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 unrelated to the circle of fifths, normalize it to 43edo steps, then round. 13–limit ratios are based on grosstone. I might do another one based on 50edo and meanpop instead...

todo: add 43edo cents column

interval	31edo steps	43edo steps	74edo steps	105edo steps	fifths	13–limit ratios
unison	0	0	0	0	0	1/1
comma unison	1	1	2	3	-12	36/35, 50/49, 56/55, 64/63
low augmented unison	1	2	3	4	+19	27/26, 33/32, 40/39, 49/48, 55/54
augmented unison	2	3	5	7	+7	21/20, 25/24, 28/27
minor second	3	4	7	10	-5	15/14, 16/15, 27/25, 35/33
lesser neutral second	4	5	9	13	-17	12/11, 13/12, 54/49
greater neutral second	4	6	10	14	+14	11/10, 49/45
major second	5	7	12	17	+2	9/8, 10/9, 28/25, 49/44, 55/49