 10/9, 9/5
- 9/8, 16/9
- 8/7, 7/4
- 7/6, 12/7
- 6/5, 5/3
- 11/9, 18/11
- 5/4, 8/5
- 14/11, 11/7
- 9/7, 14/9
- 4/3, 3/2
- 11/8, 16/11
- 7/5, 10/7
| Ratio | Size (¢) | Color name | Name | |
|---|---|---|---|---|
| 12/11 | 150.637 | 1u2 | lu 2nd | lesser undecimal neutral second |
| 11/10 | 165.004 | 1og2 | logu 2nd | greater undecimal neutral second |
| 11/9 | 347.408 | 1o3 | ilo 3rd | undecimal neutral third |
| 14/11 | 417.508 | 1uz4 | luzo 4th | undecimal major third |
| 11/8 | 551.318 | 1o4 | ilo 4th | undecimal superfourth |
| 16/11 | 648.682 | 1u5 | lu 5th | undecimal subfifth |
| 11/7 | 782.492 | 1or5 | loru 5th | undecimal minor sixth |
| 18/11 | 852.592 | 1u6 | lu 6th | undecimal neutral sixth |
| 20/11 | 1034.996 | 1uy7 | luyo 7th | lesser undecimal neutral seventh |
| 11/6 | 1049.363 | 1o7 | ilo 7th | greater undecimal neutral seventh |
The smallest equal division of the octave which is consistent in the 11-odd-limit is 22edo.
The one which is distinctly consistent in the same is 58edo (also the smallest EDO to be consistent in the 17-odd-limit).
Link to Harry Partch
The 11-odd-limit is significant to Harry Partch's instruments and scales, with his 43-tone scale unequally dividing the octave into every 11-odd-limit ratio. He theorized about a tonality diamond that would support this scale, and built his diamond marimba (along with many other instruments) around this concept. He was, importantly, one of the pioneers of this concept.
See also
- 11-limit (prime limit)
- diamond11 – as a scale