21-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 21-odd-limit is the set of all rational intervals for which neither the numerator nor the denominator of the frequency ratio exceeds 21, once all powers of 2 are removed. To the 19-odd-limit, it adds 6 interval pairs involving 21.

Below is a list of all octave-reduced intervals in the 21-odd-limit.

• 1/1
• 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
• 12/11, 11/6
• 11/10, 20/11
• 21/19, 38/21
• 10/9, 9/5
• 19/17, 34/19
• 9/8, 16/9
• 17/15, 30/17
• 8/7, 7/4
• 15/13, 26/15
• 22/19, 19/11
• 7/6, 12/7
• 20/17, 17/10
• 13/11, 22/13
• 19/16, 32/19
• 6/5, 5/3
• 17/14, 28/17
• 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
• 9/7, 14/9
• 22/17, 17/11
• 13/10, 20/13
• 17/13, 26/17
• 21/16, 32/21
• 4/3, 3/2
• 19/14, 28/19
• 15/11, 22/15
• 26/19, 19/13
• 11/8, 16/11
• 18/13, 13/9
• 7/5, 10/7
• 24/17, 17/12

Ratio	Size (¢)	Color name		Name(s)
22/21	80.537	1or1	loru unison	undecimal chromatic semitone
21/20	84.467	zg2	zogu 2nd	septimal chromatic semitone / greater septimal chroma
21/19	173.268	19uz2	nuzo 2nd	small undevicesimal whole tone
21/17	365.825	17uz3	suzo 3rd	septendecimal submajor third
26/21	369.747	3or3	thoru 3rd	tridecimal submajor third
21/16	470.781	z4	zo 4th	septimal sub-fourth
32/21	729.219	r5	ru 5th	septimal super-fifth
21/13	830.253	3uz6	thuzo 6th	tridecimal supraminor sixth
34/21	834.175	17or6	soru 6th	septendecimal supraminor sixth
38/21	1026.732	19or7	noru 7th	large undevicesimal minor seventh
40/21	1115.533	ry7	ruyo 7th	large septimal major seventh
21/11	1119.463	1uz8	luzo octave	undecimal diminished octave

The smallest equal division of the octave which is consistent in the 21-odd-limit is 94edo (by virtue of it being consistent through the 23-odd-limit); that which is distinctly consistent in the same is 282edo (by virtue of it being distinctly consistent through the 23-odd-limit as well).