User:265 993 303/Extra-Diatonic Intervals — 50edo

Like User:PiotrGrochowski/Extra-Diatonic Intervals, but with 50edo instead of 43edo. Unlike User:PiotrGrochowski/Extra-Diatonic Intervals, high and low do not stand for the septimal intervals, instead super and sub do. A 400 cent major third from 12edo is a high major third.

13-limit ratios are based on meanpop and are 69–integer–limit. They are valid to the amount of fifths, and need not necessarily convert to the same interval.

The base intervals come from the circle of fifths from -7 to 7 fifths: diminished octave, diminished fifth, minor second, minor sixth, minor third, minor seventh, fourth, unison, fifth, major second, major sixth, major third, major seventh, augmented fourth and augmented unison. This is unlike Igliashon's Extra-Diatonic Intervals, which only uses -5 to +5 fifths. The reasoning for the expanded range is that a chromatic scale is made of 6 augmented fourths and 6 diminished fifths, as well as 7 minor seconds and 5 augmented unisons. In the other hand, the diminished fourth at -8 fifths is considered a wolf major third in 5-limit, and a septimal major third in 7-limit, so this system names it a high major third instead.

Unison–second refers to the interval in the middle of augmented unison and minor second (like the ambiguous 100 cent interval in 12edo), not in the middle of unison and minor second.

interval	19edo steps	31edo steps	50edo steps	81edo steps	50edo cents	fifths	13-limit ratios
unison	0	0	0	0	0	0	1/1
high unison	0	1	1	2	24	+19
low augmented unison	1	1	2	3	48	-12
augmented unison	1	2	3	5	72	+7
unison–second	2	2	4	6	96	-24
minor second	2	3	5	8	120	-5
low neutral second	2	4	6	10	144	+14
high neutral second	3	4	7	11	168	-17
major second	3	5	8	13	192	+2
high major second	3	6	9	15	216	+21
super major second	4	6	10	16	240	-10
sub minor third	4	7	11	18	264	+9
low minor third	5	7	12	19	288	-22
minor third	5	8	13	21	312	-3
low neutral third	5	9	14	23	336	+16
high neutral third	6	9	15	24	360	-15
major third	6	10	16	26	384	+4
high major third	6	11	17	28	408	+23
super major third	7	11	18	29	432	-8
sub fourth	7	12	19	31	456	+11
low fourth	8	12	20	32	480	-20
fourth	8	13	21	34	504	-1
high fourth	8	14	22	36	528	+18
low augmented fourth	9	14	23	37	552	-13
augmented fourth	9	15	24	39	576	+6
fourth-fifth	9	16	25	41	600	+25
diminished fifth	10	16	26	42	624	-6
high diminished fifth	10	17	27	44	648	+13
low fifth	11	17	28	45	672	-18
fifth	11	18	29	47	696	+1
high fifth	11	19	30	49	720	+20
super fifth	12	19	31	50	744	-11
sub minor sixth	12	20	32	52	768	+8
low minor sixth	13	20	33	53	792	-23
minor sixth	13	21	34	55	816	-4
low neutral sixth	13	22	35	57	840	+15
high neutral sixth	14	22	36	58	864	-16
major sixth	14	23	37	60	888	+3
high major sixth	14	24	38	62	912	+22
super major sixth	15	24	39	63	936	-9
sub minor seventh	15	25	40	65	960	+10
low minor seventh	16	25	41	66	984	-21
minor seventh	16	26	42	68	1008	-2
low neutral seventh	16	27	43	70	1032	17
high neutral seventh	17	27	44	71	1056	-14
major seventh	17	28	45	73	1080	+5
seventh-octave	17	29	46	75	1104	+24
diminished octave	18	29	47	76	1128	-7
high diminished octave	18	30	48	78	1152	12
low octave	19	30	49	79	1176	-19
octave	19	31	50	81	1200	0