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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.


=== Naive modes ===
== Regular temperament properties ==
91edo possesses naive versions of heptatonic and tridecatonic scales.
{| class="wikitable"
 
|+
For example, it can recreate diatonic major by first making an equiheptatonic scale with step size 13, and then raising III, VI and VII by a desired amount. Similar approximation can be done in [[28edo]] or any edo divisible by 7.
!Subgroup
 
!Comma list
Likewise, it can also recreate Orwells from tridecatonic scale. However, there is not a "trivial" way to do it due to larger amount of notes. The "correct" way to recreate a mode in this fashion would be using the differences of [[Irvic scale|Irvian mode]] and principal mode - that is by applying the generator or construction at the original tonic. For example, [[22edo]]'s Irvian mode for Orwell[13] is 2212212221221, while for 7/6 generator from the tonic is 1221221221222, and applying the differences results in 5795795777779 scale. This scale is quite bulky for musical performance since it contains an even row of 5x7 steps. A more vibrant possible variant is 5795797597579, which is derived from differences of 2212212212221 and 1221222122122 22edo Orwells.
!Mapping
 
!Optimal 8ve stretch (¢)
Since 7 and 13 are the only factors of 91, these numbers are the only ones which can produce naive scales.  
|-
|2.3
|[-144, 91⟩
|[⟨91 144]]
|0.9634
|-
|2.3II
|[''-145'', 91⟩
|[⟨91 ''145'']]
| -3.1965
|-
|2.3.5
|[[15625/15552]], [-23, 16, -1⟩, [-29, 11, 5⟩, [-17, 21, -7⟩
|[⟨91 144 211]]
|1.2021
|-
|2.3.5.7
|225/224, 4375/4374, 15625/15552, 19683/19600, 50421/50000, 64827/64000
|[⟨91 144 211 255]]
|1.4534
|}


== Table of intervals ==
== Table of intervals ==
Line 73: Line 93:
|major tertie, minor pemptia
|major tertie, minor pemptia
|E#
|E#
|[[16/13]]
|[[16/13]], 27/22
|-
|-
|28
|28
Line 113: Line 133:
|neutral quinte
|neutral quinte
|G
|G
|
|121/81
|-
|-
|53
|53
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