43/32: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = quadracesimotertial harmonic fourth, 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''' or '''prime harmonic fourth''', is the [[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 "prime harmonic fourth" can be taken both as referring to the fact that it is a prime harmonic and to the fact that it is the simplest octave-reduced harmonic that generates [[5L 2s]], the diatonic [[mos]]. It is sharp of the [[4/3|perfect fourth (4/3)]] by [[129/128]]. | |||
== Approximation == | |||
Due to its complexity, this interval is sensitive to mistuning. Nontheless, it is tuned somewhat acceptably in [[7edo]] at 2.768{{cent}} sharp, but increasingly better [[edo]] approximations are [[40edo|17\40]], [[47edo|20\47]], [[54edo|23\54]] and especially [[61edo|26\61]], where it is less than 0.05{{cent}} flat, though some reasonable less accurate tunings in yet larger edos are [[68edo|29\68]] (< 0.25{{cent}} sharp) and [[75edo|32\75]] (< 0.5{{cent}} sharp), with good approximations becoming very noticeably more frequent in edos above this size. | |||
== See also == | == See also == | ||
* [[64/43]] – its [[octave complement]] | * [[64/43]] – its [[octave complement]] | ||
* [[Gallery of just intervals]] | |||
[[Category:Fourth]] | [[Category:Fourth]] | ||
Latest revision as of 09:51, 7 December 2024
| Interval information |
prime harmonic fourth
reduced harmonic
[sound info]
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 and to the fact that it is the simplest octave-reduced harmonic that generates 5L 2s, the diatonic mos. It is sharp of the perfect fourth (4/3) by 129/128.
Approximation
Due to its complexity, this interval 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.