32/31: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = octave-reduced 31st subharmonic, small tricesimoprimal quartertone | ||
| Color name = 31u2, thiwu 2nd | |||
| Sound = Ji-32-31-csound-foscil-220hz.mp3 | | 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 (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 == | == 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]] | ||
Latest revision as of 04:01, 8 August 2025
| Interval information |
small tricesimoprimal quartertone
reduced,
reduced subharmonic
[sound info]
32/31 is the small tricesimoprimal quartertone measuring about 55 ¢. It differs from 33/32, the undecimal quartertone, by 1024/1023 (approx. 1.69 ¢). It differs from 31/30, another tricesimoprimal quartertone, by 961/960 (approx. 1.80 ¢); they together make 16/15. This interval is approximated well (about 0.4 ¢ off) by 1\22 and extremely closely (about 0.0025 ¢ off) by 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 Ali-Naqi Vaziri.