32/27: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

~~| Ratio = 32/27~~

~~| Monzo = 5 -3~~

~~| Cents = 294.13500~~

| Name = Pythagorean minor third

| Color name = w3, wa 3rd

~~| FJS name = m3~~

| Sound = jid_32_27_pluck_adu_dr220.mp3

}}

The '''Pythagorean minor third''' of '''32/27''' is the interval between [[9/8]] and [[4/3]] which arises naturally in [[3-limit]] just intonation. Compared to the more typical [[6/5]]- with which it is conflated in [[meantone]]- this interval is more dissonant, with a [[harmonic entropy]] level roughly on par with that of 9/8.

The '''Pythagorean minor third''' of '''32/27''' is the interval between [[9/8]] and [[4/3]] which arises naturally in [[3-limit]] [[just intonation]]. Compared to the more typical [[6/5]]- with which it is conflated in [[meantone]]- this interval is more dissonant, with a [[harmonic entropy]] level roughly on par with that of 9/8.

It is 352/351 sharp of [[13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]].

== Temperaments ==

32/27 is treated as a comma in edos 3 & 6, where the best approximation of a perfect 5th is the 800 cent interval that wraps around to the octave again after only three iterations, producing [[alteraugment]]. Temperaments it can be interpreted as if used as a generator include [[Kleismic_family#Kleiboh|Kleiboh]] or [[Gariberttet]].

== Approximation ==

== See also ==

* [[27/16]] – its [[octave complement]]

* [[81/64]] – its [[fifth complement]]

* [[9/8]] – its [[fourth complement]]

* [[Gallery of just intervals]]

* [[Pythagorean tuning]]

~~[[Category:3-limit]]~~

~~[[Category:Interval]]~~

~~[[Category:Interval ratio]]~~

[[Category:Third]]

[[Category:Minor third]]

~~[[Category:Pythagorean]]~~

~~{{todo| expand }}~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
-| Ratio = 32/27
-| Monzo = 5 -3
-| Cents = 294.13500
 | Name = Pythagorean minor third
 | Color name = w3, wa 3rd
-| FJS name = m3
 | Sound = jid_32_27_pluck_adu_dr220.mp3
 }}
-The '''Pythagorean minor third''' of '''32/27''' is the interval between [[9/8]] and [[4/3]] which arises naturally in [[3-limit]] just intonation.  Compared to the more typical [[6/5]]- with which it is conflated in [[meantone]]- this interval is more dissonant, with a [[harmonic entropy]] level roughly on par with that of 9/8.
+The '''Pythagorean minor third''' of '''32/27''' is the interval between [[9/8]] and [[4/3]] which arises naturally in [[3-limit]] [[just intonation]].  Compared to the more typical [[6/5]]- with which it is conflated in [[meantone]]- this interval is more dissonant, with a [[harmonic entropy]] level roughly on par with that of 9/8.
 It is 352/351 sharp of [[13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]].
+== Temperaments ==
+/27 is treated as a comma in edos 3 & 6, where the best approximation of a perfect 5th is the 800 cent interval that wraps around to the octave again after only three iterations, producing [[alteraugment]]. Temperaments it can be interpreted as if used as a generator include [[Kleismic_family#Kleiboh|Kleiboh]] or [[Gariberttet]].
+== Approximation ==
+{{Interval edo approximation|32/27}}
 == See also ==
 * [[27/16]] – its [[octave complement]]
 * [[81/64]] – its [[fifth complement]]
+* [[9/8]] – its [[fourth complement]]
 * [[Gallery of just intervals]]
 * [[Pythagorean tuning]]
-[[Category:3-limit]]
-[[Category:Interval]]
-[[Category:Interval ratio]]
 [[Category:Third]]
 [[Category:Minor third]]
-[[Category:Pythagorean]]
-{{todo| expand }}