43/32: Difference between revisions
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'''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]]. Due to its complexity, it 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. | '''43/32''', the '''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 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]]. Due to its complexity, it 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 == | ||
Revision as of 01:35, 8 October 2024
| Interval information |
reduced harmonic
[sound info]
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.