27-odd-limit

Odd limit

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← 25-odd-limit  27-odd-limit  29-odd-limit →

The 27-odd-limit is the set of all rational intervals which can be written as 2^k(a/b) where a, b ≤ 27 and k is an integer. To the 25-odd-limit, it adds 9 pairs of octave-reduced intervals involving 27.

Below is a list of all octave-reduced intervals in the 27-odd-limit.

• 1/1
• 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
• 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
• 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
• 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
• 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
• 5/4, 8/5
• 34/27, 27/17
• 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
• 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
• 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
28/27	62.961	z2	zo 2nd	septimal third-tone
27/26	65.337	3u1	thu unison	lesser tridecimal chroma small tridecimal third-tone
27/25	133.238	gg2	gugu 2nd	large limma acute semitone
27/23	277.591	23u2	twethu 2nd	vicesimotertial augmented second
32/27	294.135	w3	wa 3rd	Pythagorean minor third
27/22	354.547	1u3	lu 3rd	rastmic neutral third
34/27	399.090	17o4	iso 4th	septendecimal major third quasi-tempered major third
27/20	519.551	g4	gu 4th	acute fourth wolf fourth
38/27	591.648	19o5	ino 5th	undevicesimal narrow tritone
27/19	608.352	19u4	inu 4th	undevicesimal high tritone
40/27	680.449	y5	yo 5th	grave fifth wolf fifth
27/17	800.910	17u5	su 5th	septendecimal minor sixth quasi-tempered minor sixth
44/27	845.453	1o6	ilo 6th	rastmic neutral sixth
27/16	905.865	w6	wa 6th	Pythagorean major sixth
46/27	922.409	23o7	twetho 7th	vicesimotertial diminished seventh
50/27	1066.762	yy7	yoyo 7th	grave major seventh
52/27	1134.663	3o8	tho octave	greater tridecimal diminished octave
27/14	1137.039	r7	ru 7th	septimal supermajor seventh

The smallest equal division of the octave that comes closest to being consistent in the 27-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.