Meantone intervals
This table shows all the simple intervals of septimal meantone, which includes the entire 7-limit tonality diamond. Other relevant tables of meantone intervals are the table of quarter-comma meantone intervals and the table of 31 edo intervals.
In 12edo the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. None of the intervals is inherently septimal in 12edo, because they all have simpler 5-limit descriptions.
In 19edo, in contrast, the *double* diminished second vanishes, so the equivalences are A1~d2, A2~d3, A3~d4, A4~dd5, AA4~d5, A5~d6, A6~d7, and A7~d8. Thus some intervals are undeniably septimal, but ambiguously so because 49/48 vanishes.
More complex meantone edos such as 31edo distinguish all intervals listed on this table.
See also Wikipedia's list of meantone intervals
| Name | Size* | Ratios |
|---|---|---|
| Unisons | ||
| Perfect unison (P1) | 0 | 1/1 |
| Augmented unison (A1) | 75.5 | 28/27~25/24~21/20 |
| Seconds | ||
| Diminished second (d2) | 42.0 | 128/125~64/63~50/49~36/35 |
| Minor second (m2) | 117.5 | 16/15~15/14 |
| Major second (M2) | 193.0 | 10/9~9/8 |
| Augmented second (A2) | 268.5 | 7/6 |
| Thirds | ||
| Diminished third (d3) | 235.0 | 8/7 |
| Minor third (m3) | 310.5 | 6/5 |
| Major third (M3) | 386.0 | 5/4 |
| Augmented third (A3) | 461.5 | 21/16 |
| Fourths | ||
| Diminished fourth (d4) | 428.0 | 9/7 (a bit 14/11-ish) |
| Perfect fourth (P4) | 503.5 | 4/3 |
| Augmented fourth (A4) | 579.0 | 7/5 |
| Double augmented fourth (AA4) | 654.5 | Close to 16/11 |
| Fifths | ||
| Double diminished fifth (dd5) | 545.5 | Close to 11/8 |
| Diminished fifth (d5) | 621.0 | 10/7 |
| Perfect fifth (P5) | 696.5 | 3/2 |
| Augmented fifth (A5) | 772.0 | 14/9 (a bit 11/7-ish) |
| Sixths | ||
| Diminished sixth (d6) | 738.5 | 32/21 |
| Minor sixth (m6) | 814.0 | 8/5 |
| Major sixth (M6) | 889.5 | 5/3 |
| Augmented sixth (A6) | 965.0 | 7/4 |
| Sevenths | ||
| Diminished seventh (d7) | 931.5 | 12/7 |
| Minor seventh (m7) | 1007.0 | 16/9~9/5 |
| Major seventh (M7) | 1082.5 | 15/8 |
| Augmented seventh (A7) | 1158.0 | 35/18~49/25~63/32 |
| Octaves | ||
| Diminished octave (d8) | 1124.5 | 27/14~48/25~40/21 |
| Perfect octave (P8) | 1200 | 2/1 |
| Augmented octave (A8) | 1275.5 | 25/12~21/10 |
- In POTE septimal meantone