91edo: Difference between revisions

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~~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|~~optimal patent val]] for 7- and 11-limit [[~~Marvel_temperaments|~~septimin]] temperament, and the 13-limit rank three [[~~Marvel_family#Tripod|~~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 144/143, or else 196/195 and hence 225/224 also. It also gives the optimal patent val for the marvel extension tripod, which adds 105/104 to 225/224 and 385/384, and so also tempers out 144/143 and 196/195. 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 c val, it is audibly indistinguishable from a closed system of 1/7 comma meantone, with a 5th only 0.018 cents sharper.

'''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 7- and 11-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 144/143, or else 196/195 and hence 225/224 also. It also gives the optimal patent val for the marvel extension tripod, which adds 105/104 to 225/224 and 385/384, and so also tempers out 144/143 and 196/195. 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 c 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; it is, in fact, the product of 7 and 13.

[http://chrisvaisvil.com/dprk-ison-chase-12-of-91-edo-ambient/ DPRK ISON CHASE] by [[~~Chris_Vaisvil|~~Chris Vaisvil]]

[http://chrisvaisvil.com/dprk-ison-chase-12-of-91-edo-ambient/ DPRK ISON CHASE] by [[Chris Vaisvil]]

== See also ==

* [[Wikipedia: 91 (number)]]

[[Category:Equal divisions of the octave]]

[[Category:Quartismic]]

[[Category:septimin]]

[[Category:tripod]]

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-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|optimal patent val]] for 7- and 11-limit [[Marvel_temperaments|septimin]] temperament, and the 13-limit rank three [[Marvel_family#Tripod|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 144/143, or else 196/195 and hence 225/224 also. It also gives the optimal patent val for the marvel extension tripod, which adds 105/104 to 225/224 and 385/384, and so also tempers out 144/143 and 196/195. 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 c val, it is audibly indistinguishable from a closed system of 1/7 comma meantone, with a 5th only 0.018 cents sharper.
+'''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 7- and 11-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 144/143, or else 196/195 and hence 225/224 also. It also gives the optimal patent val for the marvel extension tripod, which adds 105/104 to 225/224 and 385/384, and so also tempers out 144/143 and 196/195. 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 c val, it is audibly indistinguishable from a closed system of 1/7 comma meantone, with a 5th only 0.018 cents sharper.
 is the smallest composite number whose composite character is not immediately evident; it is, in fact, the product of 7 and 13.
-[http://chrisvaisvil.com/dprk-ison-chase-12-of-91-edo-ambient/ DPRK ISON CHASE] by [[Chris_Vaisvil|Chris Vaisvil]]
+[http://chrisvaisvil.com/dprk-ison-chase-12-of-91-edo-ambient/ DPRK ISON CHASE] by [[Chris Vaisvil]]
 <youtube>StCR6hcm5tM</youtube>
+== See also ==
+* [[Wikipedia: 91 (number)]]
 [[Category:Equal divisions of the octave]]
 [[Category:Quartismic]]
 [[Category:septimin]]
 [[Category:tripod]]