User:PiotrGrochowski/Extra-Diatonic Intervals — 50edo

Like User:PiotrGrochowski/Extra-Diatonic Intervals, but with 50edo instead of 43edo.

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.

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