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 ![]() |
![]() |
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 ![]() |
![]() |
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 ![]() |
![]() |
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 ![]() |
![]() |
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[]
- Intervals (music)
- Linear temperaments
- Music theory lists