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
 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
 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
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
VIII
 Octave 2:1

See also

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