91edo: Difference between revisions
→Music: Insert Instruments section before this, now that a Lumatone mapping for 91edo is now available |
→Music: Add Modern Renderings section, starting with Maretu's ''Aishite ita no ni'' (2023) – microtonal cover in 91edo by Bryan Deister (2026) |
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The [[harmonic]]s [[3/1|3]], [[5/1|5]] and [[7/1|7]] for 91edo are on the flat side, making this a mostly flat system. It [[tempering out|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 provides the [[optimal patent val]] for 11- and 13-limit [[septimin]] temperament, and the 13-limit rank-3 [[tripod]] temperament, as well as the 11-limit rank-4 temperament tempering out 245/242 and the 13-limit rank-5 temperament tempering out 105/104, or rank-4 tempering out 105/104 and 144/143, or else 105/104 and 196/195 and hence 225/224 also. | The [[harmonic]]s [[3/1|3]], [[5/1|5]] and [[7/1|7]] for 91edo are on the flat side, making this a mostly flat system. It [[tempering out|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 provides the [[optimal patent val]] for 11- and 13-limit [[septimin]] temperament, and the 13-limit rank-3 [[tripod]] temperament, as well as the 11-limit rank-4 temperament tempering out 245/242 and the 13-limit rank-5 temperament tempering out 105/104, or rank-4 tempering out 105/104 and 144/143, or else 105/104 and 196/195 and hence 225/224 also. | ||
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 corresponds to 135/128, the [[eigenmonzo]] (unchanged | 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 corresponds to 135/128, the [[eigenmonzo]] (unchanged interval) of [[1/7-comma meantone]]. Being 7 steps, what is also remarkable is that in this instance the chromatic semitone is equal to one step of [[13edo]]. Since 135/128 is also equal to 1/13 of the octave, the 91c [[val]] tempers out the [[aluminium comma]] in the 5-limit. | ||
It also tempers out the {{monzo| -11 26 -13 }}, the tridecatonic comma, which assigns [[10/9]] to 2/13 of the octave, and it supports [[trideci]] in the 7-limit, tempering out 4375/4374 and 83349/81920. It supports a variant of [[semaphore]] temperament which tempers out the {{monzo| -42 23 2 }} comma in the 2.3.7 [[subgroup]], and is generated by a 19\91 generator. It is the second highest in a series of four consecutive edos that temper out [[quartisma]] ({{monzo| 24 -6 0 1 -5 }}), and as a corollary it is a tuning for the [[quartkeenlig]] temperament, which can also act as a [[23edo and octave stretching|stretched]] [[23edo]]. In the 13-limit, it supports [[vidar]] and gives a reasonable tuning for its size. | It also tempers out the {{monzo| -11 26 -13 }}, the tridecatonic comma, which assigns [[10/9]] to 2/13 of the octave, and it supports [[trideci]] in the 7-limit, tempering out 4375/4374 and 83349/81920. It supports a variant of [[semaphore]] temperament which tempers out the {{monzo| -42 23 2 }} comma in the 2.3.7 [[subgroup]], and is generated by a 19\91 generator. It is the second highest in a series of four consecutive edos that temper out [[quartisma]] ({{monzo| 24 -6 0 1 -5 }}), and as a corollary it is a tuning for the [[quartkeenlig]] temperament, which can also act as a [[23edo and octave stretching|stretched]] [[23edo]]. In the 13-limit, it supports [[vidar]] and gives a reasonable tuning for its size. | ||
| Line 440: | Line 440: | ||
| 435.16 | | 435.16 | ||
| 9/7 | | 9/7 | ||
| [[Supermajor]] | | [[Supermajor (temperament)|Supermajor]] | ||
|- | |- | ||
| 1 | | 1 | ||
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| [[Trideci]] (91)<br>[[Aluminium]] (91c) | | [[Trideci]] (91)<br>[[Aluminium]] (91c) | ||
|} | |} | ||
<nowiki/>* [[Normal | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
<nowiki/>** Derived from scales in the Scales section, official name not decided upon yet. | <nowiki/>** Derived from scales in the Scales section, official name not decided upon yet. | ||
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== Instruments == | == Instruments == | ||
A [[Lumatone mapping for 91edo]] is available. | A [[Lumatone mapping for 91edo]] is available. | ||
== Music == | == Music == | ||
=== Modern renderings === | |||
; {{W|Maretu}} | |||
* [https://www.youtube.com/shorts/7RDvArkSJrk ''Aishite ita no ni''] (2023) – microtonal cover in 91edo by [[Bryan Deister]] (2026) | |||
=== 21st century === | |||
; [[Mercury Amalgam]] | ; [[Mercury Amalgam]] | ||
* ''Sadness - Nope'' (2022) – [https://mercuryamalgam.bandcamp.com/track/sadness-nope-the-molecular-agoge-pt-2 Bandcamp] | [https://www.youtube.com/watch?v=_5WS7AGZxm4 YouTube] | * ''Sadness - Nope'' (2022) – [https://mercuryamalgam.bandcamp.com/track/sadness-nope-the-molecular-agoge-pt-2 Bandcamp] | [https://www.youtube.com/watch?v=_5WS7AGZxm4 YouTube] | ||