45/32

Interval information

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]\displaystyle{ \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]\displaystyle{ \sqrt{nd} }[/math])	~4.16278 bits
[sound info]
Open this interval in xen-calc

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