User:PiotrGrochowski/Extra-Diatonic Intervals

Extra-Diatonic Intervals tries to base on 72edo and tries to take into account that superpyth minor seconds can reach 70 cents, although in meantone it's actually an augmented unison. However, superpyth is not suited for a diatonic scale, we can exclude it out of my version and base it on some meantone tuning like 43edo, 74edo or 105edo. To convert an interval to a name, select the closest 43edo interval. 13–limit ratios are based on grosstone and do not have numbers 70 or more. I might do another one based on 50edo and meanpop too...

interval	31edo steps	43edo steps	74edo steps	43edo cents	fifths	13–limit ratios
unison	0	0	0	0	0	1/1
high unison	1	1	2	27.907	-12	36/35, 50/49, 56/55, 64/63
low augmented unison	1	2	3	55.814	+19	27/26, 33/32, 40/39, 49/48, 55/54
augmented unison	2	3	5	83.721	+7	21/20, 25/24, 28/27
minor second	3	4	7	111.628	-5	15/14, 16/15, 27/25, 35/33
low neutral second	4	5	9	139.535	-17	12/11, 13/12, 54/49
high neutral second	4	6	10	167.442	+14	11/10, 49/45
major second	5	7	12	195.349	+2	9/8, 10/9, 28/25, 49/44, 55/49
high major second	6	8	14	223.256	-10	8/7
second–third	6	9	15	251.163	+21	15/13, 55/48
low minor third	7	10	17	279.070	+9	7/6, 33/28
minor third	8	11	19	306.977	-3	6/5, 25/21, 32/27
low neutral third	9	12	21	334.884	-15	27/22, 39/32, 40/33, 60/49, 65/54
high neutral third	9	13	22	362.791	+16	11/9, 16/13, 49/40
major third	10	14	24	390.698	+4	5/4, 56/45, 63/50
high major third	11	15	26	418.605	-8	9/7, 14/11, 32/25
third–fourth	12	16	28	446.512	-20	13/10, 64/49
low fourth	12	17	29	474.419	+11	21/16, 35/27, 55/42
fourth	13	18	31	502.326	-1	4/3, 27/20, 66/49