29-odd-limit

Odd limits:

---

• 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 29-odd-limit is the set of all rational intervals for which neither the numerator nor the denominator of the frequency ratio exceeds 29, once all powers of 2 are removed. To the 27-odd-limit, it adds 14 interval pairs involving 29.

Below is a list of all octave-reduced intervals in the 29-odd-limit.

• 1/1
• 30/29, 29/15
• 29/28, 56/29
• 28/27, 27/14
• 27/26, 52/27
• 26/25, 25/13
• 25/24, 48/25
• 24/23, 23/12
• 23/22, 44/23
• 22/21, 21/11
• 21/20, 40/21
• 20/19, 19/10
• 19/18, 36/19
• 18/17, 17/9
• 17/16, 32/17
• 16/15, 15/8
• 15/14, 28/15
• 29/27, 54/29
• 14/13, 13/7
• 27/25, 50/27
• 13/12, 24/13
• 25/23, 46/25
• 12/11, 11/6
• 23/21, 42/23
• 11/10, 20/11
• 32/29, 29/16
• 21/19, 38/21
• 10/9, 9/5
• 29/26, 52/29
• 19/17, 34/19
• 28/25, 25/14
• 9/8, 16/9
• 26/23, 23/13
• 17/15, 30/17
• 25/22, 44/25
• 8/7, 7/4
• 23/20, 40/23
• 15/13, 26/15
• 22/19, 19/11
• 29/25, 50/29
• 7/6, 12/7
• 34/29, 29/17
• 27/23, 46/27
• 20/17, 17/10
• 13/11, 22/13
• 32/27, 27/16
• 19/16, 32/19
• 25/21, 42/25
• 6/5, 5/3
• 29/24, 48/29
• 23/19, 38/23
• 17/14, 28/17
• 28/23, 23/14
• 11/9, 18/11
• 27/22, 44/27
• 16/13, 13/8
• 21/17, 34/21
• 26/21, 21/13
• 36/29, 29/18
• 5/4, 8/5
• 34/27, 27/17
• 29/23, 46/29
• 24/19, 19/12
• 19/15, 30/19
• 14/11, 11/7
• 23/18, 36/23
• 32/25, 25/16
• 9/7, 14/9
• 22/17, 17/11
• 13/10, 20/13
• 30/23, 23/15
• 17/13, 26/17
• 38/29, 29/19
• 21/16, 32/21
• 25/19, 38/25
• 29/22, 44/29
• 4/3, 3/2
• 27/20, 40/27
• 23/17, 34/23
• 19/14, 28/19
• 34/25, 25/17
• 15/11, 22/15
• 26/19, 19/13
• 11/8, 16/11
• 40/29, 29/20
• 29/21, 42/29
• 18/13, 13/9
• 25/18, 36/25
• 32/23, 23/16
• 7/5, 10/7
• 38/27, 27/19
• 24/17, 17/12

Ratio	Size (¢)	Color name		Name
30/29	58.692	29uy1	twenuyo unison	lesser vicesimononal quartertone
29/28	60.751	29or1	twenoru unison	greater vicesimononal quartertone
29/27	123.712	29o2	tweno 2nd	vicesimononal minor second
32/29	170.423	29u2	twenu 2nd	vicesimononal submajor second
29/26	189.050	29o3u2	twenothu 2nd	vicesimononal major second
29/25	256.950	29ogg3	twenogugu 3rd	vicesimononal inframinor third
34/29	275.378	29u17o3	twenuso 3rd	vicesimononal subminor third
29/24	327.622	29o3	tweno 3rd	vicesimononal minor third
36/29	374.333	29u3	twenu 3rd	vicesimononal submajor third
29/23	401.303	29o23u3	twenotwethu 3rd	vicesimononal major third
38/29	467.936	29u19o4	twenuno 4th	vicesimononal subfourth
29/22	478.259	29o1u4	twenolu 4th	vicesimononal grave fourth
40/29	556.737	29uy4	twenuyo 4th	lesser vicesimononal superfourth
29/21	558.796	29or4	twenoru 4th	greater vicesimononal superfourth
42/29	641.204	29uz5	twenuzo 5th	lesser vicesimononal subfifth
29/20	643.263	29og5	twenogu 5th	greater vicesimononal subfifth
44/29	721.741	29u1o5	twenulo 5th	vicesimononal acute fifth
29/19	732.064	29o19u5	twenonu 5th	vicesimononal superfifth
46/29	798.697	29u23o6	twenutwetho 6th	vicesimononal minor sixth
29/18	825.667	29o6	tweno 6th	vicesimononal supraminor sixth
48/29	872.378	29u6	twenu 6th	vicesimononal major sixth
29/17	924.621	29o17u6	twenosu 6th	vicesimononal supermajor sixth
50/29	943.050	29uyy6	twenuyoyo 6th	vicesimononal ultramajor sixth
52/29	1010.950	29u3o7	twenutho 7th	vicesimononal minor seventh
29/16	1029.577	29o7	tweno 7th	vicesimononal supraminor seventh
54/29	1076.288	29u7	twenu 7th	vicesimononal major seventh
56/29	1139.249	29uz8	twenuzo octave	lesser vicesimononal infraoctave
29/15	1141.308	29og8	twenogu octave	greater vicesimononal infraoctave

Note that 'vicesimononal' is exchangeable with 'undetricesimal', both denoting the presence of factor 29.

The smallest equal division of the octave which is consistent to the 29-odd-limit is 282edo; that which is distinctly consistent to the same is 1323edo.