Meantone intervals
This table shows all the simple intervals of POTE septimal meantone, which includes the entire 7-odd-limit tonality diamond. Other relevant tables of meantone intervals are the table of quarter-comma meantone intervals and the table of 31edo intervals. Intervals in limits higher than 7 are in brackets.
In 12edo the diminished second vanishes, so this cornucopia of intervals collapses to a mere 12. Except arguably for the tritone, none of the intervals are inherently septimal in 12edo, because they all have simpler 5-limit interpretations.
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.
| Name | Size (cents) |
Ratios |
|---|---|---|
| Unisons | ||
| Perfect unison (P1) | 0.00 | 1/1 |
| Augmented unison (A1) | 75.46 | 21/20, 25/24, 28/27 |
| Double-augmented unison (AA1) | 150.93 | 35/32, (12/11) |
| Seconds | ||
| Diminished second (d2) | 42.06 | 36/35, 50/49, 64/63, 128/125 |
| Minor second (m2) | 117.53 | 15/14, 16/15 |
| Major second (M2) | 192.99 | 9/8, 10/9, 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 | 49/40, (11/9) |
| Diminished fourth (d4) | 428.04 | 9/7, (14/11) |
| Perfect fourth (P4) | 503.51 | 4/3 |
| Augmented fourth (A4) | 578.97 | 7/5 |
| Double-augmented fourth (AA4) | 654.43 | 35/24, (16/11) |
| Fifths | ||
| Double-diminished fifth (dd5) | 545.57 | 48/35, (11/8) |
| Diminished fifth (d5) | 621.03 | 10/7 |
| Perfect fifth (P5) | 696.49 | 3/2 |
| Augmented fifth (A5) | 771.96 | 14/9, (11/7) |
| Double-augmented fifth (AA5) | 847.42 | 80/49, (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 | 9/5, 16/9, 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 | 64/35, (11/6) |
| Diminished octave (d8) | 1124.54 | 27/14, 40/21, 48/25 |
| Perfect octave (P8) | 1200.00 | 2/1 |