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 {{sfrac| 3 | 2 }} the minor semitone {{grey|[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 {{grey|[whose]}} extended-sixth-comma meantone corresponds to the 55 division ... extended-fifth-comma meantone {{grey|[corresponds to]}} the 43 division of the octave {{grey|[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" ({{sfrac| 1 | 11 }} comma meantone)

: "2:1 {{grey|[which]}} results in a 19 division" ({{sfrac| 1 | 3 }} comma meantone)

: "5:3, which results in a 50 division" ({{sfrac| 2 | 7 }} comma meantone)

are derived from these statements.{{cite book |author-link=Ross W. Duffin |first=R.W. |last=Duffin |year=2007 |title=How Equal Temperament Ruined Harmony (and why you should care) |place=New York, NY |publisher=W.W. Norton |pages=91–92 }}

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.

class="wikitable"

style="text-align:center;background:lightgrey;" |colspan=2| 12 EDO (≈{{sfrac|1| 11 }} c) ! Quarter- comma |colspan=2| 19 EDO (≈{{sfrac|1| 3 }}c) |colspan=2| 31 EDO (≈{{sfrac|1| 4 }}c) |colspan=2| 50 EDO (≈{{sfrac|2| 7 }}c) !rowspan=2| Note (from C) !rowspan=2| Roman numeral !rowspan=2| Name !rowspan=2| Classic ratios !rowspan=2| Septimal ratios

style="text-align:center;background:lightgrey;" | steps

cents

cents

steps

cents

steps

cents

steps

cents

rowspan=2| {{center|0}} |rowspan=2| {{center|0}} | {{center|0.00}} | {{center|0}} | {{center|0.00}} | {{center|0}} | {{center|0.00}} | {{center|0}} | {{center|0}} | {{center|C}} | {{center|I}} | Unison | 1:1

{{center|41.06}} |rowspan=2| {{center|1}} |rowspan=2| {{center|63.16}} | {{center|1}} | {{center|38.71}} | {{center|2}} | {{center|48}} | {{center|D{{music|bb}}}} | {{center|{{music|bb}}II}} | Diminished second | 128:125 | 36:35

rowspan=2| {{center|1}} | rowspan=2|{{center|100}} | {{center|76.05}} | {{center|2}} | {{center|77.42}} | {{center|3}} | {{center|72}} | {{center|C{{music|#}}}} | {{center|{{music|#}}I}} | Chromatic semitone | 25:24 | 21:20

{{center|117.11}} | {{center|2}} | {{center|126.32}} | {{center|3}} | {{center|116.13}} | {{center|5}} | {{center|120}} | {{center|D{{music|b}}}} | {{center|{{music|b}}II}} | Minor second | 16:15, 27:25 | 15:14

