43/32
Ratio | 43/32 |
Subgroup monzo | 2.43 [-5 1⟩ |
Size in cents | 511.51771¢ |
Names | quadracesimotertial harmonic fourth, prime harmonic fourth |
Color name | 43o4, fotho fourth |
FJS name | [math]\text{P4}^{43}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 10.4263 |
Weil height (log_{2} max(n, d)) | 10.8525 |
Wilson height (sopfr (nd)) | 53 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.08673 bits |
[sound info] | |
open this interval in xen-calc |
43/32, the quadracesimotertial harmonic fourth or 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 "prime harmonic fourth" can be taken both as referring to the fact that it is a prime harmonic or to the fact that it is the simplest /2^{n} 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.