32/27: Difference between revisions

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~~'''32/27'''~~

{{Infobox Interval

|~~5 -3>~~

| Name = Pythagorean minor third

| Color name = w3, wa 3rd

| Sound = jid_32_27_pluck_adu_dr220.mp3

}}

~~294~~.~~135 cents~~

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.

[[~~File:jid_32_27_pluck_adu_dr220.mp3~~]] [[~~:File:jid_32_27_pluck_adu_dr220.mp3|sound sample~~]]

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

~~The Pythagorean minor third of~~ 32/27 is the interval ~~between~~ [[~~9/8~~|~~9/8~~]] ~~and~~ [[~~4/3|4/3~~]] ~~which arises naturally in 3-limit just intonation~~. ~~It is 352~~/~~351 sharp of~~ [[13/~~11|13~~/11]]~~, and tempering 352~~/~~351 out equates it with 13/11 and leads to~~ [[~~minthmic_chords|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:Third]]

[[Category:Minor third]]

@@ Line 1: / Line 1: @@
-'''32/27'''
+{{Infobox Interval
-|5 -3&gt;
+| Name = Pythagorean minor third
+| Color name = w3, wa 3rd
+| Sound = jid_32_27_pluck_adu_dr220.mp3
+}}
-.135 cents
+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.
-[[File:jid_32_27_pluck_adu_dr220.mp3]] [[:File:jid_32_27_pluck_adu_dr220.mp3|sound sample]]
+It is 352/351 sharp of [[13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]].
-The Pythagorean minor third of 32/27 is the interval between [[9/8|9/8]] and [[4/3|4/3]] which arises naturally in 3-limit just intonation. It is 352/351 sharp of [[13/11|13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic_chords|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:Third]]
+[[Category:Minor third]]