33-odd-limit

Odd limit

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← 31-odd-limit  33-odd-limit  35-odd-limit →

The 33-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 33 and k is an integer. To the 31-odd-limit, it adds 10 pairs of octave-reduced intervals involving 33.

Below is a list of all octave-reduced intervals in the 33-odd-limit.

• 1/1
• 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
• 19/18, 36/19
• 18/17, 17/9
• 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
• 13/12, 24/13
• 25/23, 46/25
• 12/11, 11/6
• 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
• 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
• 33/29, 58/33
• 8/7, 7/4
• 31/27, 54/31
• 23/20, 40/23
• 38/33, 33/19
• 15/13, 26/15
• 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
• 13/11, 22/13
• 32/27, 27/16
• 19/16, 32/19
• 25/21, 42/25
• 31/26, 52/31
• 6/5, 5/3
• 29/24, 48/29
• 23/19, 38/23
• 40/33, 33/20
• 17/14, 28/17
• 28/23, 23/14
• 11/9, 18/11
• 38/31, 31/19
• 27/22, 44/27
• 16/13, 13/8
• 21/17, 34/21
• 26/21, 21/13
• 31/25, 50/31
• 36/29, 29/18
• 5/4, 8/5
• 34/27, 27/17
• 29/23, 46/29
• 24/19, 19/12
• 19/15, 30/19
• 33/26, 52/33
• 14/11, 11/7
• 23/18, 36/23
• 32/25, 25/16
• 9/7, 14/9
• 40/31, 31/20
• 31/24, 48/31
• 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
• 33/25, 50/33
• 4/3, 3/2
• 31/23, 46/31
• 27/20, 40/27
• 23/17, 34/23
• 42/31, 31/21
• 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
• 46/33, 33/23
• 7/5, 10/7
• 38/27, 27/19
• 31/22, 44/31
• 24/17, 17/12

Ratio	Size (¢)	Color name		Name
34/33	51.682	solu 2nd	17o1u2	greater septendecimal quartertone
33/32	53.273	ilo unison	1o1	undecimal quartertone
33/31	108.237	thiwulo 2nd	31u1o2	trigesimoprimal semitone
33/29	223.696	twenulo 2nd	29u1o2	vigesimononal whole tone
38/33	244.24	nolu 3rd	19o1u3	undevigesimal inframinor third
33/28	284.447	loru 2nd	1or2	undecimal ultramajor second
40/33	333.041	luyo 3rd	1uy3	undecimal supraminor third
33/26	412.745	lothu 3rd	1o3u3	tridecimal major third, major minthmic major third
33/25	480.646	logugu 4th	1ogg4	undecimal grave fourth
46/33	575.001	twetholu 5th	23o1u5	preziosismic vigesimotertial narrow tritone
33/23	624.999	twethulo 4th	23u1o4	preziosismic vigesimotertial wide tritone
50/33	719.354	luyoyo 5th	1uyy5	undecimal acute fifth
52/33	787.255	lutho 6th	1u3o6	tridecimal minor sixth, major minthmic minor sixth
33/20	866.959	logu 6th	1og6	undecimal submajor sixth
56/33	915.553	luzo 7th	1uz7	undecimal inframinor seventh
33/19	955.76	nulo 6th	19u1o6	undevigesimal ultramajor sixth
58/33	976.304	twenolu 2nd	29o1u7	vigesimononal minor seventh
62/33	1091.763	thiwolu 7th	31o1u7	trigesimoprimal major seventh
64/33	1146.727	ilu octave	1u8	undecimal infraoctave
33/17	1148.318	sulo 7th	17u1o7	lesser septendecimal infraoctave

The smallest equal division of the octave which is consistent to the 33-odd-limit is 311edo (by virtue of it being consistent through the 41-odd-limit); that which is distinctly consistent to the same is 1600edo (by virtue of it being distinctly consistent through the 37-odd-limit).