From Xenharmonic Wiki
(Redirected from 15-odd-limit intervals)
Jump to navigation Jump to search

The 15-odd-limit is the set of all rational intervals for which neither the numerator nor the denominator of the frequency ratio exceeds 15, once all powers of 2 are removed. To the 13-odd-limit, it adds 4 interval pairs involving 15.

Below is a list of all octave-reduced intervals in the 15-odd-limit. This collection of intervals has proven to be useful for illustrating certain characteristics of medium-sized EDOs (~15 to 41 steps).

Ratio Size (¢) Color name Name(s)
16/15 111.731 g2 gu 2nd classic diatonic semitone
15/14 119.443 ry1 ruyo unison septimal diatonic semitone
15/13 247.741 3uy2 thuyo 2nd tridecimal supermajor second / tridecimal second-third
15/11 536.951 1uy4 luyo 4th undecimal acute fourth
22/15 663.049 1og5 logu 5th undecimal grave fifth
26/15 952.259 3og7 thogu 7th tridecimal subminor seventh / tridecimal sixth-seventh
28/15 1080.557 zg8 zogu octave small septimal major seventh
15/8 1088.269 y7 yo 7th just major seventh

The smallest EDO which is consistent in the 15-odd-limit is 29edo; that which is distinctly consistent in the same is 111edo.

See also