91edo: Difference between revisions
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== Music == | == Music == | ||
* [http://chrisvaisvil.com/dprk-ison-chase-12-of-91-edo-ambient/ DPRK ISON CHASE] by [[Chris Vaisvil]] | * [http://chrisvaisvil.com/dprk-ison-chase-12-of-91-edo-ambient/ DPRK ISON CHASE] by [[Chris Vaisvil]] | ||
* [https://www.youtube.com/watch?v=StCR6hcm5tM DPRK ISON CHASE - YouTube] | |||
== See also == | == See also == | ||
Revision as of 10:14, 25 July 2021
91edo, the 91 equal division divides the octave into 91 parts of 13.187 cents each. The 3, 5 and 7 for 91 are on the flat side, making this a mostly flat system. It provides the optimal patent val for 11- and 13-limit septimin temperament, and the 13-limit rank three tripod temperament, as well as the 11-limit rank four temperament tempering out 245/242 and the 13-limit rank five temperament tempering out 105/104, or rank four tempering out 105/104 and 144/143, or else 105/104 and 196/195 and hence 225/224 also. It tempers out 15625/15552 in the 5-limit, 225/224 and 4375/4374 in the 7-limit, 245/242, 385/384 in the 11-limit, and 105/104, 144/143, 196/195 in the 13-limit. It is the second highest it a series of four consecutive EDOs that temper out quartisma (117440512/117406179). Using the 91c val, it is audibly indistinguishable from a closed system of 1/7 comma meantone, with a 5th only 0.018 cents sharper.
91 is the smallest composite number whose composite character is not immediately evident in the decimal system; it is, in fact, the product of 7 and 13.