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Interval information
Ratio 16/15
Factorization 24 × 3-1 × 5-1
Monzo [4 -1 -1
Size in cents 111.73129¢
Names just diatonic semitone,
classic(al) diatonic semitone,
ptolemaic diatonic semitone
Color name g2, gu 2nd
FJS name [math]\text{m2}_{5}[/math]
Special properties square superparticular,
Tenney height (log2 nd) 7.90689
Weil height (log2 max(n, d)) 8
Wilson height (sopfr (nd)) 16
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.27487 bits
Comma size large
S-expressions S4,
S6 × S7 × S8

[sound info]
open this interval in xen-calc
English Wikipedia has an article on:

The 5-limit superparticular interval 16/15 is the just diatonic semitone, classic(al) diatonic semitone or ptolemaic diatonic semitone[1] – the difference between the major third 5/4 and the fourth 4/3, and between 3/2 and 8/5.


When this ratio is taken as a comma to be tempered, it produces father temperament, where 4/3 and 5/4 are equated. In this temperament, major thirds and fifths become octave complements of each other.

See also


  1. For reference, see 5-limit.