List of meantone intervals
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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 Template:Sfrac the minor semitone Template:Grey creates a 31 note division of the octave, which, in turn, closely corresponds to extended-quarter-comma meantone ... the 5:4 ratio Template:Grey extended-sixth-comma meantone corresponds to the 55 division ... extended-fifth-comma meantone Template:Grey the 43 division of the octave Template:Grey ratio of the major to minor semitone is 4:3."
The other meantone correspondencies:
- "a 1:1 ratio produces a 12 division" (Template:Sfrac comma meantone)
- "2:1 Template:Grey results in a 19 division" (Template:Sfrac comma meantone)
- "5:3, which results in a 50 division" (Template:Sfrac comma meantone)
are derived from these statements.[1]
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 (≈Template:Sfrac c) |
Quarter- comma |
19 EDO (≈Template:Sfracc) |
31 EDO (≈Template:Sfracc) |
50 EDO (≈Template:Sfracc) |
Note (from C) |
Roman numeral |
Name | Classic ratios |
Septimal ratios | ||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| steps | cents | cents | steps | cents | steps | cents | steps | cents | |||||
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Script error: No such module "Check for unknown parameters". | Unison | 1:1 | |
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38.71 Script error: No such module "Check for unknown parameters".
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48 Script error: No such module "Check for unknown parameters".
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Script error: No such module "Check for unknown parameters". | Script error: No such module "Check for unknown parameters". | Diminished second | 128:125 | 36:35 | ||
1 Script error: No such module "Check for unknown parameters".
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100 Script error: No such module "Check for unknown parameters".
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76.05 Script error: No such module "Check for unknown parameters".
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2 Script error: No such module "Check for unknown parameters".
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77.42 Script error: No such module "Check for unknown parameters".
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72 Script error: No such module "Check for unknown parameters".
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C♯ Script error: No such module "Check for unknown parameters".
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Chromatic semitone | 25:24 | 21:20 | ||
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126.32 Script error: No such module "Check for unknown parameters".
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116.13 Script error: No such module "Check for unknown parameters".
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120 Script error: No such module "Check for unknown parameters".
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Minor second | 16:15, 27:25 | 15:14 | ||
2 Script error: No such module "Check for unknown parameters". |
200 Script error: No such module "Check for unknown parameters". |
193.16 Script error: No such module "Check for unknown parameters". |
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189.47 Script error: No such module "Check for unknown parameters". |
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193.55 Script error: No such module "Check for unknown parameters". |
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192 Script error: No such module "Check for unknown parameters". |
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Whole tone | 9:8, 10:9 | |
234.22 Script error: No such module "Check for unknown parameters". |
4 Script error: No such module "Check for unknown parameters". |
252.63 Script error: No such module "Check for unknown parameters". |
6 Script error: No such module "Check for unknown parameters". |
232.26 Script error: No such module "Check for unknown parameters". |
10 Script error: No such module "Check for unknown parameters". |
240 Script error: No such module "Check for unknown parameters". |
Script error: No such module "Check for unknown parameters". | double flatIII Script error: No such module "Check for unknown parameters". |
Diminished third | 144:125 | 8:7 | ||
3 Script error: No such module "Check for unknown parameters". |
300 Script error: No such module "Check for unknown parameters". |
269.21 Script error: No such module "Check for unknown parameters". |
7 Script error: No such module "Check for unknown parameters". |
270.97 Script error: No such module "Check for unknown parameters". |
11 Script error: No such module "Check for unknown parameters". |
264 Script error: No such module "Check for unknown parameters". |
D♯ Script error: No such module "Check for unknown parameters". |
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Augmented second | 75:64, 125:108 | 7:6 | ||
310.26 Script error: No such module "Check for unknown parameters". |
5 Script error: No such module "Check for unknown parameters". |
315.79 Script error: No such module "Check for unknown parameters". |
8 Script error: No such module "Check for unknown parameters". |
309.68 Script error: No such module "Check for unknown parameters". |
