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
|
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
|
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
|
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
|
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 |