31 equal temperament
interval name size ( steps ) size ( cents ) midi just ratio just ( cents ) midi error
octave 31 1200 2:1 1200 0
minor seventh 26 1006.45 9:5 1017.60 - 0 11.15
small just minor seventh 26 1006.45 16:9 996.09 + 0 10.36
harmonic seventh 25 967.74 Play ( help · info ) 7:4 968.83 Play ( help · info ) − 0 1.09
perfect fifth 18 696.77 Play ( help · info ) 3:2 701.96 Play ( help · info ) − 0 5.19
greater septimal tritone 16 619.35 10:7 0 617.49 + 0 1.87
lesser septimal tritone 15 580.65 Play ( help · info ) 7:5 582.51 Play ( help · info ) − 0 1.86
undecimal tritone , 11th harmonic 14 541.94 Play ( help · info ) 11:8 0 551.32 Play ( help · info ) − 0 9.38
perfect fourth 13 503.23 Play ( help · info ) 4:3 498.04 Play ( help · info ) + 0 5.19
septimal narrow fourth 12 464.52 Play ( help · info ) 21:16 470.78 Play ( help · info ) − 0 6.26
tridecimal augmented third , and greater major third 12 464.52 Play ( help · info ) 13:10 454.21 Play ( help · info ) +10.31
septimal major third 11 425.81 Play ( help · info ) 9:7 435.08 Play ( help · info ) − 0 9.27
diminished fourth 11 425.81 Play ( help · info ) 32:25 427.37 Play ( help · info ) − 0 1.56
undecimal major third 11 425.81 Play ( help · info ) 14:11 417.51 Play ( help · info ) + 0 8.30
major third 10 387.10 Play ( help · info ) 5:4 386.31 Play ( help · info ) + 0 0.79
tridecimal neutral third 0 9 348.39 Play ( help · info ) 16:13 359.47 Play ( help · info ) −11.09
undecimal neutral third 0 9 348.39 Play ( help · info ) 11:9 0 347.41 Play ( help · info ) + 0 0.98
minor third 0 8 309.68 Play ( help · info ) 6:5 315.64 Play ( help · info ) − 0 5.96
septimal minor third 0 7 270.97 Play ( help · info ) 7:6 266.87 Play ( help · info ) + 0 4.10
septimal whole tone 0 6 232.26 Play ( help · info ) 8:7 231.17 Play ( help · info ) + 0 1.09
Interval size
Here are the sizes of some common intervals :
In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET, 31-EDO (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equal-sized steps (equal frequency ratios). Each step represents a frequency ratio of , or 38.71 cents (). 31-ET is a very good approximation of quarter-comma meantone temperament. More generally, it is a regular diatonic tuning in which the tempered perfect fifth is equal to 696.77 cents, as shown in Figure 1. On an isomorphic keyboard, the fingering of music composed in 31-ET is precisely the same as it is in any other syntonic tuning (such as 12-ET), so long as the notes are spelled properly - that is, with no assumption of enharmonicity.