13 Script error: No such module "Check for unknown parameters". |
312 Script error: No such module "Check for unknown parameters". |
E♭ Script error: No such module "Check for unknown parameters". |
♭III Script error: No such module "Check for unknown parameters". |
Minor third | 6:5, 32:27 | |||
4 Script error: No such module "Check for unknown parameters". |
400 Script error: No such module "Check for unknown parameters". |
386.31 Script error: No such module "Check for unknown parameters". |
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378.95 Script error: No such module "Check for unknown parameters". |
10 Script error: No such module "Check for unknown parameters". |
387.10 Script error: No such module "Check for unknown parameters". |
16 Script error: No such module "Check for unknown parameters". |
384 Script error: No such module "Check for unknown parameters". |
E Script error: No such module "Check for unknown parameters". |
Script error: No such module "Check for unknown parameters". | Major third | 5:4 | |
427.37 Script error: No such module "Check for unknown parameters". |
7 Script error: No such module "Check for unknown parameters". |
442.11 Script error: No such module "Check for unknown parameters". |
11 Script error: No such module "Check for unknown parameters". |
425.81 Script error: No such module "Check for unknown parameters". |
18 Script error: No such module "Check for unknown parameters". |
432 Script error: No such module "Check for unknown parameters". |
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Diminished fourth | 32:25 | 9:7 | ||
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500 Script error: No such module "Check for unknown parameters". |
462.36 Script error: No such module "Check for unknown parameters". |
12 Script error: No such module "Check for unknown parameters". |
464.52 Script error: No such module "Check for unknown parameters". |
19 Script error: No such module "Check for unknown parameters". |
456 Script error: No such module "Check for unknown parameters". |
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Augmented third | 125:96 | 21:16 | ||
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F Script error: No such module "Check for unknown parameters". |
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Perfect fourth | 4:3, 27:20 | |||
6 Script error: No such module "Check for unknown parameters". |
600 Script error: No such module "Check for unknown parameters". |
579.47 Script error: No such module "Check for unknown parameters". |
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568.42 Script error: No such module "Check for unknown parameters". |
15 Script error: No such module "Check for unknown parameters". |
580.65 Script error: No such module "Check for unknown parameters". |
24 Script error: No such module "Check for unknown parameters". |
576 Script error: No such module "Check for unknown parameters". |
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Augmented fourth | 25:18, 45:32 | 7:5 |
620.53 Script error: No such module "Check for unknown parameters". |
10 Script error: No such module "Check for unknown parameters". |
631.58 Script error: No such module "Check for unknown parameters". |
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619.35 Script error: No such module "Check for unknown parameters". |
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624 Script error: No such module "Check for unknown parameters". |
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Diminished fifth | 36:25, 64:45 | 10:7 | ||
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696.77 Script error: No such module "Check for unknown parameters". |
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G Script error: No such module "Check for unknown parameters". |
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Perfect fifth | 3:2, 40:27 | |
737.64 Script error: No such module "Check for unknown parameters". |
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19 Script error: No such module "Check for unknown parameters". |
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Script error: No such module "Check for unknown parameters". | Script error: No such module "Check for unknown parameters". | Diminished sixth | 192:125 | 32:21 | ||
8 Script error: No such module "Check for unknown parameters". |
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768 Script error: No such module "Check for unknown parameters". |
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Augmented fifth | 25:16 | 14:9 | ||
813.69 Script error: No such module "Check for unknown parameters". |
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821.05 Script error: No such module "Check for unknown parameters". |
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812.90 Script error: No such module "Check for unknown parameters". |
34 Script error: No such module "Check for unknown parameters". |
816 Script error: No such module "Check for unknown parameters". |
A♭ Script error: No such module "Check for unknown parameters". |
♭VI Script error: No such module "Check for unknown parameters". |
Minor sixth | 8:5 | |||
9 Script error: No such module "Check for unknown parameters". |
900 Script error: No such module "Check for unknown parameters". |
889.74 Script error: No such module "Check for unknown parameters". |
