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.

== 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 ==

@@ Line 7: / Line 7: @@
 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 ==