39-odd-limit

Odd limit

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1-odd-limit  3-odd-limit →

The 39-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 39 and k is an integer. To the 37-odd-limit, it adds 11 pairs of octave-reduced intervals involving 39.

Below is a list of all octave-reduced intervals in the 39-odd-limit.

• 1/1
• 40/39, 39/20
• 39/38, 76/39
• 38/37, 37/19
• 37/36, 72/37
• 36/35, 35/18
• 35/34, 68/35
• 34/33, 33/17
• 33/32, 64/33
• 32/31, 31/16
• 31/30, 60/31
• 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
• 39/37, 74/39
• 19/18, 36/19
• 37/35, 70/37
• 18/17, 17/9
• 35/33, 66/35
• 17/16, 32/17
• 33/31, 62/33
• 16/15, 15/8
• 31/29, 58/31
• 15/14, 28/15
• 29/27, 54/29
• 14/13, 13/7
• 27/25, 50/27
• 40/37, 37/20
• 13/12, 24/13
• 38/35, 35/19
• 25/23, 46/25
• 37/34, 68/37
• 12/11, 11/6
• 35/32, 64/35
• 23/21, 42/23
• 34/31, 31/17
• 11/10, 20/11
• 32/29, 29/16
• 21/19, 38/21
• 31/28, 56/31
• 10/9, 9/5
• 39/35, 70/39
• 29/26, 52/29
• 19/17, 34/19
• 28/25, 25/14
• 37/33, 66/37
• 9/8, 16/9
• 44/39, 39/22
• 35/31, 62/35
• 26/23, 23/13
• 17/15, 30/17
• 42/37, 37/21
• 25/22, 44/25
• 33/29, 58/33
• 8/7, 7/4
• 39/34, 68/39
• 31/27, 54/31
• 23/20, 40/23
• 38/33, 33/19
• 15/13, 26/15
• 37/32, 64/37
• 22/19, 19/11
• 29/25, 50/29
• 36/31, 31/18
• 7/6, 12/7
• 34/29, 29/17
• 27/23, 46/27
• 20/17, 17/10
• 33/28, 56/33
• 46/39, 39/23
• 13/11, 22/13
• 32/27, 27/16
• 19/16, 32/19
• 44/37, 37/22
• 25/21, 42/25
• 31/26, 52/31
• 37/31, 62/37
• 6/5, 5/3
• 35/29, 58/35
• 29/24, 48/29
• 23/19, 38/23
• 40/33, 33/20
• 17/14, 28/17
• 28/23, 23/14
• 39/32, 64/39
• 11/9, 18/11
• 38/31, 31/19
• 27/22, 44/27
• 16/13, 13/8
• 37/30, 60/37
• 21/17, 34/21
• 26/21, 21/13
• 31/25, 50/31
• 36/29, 29/18
• 46/37, 37/23
• 5/4, 8/5
• 44/35, 35/22
• 39/31, 62/39
• 34/27, 27/17
• 29/23, 46/29
• 24/19, 19/12
• 19/15, 30/19
• 33/26, 52/33
• 14/11, 11/7
• 37/29, 58/37
• 23/18, 36/23
• 32/25, 25/16
• 50/39, 39/25
• 9/7, 14/9
• 40/31, 31/20
• 31/24, 48/31
• 22/17, 17/11
• 35/27, 54/35
• 48/37, 37/24
• 13/10, 20/13
• 30/23, 23/15
• 17/13, 26/17
• 38/29, 29/19
• 21/16, 32/21
• 46/35, 35/23
• 25/19, 38/25
• 29/22, 44/29
• 33/25, 50/33
• 37/28, 56/37
• 4/3, 3/2
• 39/29, 58/39
• 35/26, 52/35
• 31/23, 46/31
• 27/20, 40/27
• 50/37, 37/25
• 23/17, 34/23
• 42/31, 31/21
• 19/14, 28/19
• 34/25, 25/17
• 15/11, 22/15
• 26/19, 19/13
• 37/27, 54/37
• 48/35, 35/24
• 11/8, 16/11
• 40/29, 29/20
• 29/21, 42/29
• 18/13, 13/9
• 25/18, 36/25
• 32/23, 23/16
• 39/28, 56/39
• 46/33, 33/23
• 7/5, 10/7
• 52/37, 37/26
• 38/27, 27/19
• 31/22, 44/31
• 24/17, 17/12

Ratio	Size (¢)	Color name	Name
40/39	43.831
39/38	44.97
39/37	91.139
39/35	187.343
44/39	208.835
39/34	237.527
46/39	285.792
39/31	397.447
50/39	430.145
39/29	512.905
39/28	573.657
56/39	626.343
58/39	687.095
39/25	769.855
62/39	802.553
39/23	914.208
68/39	962.473
39/22	991.165
70/39	1012.657
74/39	1108.861
76/39	1155.03
39/20	1156.169

The smallest equal division of the octave which is consistent to the 39-odd-limit is 311edo (by virtue of it being consistent in the 41-odd-limit); that which is distinctly consistent to the same is 20567edo (by virtue of it being distinctly consistent through the 57-odd-limit).