91edo: Difference between revisions
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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. | 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. | ||
== Scales == | |||
Non-JI themed scales that are derived from 7 and 13 note scales, the 2 divisors of 91: | |||
* NaiveMajor[7]: 13 16 10 13 16 13 10 | |||
* NaiveMajor[7]: 13 16 10 15 14 13 10 - fifth adjusted to match with the next scale | |||
* NaiveOrwell[13]: 5795797579579 | |||
* ArabicNaiveOrwell[13]: 1 11 9 5 1 15 7 5 7 9 1 11 9 - above scale with 2, 6, and 12 degrees lowered 4 steps | |||
== Music == | == Music == | ||
Revision as of 07:54, 21 October 2021
91edo, the 91 equal division divides the octave into 91 parts of 13.187 cents each.
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.
Theory
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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.
Scales
Non-JI themed scales that are derived from 7 and 13 note scales, the 2 divisors of 91:
- NaiveMajor[7]: 13 16 10 13 16 13 10
- NaiveMajor[7]: 13 16 10 15 14 13 10 - fifth adjusted to match with the next scale
- NaiveOrwell[13]: 5795797579579
- ArabicNaiveOrwell[13]: 1 11 9 5 1 15 7 5 7 9 1 11 9 - above scale with 2, 6, and 12 degrees lowered 4 steps