16/15
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Ratio
16/15
Factorization
24 × 3-1 × 5-1
Monzo
[4 -1 -1⟩
Size in cents
111.7313¢
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
| Interval information |
classic(al) diatonic semitone,
ptolemaic diatonic semitone
reduced,
reduced subharmonic
(Shannon, [math]\sqrt{nd}[/math])
S6 × S7 × S8
[sound info]
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