List of meantone intervals

The following is a list of intervals of extended meantone temperament. These intervals constitute the standard vocabulary of intervals for the Western common practice era. Here 12-EDO refers to the size of the interval in 12 equal divisions of the octave temperament, which is the most common meantone temperament of the modern era, 19-EDO to 19 equal temperament, 31-EDO to 31 equal temperament, and 50-EDO to 50 equal temperament. Note that several of the intervals for 31-EDO and 50-EDO are absent from the table.

In How Equal Temperament Ruined Harmony (and Why You Should Care), pp. 91–92, Ross W. Duffin states: "specifying that the major semitone should be 3/2 the minor semitone [a 3:2 ratio] creates a 31-note division of the octave, which, in turn, closely corresponds to extended-quarter-comma meantone... the 5:4 ratio [whose] extended-sixth-comma meantone corresponds to the 55-division... extended-fifth-comma meantone [corresponds to] the 43-division of the octave [in which the] ratio of the major to minor semitone is 4:3." The other meantone correspondencies: a 1:1 ratio producing a 12-division (1/11-comma meantone)... "2:1 [which] results in a 19-division (1/3-comma meantone)... 5:3, which results in a 50-division" (2/7-comma meantone) are derived from these statements. [Brackets added for readability.]

The column of ratios gives a ratio or ratios approximated by the interval in septimal meantone temperament. An augmented interval is increased by a chromatic semitone, and a diminished interval decreased.

12-EDO (≈1/11c)		Quarter- comma	19-EDO (≈1/3c)		31-EDO (≈1/4c)		50-EDO (≈2/7c)		Note (from C)	Roman No.	Name	Classic ratios	Septimal ratios
Steps	Cents	Cents	Steps	Cents	Steps	Cents	Steps	Cents
0	0	0.00	0	0.00	0	0.00	0	0	C	I	Unison	1:1
		41.06	1	63.16	1	38.71	2	48	D	II	Diminished second	128:125	36:35
1	100	76.05			2	77.42	3	72	C♯	♯I	Chromatic semitone	25:24	21:20
		117.11	2	126.32	3	116.13	5	120	D♭	♭II	Minor second	16:15, 27:25	15:14
2	200	193.16	3	189.47	5	193.55	8	192	D	II	Whole tone	9:8, 10:9
		234.22	4	252.63	6	232.26	10	240	E	III	Diminished third	144:125	8:7
3	300	269.21			7	270.97	11	264	D♯	♯II	Augmented second	75:64, 125:108	7:6
		310.26	5	315.79	8	309.68	13	312	E♭	♭III	Minor third	6:5, 32:27
4	400	386.31	6	378.95	10	387.10	16	384	E	III	Major third	5:4
		427.37	7	442.11	11	425.81	18	432	F♭	♭IV	Diminished fourth	32:25	9:7
5	500	462.36			12	464.52	19	456	E♯	♯III	Augmented third	125:96	21:16
		503.42	8	505.26	13	503.23	21	504	F	IV	Perfect fourth	4:3, 27:20
6	600	579.47	9	568.42	15	580.65	24	576	F♯	♯IV	Augmented fourth	25:18, 45:32	7:5
		620.53	10	631.58	16	619.35	26	624	G♭	♭V	Diminished fifth	36:25, 64:45	10:7
7	700	696.58	11	694.74	18	696.77	29	696	G	V	Perfect fifth	3:2, 40:27
		737.64	12	757.89	19	735.48	31	744	A	VI	Diminished sixth	192:125	32:21
8	800	772.63			20	774.19	32	768	G♯	♯V	Augmented fifth	25:16	14:9
		813.69	13	821.05	21	812.90	34	816	A♭	♭VI	Minor sixth	8:5
9	900	889.74	14	884.21	23	890.32	37	888	A	VI	Major sixth	5:3, 27:16
		930.79	15	947.37	24	929.03	39	936	B	VII	Diminished seventh	128:75, 216:125	12:7
10	1000	965.78			25	967.74	40	960	A♯	♯VI	Augmented sixth	125:72	7:4
		1006.84	16	1010.53	26	1006.45	42	1008	B♭	♭VII	Minor seventh	9:5, 16:9
11	1100	1082.89	17	1073.68	28	1083.87	45	1080	B	VII	Major seventh	15:8, 50:27	28:15
		1123.95	18	1136.84	29	1122.58	47	1128	C♭	♭VIII	Diminished octave	48:25	40:21
12	1200	1158.94			30	1161.29	48	1152	B♯	♯VII	Augmented seventh	125:64	35:18
		1200.00	19	1200.00	31	1200.00	50	1200	C	VIII	Octave	2:1

See also

• List of musical intervals
• List of pitch intervals