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 the temperament with 12 equal divisions of the octave, which is the most common meantone temperament in the modern era, 19 EDO to 19 equal temperament, 31 EDO to 31 equal temperament, and 50 EDO to 50 equal temperament. Note that for brevity, several of the intervals for 31 EDO and 50 EDO are omitted from the table.
R.W. Duffin writes:
"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 produces 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.[1][full citation needed]
[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/ 11 c)
Quarter- comma
19 EDO (≈1/ 3 c)
31 EDO (≈1/ 4 c)
50 EDO (≈2/ 7 c)
Note (from C)
Roman numeral
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
^Duffin, R.W. How Equal Temperament Ruined Harmony (and why you should care). pp. 91–92.
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