43/32: Difference between revisions

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'''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 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 '''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]].

== 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 ==

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-'''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 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 '''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]].
+== 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 ==