# 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.

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