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. 91edo supports a variant of [[semaphore]] temperament which tempers out the 4613015762523/4398046511104 comma in the 2.3.7 subgroup, and is produced by a 19\91 generator.

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 chromatic semitone in this scale also corresponds to 135/128, the [[eigenmonzo]] (unchanged-interval) of 1/7 comma meantone, both being 7 steps. What's also remarkable is that in this instance the chromatic semitone is equal to one step of [[13edo]]. Since 135/128 is also equal to 1/13th of the octave, 91c val tempers out the [[aluminium comma]] in the 5-limit.

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 chromatic semitone in this scale also corresponds to 135/128, the [[eigenmonzo]] (unchanged-interval) of [[1/7-comma meantone]], both being 7 steps. What's also remarkable is that in this instance the chromatic semitone is equal to one step of [[13edo]]. Since 135/128 is also equal to 1/13th of the octave, 91c val tempers out the [[aluminium comma]] in the 5-limit.

91edo also tempers out the [[Decaononic|devil's tridecalimma]], which assigns 10/9 to 2/13ths of the octave. It also supports the [[trideci]] temperament, which in the 7-limit tempers out 4375/4374 and 83349/81920.

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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. 91edo supports a variant of [[semaphore]] temperament which tempers out the 4613015762523/4398046511104 comma in the 2.3.7 subgroup, and is produced by a 19\91 generator.
-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 chromatic semitone in this scale also corresponds to 135/128, the [[eigenmonzo]] (unchanged-interval) of 1/7 comma meantone, both being 7 steps. What's also remarkable is that in this instance the chromatic semitone is equal to one step of [[13edo]]. Since 135/128 is also equal to 1/13th of the octave, 91c val tempers out the [[aluminium comma]] in the 5-limit.
+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 chromatic semitone in this scale also corresponds to 135/128, the [[eigenmonzo]] (unchanged-interval) of [[1/7-comma meantone]], both being 7 steps. What's also remarkable is that in this instance the chromatic semitone is equal to one step of [[13edo]]. Since 135/128 is also equal to 1/13th of the octave, 91c val tempers out the [[aluminium comma]] in the 5-limit.
 edo also tempers out the [[Decaononic|devil's tridecalimma]], which assigns 10/9 to 2/13ths of the octave. It also supports the [[trideci]] temperament, which in the 7-limit tempers out 4375/4374 and 83349/81920.