25-odd-limit

Odd limit

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← 23-odd-limit  25-odd-limit  27-odd-limit →

The 25-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 25 and k is an integer. To the 23-odd-limit, it adds 10 pairs of octave-reduced intervals involving 25.

Below is a list of all octave-reduced intervals in the 25-odd-limit.

• 1/1
• 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
• 14/13, 13/7
• 13/12, 24/13
• 25/23, 46/25
• 12/11, 11/6
• 23/21, 42/23
• 11/10, 20/11
• 21/19, 38/21
• 10/9, 9/5
• 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
• 7/6, 12/7
• 20/17, 17/10
• 13/11, 22/13
• 19/16, 32/19
• 25/21, 42/25
• 6/5, 5/3
• 23/19, 38/23
• 17/14, 28/17
• 28/23, 23/14
• 11/9, 18/11
• 16/13, 13/8
• 21/17, 34/21
• 26/21, 21/13
• 5/4, 8/5
• 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
• 21/16, 32/21
• 25/19, 38/25
• 4/3, 3/2
• 23/17, 34/23
• 19/14, 28/19
• 34/25, 25/17
• 15/11, 22/15
• 26/19, 19/13
• 11/8, 16/11
• 18/13, 13/9
• 25/18, 36/25
• 32/23, 23/16
• 7/5, 10/7
• 24/17, 17/12

Ratio	Size (¢)	Color name		Name
26/25	67.900	3ogg	thogugu 2nd	greater tridecimal chroma large tridecimal third-tone
25/24	70.672	yy1	yoyo unison	classic chromatic semitone
25/23	144.353	23uyy2	twethuyoyo 2nd	small vicesimotertial neutral second
28/25	196.198	zgg3	zogugu 3rd	septimal middle major second sepimal middle whole tone
25/22	221.309	1uyy2	luyoyo 2nd	undecimal acute major second undecimal acute whole tone
25/21	301.847	ryy2	ruyoyo 2nd	septimal quasi-tempered minor third
32/25	427.373	gg4	gugu 4th	classic diminished fourth
25/19	475.114	19uyy3	nuyoyo 3rd	undevicesimal augmented third undevicesimal grave fourth
34/25	532.328	17ogg5	sogugu 5th	septendecimal acute fourth
25/18	568.717	yy4	yoyo 4th	classic narrow tritone classic augmented fourth
36/25	631.283	gg5	gugu 5th	classic high tritone classic diminished fifth
25/17	667.672	17uyy4	suyoyo 4th	septendecimal grave fifth
38/25	724.886	19ogg6	nogugu 6th	undevicesimal diminished sixth undevicesimal acute fifth
25/16	772.627	yy5	yoyo 5th	classic augmented fifth
42/25	898.153	zgg7	zogugu 7th	septimal quasi-tempered major sixth
44/25	978.691	1ogg7	logugu 7th	undecimal grave minor seventh
25/14	1003.802	ryy6	ruyoyo 6th	septimal middle minor seventh
46/25	1055.647	23ogg7	twethogugu 7th	large vicesimotertial neutral seventh
48/25	1129.328	gg8	gugu octave	classic diminished octave
25/13	1132.100	3uyy7	thuyoyo 7th	lesser tridecimal diminished octave

The smallest equal division of the octave that comes closest to being consistent in the 25-odd-limit is 217edo (misses 23/14, 23/21, 28/23, 42/23).

The one which is truly consistent is 282edo (by virtue of it being consistent through the 29-odd-limit)

The one which is distinctly consistent in the same is 388edo (by virtue of it being distinctly consistent through the 27-odd-limit).