43/32

Interval information

Ratio	43/32
Subgroup monzo	2.43 [-5 1⟩
Size in cents	511.5177¢
Name	prime harmonic fourth
Color name	43o4, fotho fourth
FJS name	[math]\displaystyle{ \text{P4}^{43} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	10.4263
Weil height (log2 max(n, d))	10.8525
Wilson height (sopfr(nd))	53
[sound info]
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43/32, the prime harmonic fourth, is the octave-reduced 43rd harmonic. It is a wide fourth close to those of 7edo and 26edo, and, is the first octave-reduced harmonic that is a diatonic fourth. The "prime" in the name can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2ⁿ interval that generates 5L 2s, the diatonic MOS. Due to its complexity, it is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in 7edo at 2.768 ¢ sharp, but increasingly better edo approximations are 17\40, 20\47, 23\54 and especially 26\61, where it is less than 0.05 ¢ flat, though some reasonable less accurate tunings in yet larger edos are 29\68 (<0.25 ¢ sharp) and 32\75 (<0.5 ¢ sharp), with good approximations becoming very noticeably more frequent in edos above this size.

See also

• 64/43 – its octave complement
• Gallery of just intervals