11-odd-limit

Odd limit

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← 9-odd-limit  11-odd-limit  13-odd-limit →

The 11-odd-limit is the set of all rational intervals which can be written as 2^k(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