43/32: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = octave-reduced 43rd harmonic
| Name = prime harmonic fourth
| Color name = 43o4, fotho fourth
| Color name = 43o4, fotho fourth
| Sound = Ji-43-32-csound-foscil-220hz.mp3
| Sound = Ji-43-32-csound-foscil-220hz.mp3
}}
}}


'''43/32''', the '''quadracesimotertial harmonic fourth''', is [[Octave reduction|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.
'''43/32''', the '''prime harmonic fourth''', is [[Octave reduction|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 [[5L 2s|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 /2<sup>n</sup> interval that generates [[5L 2s]], the diatonic [[MOS]].


== See also ==
== See also ==

Revision as of 01:17, 8 October 2024

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]
Open this interval in xen-calc

43/32, the prime harmonic fourth, is 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.

See also