User:PiotrGrochowski/Extra-Diatonic Intervals — 50edo

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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