16/15
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| 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, reduced, reduced subharmonic |
| 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 | |
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.
Temperaments
When this ratio is taken as a comma to be tempered out, it produces father temperament, and lends itself the name father comma. In this exotemperament, 4/3 and 5/4 are equated, and major thirds and fifths become octave complements of each other. It is a Mersenne comma.
See also
- 15/8 – its octave complement
- 45/32 – its fifth complement
- 5/4 – its fourth complement
- 256/243 – the Pythagorean (3-limit) diatonic semitone
- Gallery of just intervals
- List of superparticular intervals
- 16/15 equal-step tuning – equal multiplication of this interval