32/31: Difference between revisions
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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]]. 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. | '''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). | ||
This interval is significant in [[ | == 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 == | == See also == | ||
* [[31/16]] – its [[octave complement]] | * [[31/16]] – its [[octave complement]] | ||
* [[31/24]] – its [[ | * [[31/24]] – its [[fourth complement]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Quartertone]] | [[Category:Quartertone]] | ||