17-odd-limit

Odd limit

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← 15-odd-limit  17-odd-limit  19-odd-limit →

The 17-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 17 and k is an integer. To the 15-odd-limit, it adds 8 pairs of octave-reduced intervals involving 17.

Below is a list of all octave-reduced intervals in the 17-odd-limit.

• 1/1
• 18/17, 17/9
• 17/16, 32/17
• 16/15, 15/8
• 15/14, 28/15
• 14/13, 13/7
• 13/12, 24/13
• 12/11, 11/6
• 11/10, 20/11
• 10/9, 9/5
• 9/8, 16/9
• 17/15, 30/17
• 8/7, 7/4
• 15/13, 26/15
• 7/6, 12/7
• 20/17, 17/10
• 13/11, 22/13
• 6/5, 5/3
• 17/14, 28/17
• 11/9, 18/11
• 16/13, 13/8
• 5/4, 8/5
• 14/11, 11/7
• 9/7, 14/9
• 22/17, 17/11
• 13/10, 20/13
• 17/13, 26/17
• 4/3, 3/2
• 15/11, 22/15
• 11/8, 16/11
• 18/13, 13/9
• 7/5, 10/7
• 24/17, 17/12

Ratio	Size (¢)	Color name		Name
18/17	98.955	17u1	su unison	small septendecimal semitone
17/16	104.955	17o2	iso 2nd	large septendecimal semitone
17/15	216.687	17og3	sogu 3rd	septendecimal whole tone
20/17	281.358	17uy2	suyo 2nd	septendecimal minor third
17/14	336.130	17or3	soru 3rd	septendecimal supraminor third
22/17	446.363	17u1o3	sulo 3rd	septendecimal supermajor third
17/13	464.428	17o3u4	sothu 4th	septendecimal sub-fourth
24/17	597.000	17u4	su 4th	lesser septendecimal tritone
17/12	603.000	17o5	iso 5th	greater septendecimal tritone
26/17	735.572	17u3o5	sutho 5th	septendecimal super-fifth
17/11	753.637	17o1u6	solu 6th	septendecimal subminor sixth
28/17	863.870	17uz6	suzo 6th	septendecimal submajor sixth
17/10	918.642	17og7	sogu 7th	septendecimal major sixth
30/17	983.313	17uy6	suyo 6th	septendecimal minor seventh
32/17	1095.045	17u7	su 7th	small septendecimal major seventh
17/9	1101.045	17o8	iso octave	large septendecimal major seventh

The smallest equal division of the octave which is consistent in the 17-odd-limit is 58edo.

The one which is distinctly consistent in the same is 149edo.

See also

• 17-limit (prime limit)