31 equal temperament
Interval size
Here are the sizes of some common intervals: The 31 equal temperament has a very close fit to the 7:6, 8:7, and 7:5 ratios, which have no approximate fits in 12 equal temperament and only poor fits in 19 equal temperament.

31 equal temperament

Section Title: Interval size
Table Section Text: Here are the sizes of some common intervals: The 31 equal temperament has a very close fit to the 7:6, 8:7, and 7:5 ratios, which have no approximate fits in 12 equal temperament and only poor fits in 19 equal temperament.

interval name	size (steps)	size (cents)	midi	just ratio	just (cents)	midi	error

octave	31	1200	2:1	1200	0

harmonic seventh	25	967.74	About this soundPlay (help·info)	7:4	968.83	About this soundPlay (help·info)	−1.09

perfect fifth	18	696.77	About this soundPlay (help·info)	3:2	701.96	About this soundPlay (help·info)	−5.19

greater septimal tritone	16	619.35	10:7	617.49	+1.87

lesser septimal tritone	15	580.65	About this soundPlay (help·info)	7:5	582.51	About this soundPlay (help·info)	−1.86

undecimal tritone, 11th harmonic	14	541.94	About this soundPlay (help·info)	11:8	551.32	About this soundPlay (help·info)	−9.38

perfect fourth	13	503.23	About this soundPlay (help·info)	4:3	498.04	About this soundPlay (help·info)	+5.19

septimal narrow fourth	12	464.52	About this soundPlay (help·info)	21:16	470.78	About this soundPlay (help·info)	−6.26

tridecimal augmented third, and greater major third	12	464.52	About this soundPlay (help·info)	13:10	454.21	About this soundPlay (help·info)	+10.31

septimal major third	11	425.81	About this soundPlay (help·info)	9:7	435.08	About this soundPlay (help·info)	−9.27

undecimal major third	11	425.81	About this soundPlay (help·info)	14:11	417.51	About this soundPlay (help·info)	+8.30

major third	10	387.10	About this soundPlay (help·info)	5:4	386.31	About this soundPlay (help·info)	+0.79

tridecimal neutral third	9	348.39	About this soundPlay (help·info)	16:13	359.47	About this soundPlay (help·info)	−11.09

undecimal neutral third	9	348.39	About this soundPlay (help·info)	11:9	347.41	About this soundPlay (help·info)	+0.98

minor third	8	309.68	About this soundPlay (help·info)	6:5	315.64	About this soundPlay (help·info)	−5.96

septimal minor third	7	270.97	About this soundPlay (help·info)	7:6	266.87	About this soundPlay (help·info)	+4.10

septimal whole tone	6	232.26	About this soundPlay (help·info)	8:7	231.17	About this soundPlay (help·info)	+1.09

whole tone, major tone	5	193.55	About this soundPlay (help·info)	9:8	203.91	About this soundPlay (help·info)	−10.36

whole tone, minor tone	5	193.55	About this soundPlay (help·info)	10:9	182.40	About this soundPlay (help·info)	+11.15

greater undecimal neutral second	4	154.84	About this soundPlay (help·info)	11:10	165.00	−10.16

lesser undecimal neutral second	4	154.84	About this soundPlay (help·info)	12:11	150.64	About this soundPlay (help·info)	+4.20

septimal diatonic semitone	3	116.13	About this soundPlay (help·info)	15:14	119.44	About this soundPlay (help·info)	−3.31

diatonic semitone, just	3	116.13	About this soundPlay (help·info)	16:15	111.73	About this soundPlay (help·info)	+4.40

septimal chromatic semitone	2	77.42	About this soundPlay (help·info)	21:20	84.47	About this soundPlay (help·info)	−7.05

chromatic semitone, Just	2	77.42	About this soundPlay (help·info)	25:24	70.67	About this soundPlay (help·info)	+6.75

lesser diesis	1	38.71	About this soundPlay (help·info)	128:125	41.06	About this soundPlay (help·info)	−2.35

undecimal diesis	1	38.71	About this soundPlay (help·info)	45:44	38.91	About this soundPlay (help·info)	−0.20

septimal diesis	1	38.71	About this soundPlay (help·info)	49:48	35.70	About this soundPlay (help·info)	+3.01

Sentence(s)

The fifth has 696.77 cents in size.

final_sentence: The fifth has 696.77 cents in size.