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 [[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}}. | 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}}. | ||
Revision as of 01:59, 25 March 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).
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 Ali-Naqi Vaziri.