32/31: Difference between revisions

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| Sound = Ji-32-31-csound-foscil-220hz.mp3

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'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].

'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]]. This interval is approximated well (about 0.4{{~~cent~~}} off) by [[22edo|1\22]] and extremely closely (about 0.0025{{~~cent~~}} off) by [[131edo|6\131]]. ~~It can also serve as a generator for the [[escapade]] temperament.~~

== Approximation ==

This interval is approximated well (about 0.4{{c}} off) by [[22edo|1\22]] and extremely closely (about 0.0025{{c}} off) by [[131edo|6\131]].

This interval is significant in [[~~Helmholtz-Ellis~~ notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols ~~being used~~ are ~~virtually identical to~~ Persian quartertones accidentals invented by {{w|Ali-Naqi Vaziri}}.

== Notation ==

This interval is significant in [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols are adapted from Persian quartertones accidentals invented by {{w|Ali-Naqi Vaziri}}.

== Temperaments ==

This interval can serve as a generator for the [[escapade]] temperament (which both 22 and 131edo, among others, [[support]]).

== See also ==

* [[31/16]] – its [[octave complement]]

* [[31/24]] – its [[~~fifth~~ complement]]

* [[31/24]] – its [[fourth complement]]

* [[Gallery of just intervals]]

[[Category:Quartertone]]

@@ Line 4: / Line 4: @@
 | Sound = Ji-32-31-csound-foscil-220hz.mp3
 }}
+'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]].
-'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55{{cent}}. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (approx. 1.69{{cent}}). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (approx. 1.80{{cent}}); they together make [[16/15]]. This interval is approximated well (about 0.4{{cent}} off) by [[22edo|1\22]] and extremely closely (about 0.0025{{cent}} off) by [[131edo|6\131]]. It can also serve as a generator for the [[escapade]] temperament.
+== Approximation ==
+This interval is approximated well (about 0.4{{c}} off) by [[22edo|1\22]] and extremely closely (about 0.0025{{c}} off) by [[131edo|6\131]].
+{{Interval edo approximation}}
-This interval is significant in [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols being used are virtually identical to Persian quartertones accidentals invented by {{w|Ali-Naqi Vaziri}}.
+== Notation ==
+This interval is significant in [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby tricesimoprimal (31-limit) interval. The symbols are adapted from Persian quartertones accidentals invented by {{w|Ali-Naqi Vaziri}}.
+== Temperaments ==
+This interval can serve as a generator for the [[escapade]] temperament (which both 22 and 131edo, among others, [[support]]).
 == See also ==
 * [[31/16]] – its [[octave complement]]
-* [[31/24]] – its [[fifth complement]]
+* [[31/24]] – its [[fourth complement]]
 * [[Gallery of just intervals]]
 [[Category:Quartertone]]