13-odd-limit

Odd limits:

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• 1-odd-limit
• 3-odd-limit
• 5-odd-limit
• 7-odd-limit
• 9-odd-limit
• 11-odd-limit
• 13-odd-limit
• 15-odd-limit
• 17-odd-limit
• 19-odd-limit
• 21-odd-limit
• 23-odd-limit
• 25-odd-limit
• 27-odd-limit
• 29-odd-limit
• 31-odd-limit

The 13-odd-limit is the set of all rational intervals for which neither the numerator nor the denominator of the frequency ratio exceeds 13, once all powers of 2 are removed. To the 11-odd-limit, it adds 6 interval pairs involving 13.

Below is a list of all octave-reduced intervals in the 13-odd-limit.

• 1/1
• 14/13, 13/7
• 13/12, 24/13
• 12/11, 11/6
• 11/10, 20/11
• 10/9, 9/5
• 9/8, 16/9
• 8/7, 7/4
• 7/6, 12/7
• 13/11, 22/13
• 6/5, 5/3
• 11/9, 18/11
• 16/13, 13/8
• 5/4, 8/5
• 14/11, 11/7
• 9/7, 14/9
• 13/10, 20/13
• 4/3, 3/2
• 11/8, 16/11
• 18/13, 13/9
• 7/5, 10/7

Ratio	Size (¢)	Color name		Name(s)
14/13	128.298	3uz2	thuzo 2nd	tridecimal large semitone
13/12	138.573	3o2	tho 2nd	tridecimal supraminor second / tridecimal subneutral second
13/11	289.210	3o1u3	tholu 3rd	tridecimal minor third
16/13	359.472	3u3	thu 3rd	tridecimal supra-neutral third
13/10	454.214	3og4	thogu 4th	tridecimal subfourth / tridecimal third-fourth
18/13	563.382	3u4	thu 4th	tridecimal superfourth
13/9	636.618	3o5	tho 5th	tridecimal subfifth
20/13	745.786	3uy5	thuyo 5th	tridecimal superfifth / tridecimal fifth-sixth
13/8	840.528	3o6	tho 6th	tridecimal subneutral sixth
22/13	910.790	3u1o6	thulo 6th	tridecimal major sixth
24/13	1061.427	3u7	thu 7th	tridecimal supra-neutral seventh
13/7	1071.702	3or7	thoru 7th	tridecimal submajor seventh

The smallest equal division of the octave which is consistent in the 13-odd-limit is 26edo; that which is distinctly consistent in the same is 87edo.

See also

• 13-limit (prime limit)
• Diamond13 – as a scale