List of meantone intervals
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The following is a list of intervals of 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, and 31-EDO to 31 equal temperament.
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 | 19-EDO | 31-EDO | Note spelling (from C) |
Roman No. |
Name | Just intonation ratios |
|||
|---|---|---|---|---|---|---|---|---|---|
| Steps | Cents | Steps | Cents | Steps | Cents | ||||
| 0 |
0.00
|
0 |
0.00
|
0 |
0.00
|
C | I | Unison | 1:1, 81:80, 126:125 |
| 1 |
38.71
|
D |
II |
Diminished second or Diesis | 128:125, 36:35 | ||||
| 1 |
100.0
|
1 |
63.16
|
2 |
77.42
|
C♯ | ♯I | Augmented unison or Chromatic semitone | 21:20, 25:24 |
| 2 |
126.32
|
3 |
116.13
|
D♭ | ♭II | Minor second or Diatonic semitone | 15:14, 16:15 | ||
| 2 |
200.0
|
3 |
189.47
|
5 |
193.55
|
D | II | Major second or tone | 9:8, 10:9 |
| 4 |
252.63
|
6 |
232.26
|
E |
III |
Diminished third | 8:7 | ||
| 3 |
300.0
|
7 |
270.97
|
D♯ | ♯II | Augmented second | 7:6 | ||
| 5 |
315.79
|
8 |
309.68
|
E♭ | ♭III | Minor third | 6:5 | ||
| 4 |
400.0
|
6 |
378.95
|
10 |
387.10
|
E | III | Major third | 5:4 |
| 7 |
442.11
|
11 |
425.81
|
F♭ | ♭IV | Diminished fourth | 9:7 | ||
| 5 |
500.0
|
12 |
464.52
|
E♯ | ♯III | Augmented third | 21:16 | ||
| 8 |
505.26
|
13 |
503.23
|
F | IV | Perfect fourth | 4:3 | ||
| 6 |
600.0
|
9 |
568.42
|
15 |
580.65
|
F♯ | ♯IV | Augmented fourth or Tritone | 7:5 |
| 10 |
631.58
|
16 |
619.35
|
G♭ | ♭V | Diminished fifth | 10:7 | ||
| 7 |
700.0
|
11 |
694.74
|
18 |
696.77
|
G | V | Perfect fifth | 3:2 |
| 12 |
757.89
|
19 |
735.48
|
A |
VI |
Diminished sixth or Wolf fifth | 32:21 | ||
| 8 |
800.0
|
20 |
774.19
|
G♯ | ♯V | Augmented fifth | 14:9 | ||
| 13 |
821.05
|
21 |
812.90
|
A♭ | ♭VI | Minor sixth | 8:5 | ||
| 9 |
900.0
|
14 |
884.21
|
23 |
890.32
|
A | VI | Major sixth | 5:3 |
| 15 |
947.37
|
24 |
929.03
|
B |
VII |
Diminished seventh | 12:7 | ||
| 10 |
1000.0
|
25 |
967.74
|
A♯ | ♯VI | Augmented sixth | 7:4 | ||
| 16 |
1010.53
|
26 |
1006.45
|
B♭ | ♭VII | Minor seventh | 9:5, 16:9 | ||
| 11 |
1100.0
|
17 |
1073.68
|
28 |
1083.87
|
B | VII | Major seventh | 15:8, 28:15 |
| 18 |
1136.84
|
29 |
1122.58
|
C♭ | ♭VIII | Diminished octave | 48:25 | ||
| 12 |
1200.00
|
19 |
1200.00
|
30 |
1161.29
|
B♯ | ♯VII | Augmented seventh | 125:64 |
| 31 |
1200.00
|
C | VIII | Octave or diapason | 2:1 | ||||
