45/32
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Ratio
45/32
Factorization
2-5 × 32 × 5
Monzo
[-5 2 1⟩
Size in cents
590.2237¢
Names
smaller pental tritone,
smaller diatonic tritone,
ptolemaic augmented fourth
Color name
y4, yo 4th
FJS name
[math]\text{A4}^{5}[/math]
Special properties
reduced,
reduced harmonic
Tenney height (log2 nd)
10.4919
Weil height (log2 max(n, d))
10.9837
Wilson height (sopfr(nd))
21
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.16278 bits
[sound info]
open this interval in xen-calc
| Interval information |
smaller diatonic tritone,
ptolemaic augmented fourth
reduced harmonic
(Shannon, [math]\sqrt{nd}[/math])
[sound info]
45/32 is the smaller pental tritone, a diatonic tritone of 5-limit just intonation- specifically, it is the ptolemaic augmented fourth. It is a syntonic comma away from the Pythagorean augmented fourth 729/512, which means it is justly tuned in 1/6 syntonic comma meantone. It is separated from its inversion of 64/45 by the diaschisma, 2048/2025 (c. 19.6 cents).
See also
- 64/45 – its octave complement
- 16/15 – its fifth complement