43/32: Difference between revisions

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{{Infobox Interval

~~| Ratio = 43/32~~

| Name = quadracesimotertial harmonic fourth, prime harmonic fourth

~~| Monzo = -5 0 0 0 0 0 0 0 0 0 0 0 0 1~~

| Color name = 43o4, fotho fourth

~~| Cents = 511.51771~~

| Name = ~~octave-reduced 43rd~~ harmonic

| Color name = ~~43o~~ fourth~~, 43o4~~

| 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]].

~~'''43/32'''~~ is ~~the~~ [[~~Octave reduction~~|~~octave-reduced~~]] ~~43rd~~ [[~~harmonic~~]]. ~~It is a slightly~~ sharp ~~perfect fourth~~.

== 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 ==

* [[64/43]] – its [[octave complement]]

* [[Gallery of just intervals]]

~~[[Category:43-limit]]~~

[[Category:Fourth]]

~~[[Category:Octave-reduced harmonics]]~~

~~[[Category:Pages with internal sound examples]]~~

~~[[Category:Todo:expand]]~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 43/32
+| Name = quadracesimotertial harmonic fourth, prime harmonic fourth
-| Monzo = -5 0 0 0 0 0 0 0 0 0 0 0 0 1
+| Color name = 43o4, fotho fourth
-| Cents = 511.51771
-| Name = octave-reduced 43rd harmonic
-| Color name = 43o fourth, 43o4
 | 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]].
-'''43/32''' is the [[Octave reduction|octave-reduced]] 43rd [[harmonic]]. It is a slightly sharp perfect fourth.
+== 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 ==
+* [[64/43]] – its [[octave complement]]
+* [[Gallery of just intervals]]
-[[Category:43-limit]]
 [[Category:Fourth]]
-[[Category:Octave-reduced harmonics]]
-[[Category:Pages with internal sound examples]]
-[[Category:Todo:expand]]