rowspan=2|{{center|2}}

rowspan=2|{{center|200}}

{{center|193.16}}

{{center|3}}

{{center|189.47}}

{{center|5}}

{{center|193.55}}

{{center|8}}

{{center|192}}

{{center|D}}

{{center|II}}

Whole tone

9:8, 10:9

{{center|234.22}}

rowspan=2|{{center|4}}

rowspan=2|{{center|252.63}}

{{center|6}}

{{center|232.26}}

{{center|10}}

{{center|240}}

{{center|E{{music|bb}}}}

{{center|{{music|bb}}III}}

Diminished third

144:125

8:7

rowspan=2|{{center|3}}

rowspan=2|{{center|300}}

{{center|269.21}}

{{center|7}}

{{center|270.97}}

{{center|11}}

{{center|264}}

{{center|D{{music|#}}}}

{{center|{{music|#}}II}}

Augmented second

75:64, 125:108

7:6

{{center|310.26}}

{{center|5}}

{{center|315.79}}

{{center|8}}

{{center|309.68}}

{{center|13}}

{{center|312}}

{{center|E{{music|b}}}}

{{center|{{music|b}}III}}

Minor third

6:5, 32:27

rowspan=2|{{center|4}}

rowspan=2|{{center|400}}

{{center|386.31}}

{{center|6}}

{{center|378.95}}

{{center|10}}

{{center|387.10}}

{{center|16}}

{{center|384}}

{{center|E}}

{{center|III}}

Major third

5:4

{{center|427.37}}

rowspan=2|{{center|7}}

rowspan=2|{{center|442.11}}

{{center|11}}

{{center|425.81}}

{{center|18}}

{{center|432}}

{{center|F{{music|b}}}}

{{center|{{music|b}}IV}}

Diminished fourth

32:25

9:7

rowspan=2|{{center|5}}

rowspan=2|{{center|500}}

{{center|462.36}}

{{center|12}}

{{center|464.52}}

{{center|19}}

{{center|456}}

{{center|E{{music|#}}}}

{{center|{{music|#}}III}}

Augmented third

125:96

21:16

{{center|503.42}}

{{center|8}}

{{center|505.26}}

{{center|13}}

{{center|503.23}}

{{center|21}}

{{center|504}}

{{center|F}}

{{center|IV}}

Perfect fourth

4:3, 27:20

rowspan=2|{{center|6}}

rowspan=2|{{center|600}}

{{center|579.47}}

{{center|9}}

{{center|568.42}}

{{center|15}}

{{center|580.65}}

{{center|24}}

{{center|576}}

{{center|F{{music|#}}}}

{{center|{{music|#}}IV}}

Augmented fourth

25:18, 45:32

7:5

{{center|620.53}}

{{center|10}}

{{center|631.58}}

{{center|16}}

{{center|619.35}}

{{center|26}}

{{center|624}}

{{center|G{{music|b}}}}

{{center|{{music|b}}V}}

Diminished fifth

36:25, 64:45

10:7

rowspan=2|{{center|7}}

rowspan=2|{{center|700}}

{{center|696.58}}

{{center|11}}

{{center|694.74}}

{{center|18}}

{{center|696.77}}

{{center|29}}

{{center|696}}

{{center|G}}

{{center|V}}

Perfect fifth

3:2, 40:27

{{center|737.64}}

rowspan=2|{{center|12}}

rowspan=2|{{center|757.89}}

{{center|19}}

{{center|735.48}}

{{center|31}}

{{center|744}}

{{center|A{{music|bb}}}}

{{center|{{music|bb}}VI}}

Diminished sixth

192:125

32:21

rowspan=2|{{center|8}}

rowspan=2|{{center|800}}

{{center|772.63}}

{{center|20}}

{{center|774.19}}

{{center|32}}

{{center|768}}

{{center|G{{music|#}}}}

{{center|{{music|#}}V}}

Augmented fifth

25:16

14:9

{{center|813.69}}

{{center|13}}

{{center|821.05}}

{{center|21}}

{{center|812.90}}

{{center|34}}

{{center|816}}

{{center|A{{music|b}}}}

{{center|{{music|b}}VI}}

Minor sixth

8:5

rowspan=2|{{center|9}}

rowspan=2|{{center|900}}

{{center|889.74}}

{{center|14}}

{{center|884.21}}

{{center|23}}

{{center|890.32}}

{{center|37}}

{{center|888}}

{{center|A}}

{{center|VI}}

Major sixth

5:3, 27:16

{{center|930.79}}

rowspan=2|{{center|15}}

rowspan=2|{{center|947.37}}

{{center|24}}

{{center|929.03}}

{{center|39}}

{{center|936}}

{{center|B{{music|bb}}}}

{{center|{{music|bb}}VII}}

Diminished seventh

128:75, 216:125

12:7

rowspan=2|{{center|10}}

rowspan=2|{{center|1000}}

{{center|965.78}}

{{center|25}}

{{center|967.74}}

{{center|40}}

{{center|960}}

{{center|A{{music|#}}}}

{{center|{{music|#}}VI}}

Augmented sixth

125:72

7:4

{{center|1006.84}}

{{center|16}}

{{center|1010.53}}

{{center|26}}

{{center|1006.45}}

{{center|42}}

{{center|1008}}

{{center|B{{music|b}}}}

{{center|{{music|b}}VII}}

Minor seventh

9:5, 16:9

rowspan=2|{{center|11}}

rowspan=2|{{center|1100}}

{{center|1082.89}}

{{center|17}}

{{center|1073.68}}

{{center|28}}

{{center|1083.87}}

{{center|45}}

{{center|1080}}

{{center|B}}

{{center|VII}}

Major seventh

15:8, 50:27

28:15

{{center|1123.95}}

rowspan=2|{{center|18}}

rowspan=2|{{center|1136.84}}

{{center|29}}

{{center|1122.58}}

{{center|47}}

{{center|1128}}

{{center|C{{music|b}}}}

{{center|{{music|b}}VIII}}

Diminished octave

48:25

40:21

rowspan=2|{{center|12}}

rowspan=2|{{center|1200}}

{{center|1158.94}}

{{center|30}}

{{center|1161.29}}

{{center|48}}

{{center|1152}}

{{center|B{{music|#}}}}

{{center|{{music|#}}VII}}

Augmented seventh

125:64

35:18

{{center|1200.00}}

{{center|19}}

{{center|1200.00}}

{{center|31}}

{{center|1200.00}}

{{center|50}}

{{center|1200}}

{{center|C}}

{{center|VIII}}

Octave

2:1