91edo: Difference between revisions
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Added information on a certain comma that this EDO tempers out |
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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. | 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 [[Quartismic temperaments|117440512/117406179]]. | ||
91 is the smallest composite number whose composite character is not immediately evident; it is, in fact, the product of 7 and 13. | 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|Chris Vaisvil]] | ||
<youtube>StCR6hcm5tM</youtube> | <youtube>StCR6hcm5tM</youtube> | ||
Revision as of 01:34, 9 September 2020
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 117440512/117406179.
91 is the smallest composite number whose composite character is not immediately evident; it is, in fact, the product of 7 and 13.
DPRK ISON CHASE by Chris Vaisvil