Meantone intervals
This table shows all the simple intervals of POTE 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 tunings such as 31edo distinguish all intervals listed on this table.
See also Wikipedia: List of meantone intervals
| Name | Size (cents) |
Ratios |
|---|---|---|
| Unisons | ||
| Perfect unison (P1) | 0.00 | 1/1 |
| Augmented unison (A1) | 75.46 | 28/27~25/24~21/20 |
| Double augmented unison (AA1) | 150.93 | Close to 12/11 |
| Seconds | ||
| Diminished second (d2) | 42.06 | 128/125~64/63~50/49~36/35 |
| Minor second (m2) | 117.53 | 16/15~15/14 |
| Major second (M2) | 192.99 | 10/9~9/8~28/25 |
| Augmented second (A2) | 268.45 | 7/6 |
| Thirds | ||
| Diminished third (d3) | 235.05 | 8/7 |
| Minor third (m3) | 310.52 | 6/5 |
| Major third (M3) | 385.98 | 5/4 |
| Augmented third (A3) | 461.44 | 21/16 |
| Fourths | ||
| Double diminished fourth (dd4) | 352.58 | Close to 11/9 |
| Diminished fourth (d4) | 428.04 | 9/7 (a bit 14/11-ish) |
| Perfect fourth (P4) | 503.51 | 4/3 |
| Augmented fourth (A4) | 578.97 | 7/5 |
| Double augmented fourth (AA4) | 654.43 | Close to 16/11 |
| Fifths | ||
| Double diminished fifth (dd5) | 545.57 | Close to 11/8 |
| Diminished fifth (d5) | 621.03 | 10/7 |
| Perfect fifth (P5) | 696.49 | 3/2 |
| Augmented fifth (A5) | 771.96 | 14/9 (a bit 11/7-ish) |
| Double augmented fifth (AA5) | 847.42 | Close to 18/11 |
| Sixths | ||
| Diminished sixth (d6) | 738.56 | 32/21 |
| Minor sixth (m6) | 814.02 | 8/5 |
| Major sixth (M6) | 889.48 | 5/3 |
| Augmented sixth (A6) | 964.95 | 7/4 |
| Sevenths | ||
| Diminished seventh (d7) | 931.55 | 12/7 |
| Minor seventh (m7) | 1007.01 | 16/9~9/5~25/14 |
| Major seventh (M7) | 1082.47 | 15/8~28/15 |
| Augmented seventh (A7) | 1157.94 | 35/18~49/25~63/32 |
| Octaves | ||
| Double diminished octave (dd8) | 1049.07 | Close to 11/6 |
| Diminished octave (d8) | 1124.54 | 27/14~48/25~40/21 |
| Perfect octave (P8) | 1200.00 | 2/1 |