14 Script error: No such module "Check for unknown parameters". |
884.21 Script error: No such module "Check for unknown parameters". |
23 Script error: No such module "Check for unknown parameters". |
890.32 Script error: No such module "Check for unknown parameters". |
37 Script error: No such module "Check for unknown parameters". |
888 Script error: No such module "Check for unknown parameters". |
A Script error: No such module "Check for unknown parameters". |
Script error: No such module "Check for unknown parameters". | Major sixth | 5:3, 27:16 | |
930.79 Script error: No such module "Check for unknown parameters". |
15 Script error: No such module "Check for unknown parameters". |
947.37 Script error: No such module "Check for unknown parameters". |
24 Script error: No such module "Check for unknown parameters". |
929.03 Script error: No such module "Check for unknown parameters". |
39 Script error: No such module "Check for unknown parameters". |
936 Script error: No such module "Check for unknown parameters". |
Script error: No such module "Check for unknown parameters". | double flatVII Script error: No such module "Check for unknown parameters". |
Diminished seventh | 128:75, 216:125 | 12:7 | ||
10 Script error: No such module "Check for unknown parameters". |
1000 Script error: No such module "Check for unknown parameters". |
965.78 Script error: No such module "Check for unknown parameters". |
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40 Script error: No such module "Check for unknown parameters". |
960 Script error: No such module "Check for unknown parameters". |
A♯ Script error: No such module "Check for unknown parameters". |
♯VI Script error: No such module "Check for unknown parameters". |
Augmented sixth | 125:72 | 7:4 | ||
1006.84 Script error: No such module "Check for unknown parameters". |
16 Script error: No such module "Check for unknown parameters". |
1010.53 Script error: No such module "Check for unknown parameters". |
26 Script error: No such module "Check for unknown parameters". |
1006.45 Script error: No such module "Check for unknown parameters". |
42 Script error: No such module "Check for unknown parameters". |
1008 Script error: No such module "Check for unknown parameters". |
B♭ Script error: No such module "Check for unknown parameters". |
♭VII Script error: No such module "Check for unknown parameters". |
Minor seventh | 9:5, 16:9 | |||
11 Script error: No such module "Check for unknown parameters". |
1100 Script error: No such module "Check for unknown parameters". |
1082.89 Script error: No such module "Check for unknown parameters". |
17 Script error: No such module "Check for unknown parameters". |
1073.68 Script error: No such module "Check for unknown parameters". |
28 Script error: No such module "Check for unknown parameters". |
1083.87 Script error: No such module "Check for unknown parameters". |
45 Script error: No such module "Check for unknown parameters". |
1080 Script error: No such module "Check for unknown parameters". |
Script error: No such module "Check for unknown parameters". | VII Script error: No such module "Check for unknown parameters". |
Major seventh | 15:8, 50:27 | 28:15 |
1123.95 Script error: No such module "Check for unknown parameters". |
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1136.84 Script error: No such module "Check for unknown parameters". |
29 Script error: No such module "Check for unknown parameters". |
1122.58 Script error: No such module "Check for unknown parameters". |
47 Script error: No such module "Check for unknown parameters". |
1128 Script error: No such module "Check for unknown parameters". |
C♭ Script error: No such module "Check for unknown parameters". |
♭VIII Script error: No such module "Check for unknown parameters". |
Diminished octave | 48:25 | 40:21 | ||
12 Script error: No such module "Check for unknown parameters". |
1200 Script error: No such module "Check for unknown parameters". |
1158.94 Script error: No such module "Check for unknown parameters". |
30 Script error: No such module "Check for unknown parameters". |
1161.29 Script error: No such module "Check for unknown parameters". |
48 Script error: No such module "Check for unknown parameters". |
1152 Script error: No such module "Check for unknown parameters". |
B♯ Script error: No such module "Check for unknown parameters". |
♯VII Script error: No such module "Check for unknown parameters". |
Augmented seventh | 125:64 | 35:18 | ||
1200.00 Script error: No such module "Check for unknown parameters". |
19 Script error: No such module "Check for unknown parameters". |
1200.00 Script error: No such module "Check for unknown parameters". |
31 Script error: No such module "Check for unknown parameters". |
1200.00 Script error: No such module "Check for unknown parameters". |
50 Script error: No such module "Check for unknown parameters". |
1200 Script error: No such module "Check for unknown parameters". |
Script error: No such module "Check for unknown parameters". | VIII Script error: No such module "Check for unknown parameters". |
Octave | 2:1 | |||
See also
Script error: No such module "Navbox". Template:Music theory lists
References
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- ↑ Script error: No such module "citation/CS1".
Script error: No such module "Check for unknown parameters".