32/31: Difference between revisions

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{{Infobox Interval

| ~~Icon =~~

| Name = octave-reduced 31st subharmonic, small tricesimoprimal quartertone

~~| Ratio = 32/31~~

| Color name = 31u2, thiwu 2nd

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

~~| Cents = 54.96443~~

~~| Name = 31th~~ subharmonic, ~~<br>~~small tricesimoprimal quartertone

| Color name =

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

}}

'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55 ~~cents~~. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (~~''c''~~. 1.69 ~~cents~~). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (~~''c''~~. 1.80 ~~cents~~); 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 (which both 22 and 131edo, among others, support).

== 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}}.

== See also ==

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

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

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

* [[Gallery of just intervals]]

~~[[Category:31-limit]]~~

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

[[Category:Quartertone]]

~~[[Category:Superparticular]]~~

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

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

~~[[Category:Todo:add color name]]~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = octave-reduced 31st subharmonic, small tricesimoprimal quartertone
-| Ratio = 32/31
+| Color name = 31u2, thiwu 2nd
-| Monzo = 5 0 0 0 0 0 0 0 0 0 -1
-| Cents = 54.96443
-| Name = 31th subharmonic, <br>small tricesimoprimal quartertone
-| Color name =
 | Sound = Ji-32-31-csound-foscil-220hz.mp3
 }}
-'''32/31''' is the '''small tricesimoprimal quartertone''' measuring about 55 cents. It differs from [[33/32]], the undecimal quartertone, by [[1024/1023]] (''c''. 1.69 cents). It differs from [[31/30]], another tricesimoprimal quartertone, by [[961/960]] (''c''. 1.80 cents); 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 (which both 22 and 131edo, among others, support).
+== 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}}.
 == See also ==
 * [[31/16]] – its [[octave complement]]
-* [[31/24]] – its [[fifth complement]]
+* [[31/24]] – its [[fourth complement]]
 * [[Gallery of just intervals]]
-[[Category:31-limit]]
-[[Category:Interval ratio]]
 [[Category:Quartertone]]
-[[Category:Superparticular]]
-[[Category:Octave-reduced subharmonics]]
-[[Category:Todo:expand]]
-[[Category:Todo:add color name]]