49edo: Difference between revisions
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→Music: Add Cam Taylor's ''49-equal: 7-equal meets superpyth'' (2023) |
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== Theory == | == Theory == | ||
49edo is very much on the sharp side of things, with sharp tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]]. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]), and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments, being almost exactly equal to {{frac|3|10}}-comma superpyth | 49edo is very much on the sharp side of things, with sharp tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]]. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]), and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments, being almost exactly equal to {{frac|3|10}}-comma superpyth. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit. | ||
=== Harmonics === | === Harmonics === | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 49 factors into {{factorization|49}}, 49edo contains [[7edo]] as its only nontrivial subset. 49edo is the first square edo with a [[enfactoring|non-enfactored]] diatonic fifth. | Since 49 factors into {{factorization|49}}, 49edo contains [[7edo]] as its only nontrivial subset. 49edo is the first square edo with a [[enfactoring|non-enfactored]] diatonic fifth. | ||
== Intervals == | == Intervals == | ||
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{{Q-odd-limit intervals|49}} | {{Q-odd-limit intervals|49}} | ||
=== Zeta | === Zeta peaks === | ||
The strongest [[The Riemann zeta function and tuning|local zeta peak]] around 49edo is its second closest, 49.141 edo. One step is 24.419 cents, and two steps, 48.839 cents, is a good generator for [[Triple BP]]. | The strongest [[The Riemann zeta function and tuning|local zeta peak]] around 49edo is its second closest, 49.141 edo. One step is 24.419 cents, and two steps, 48.839 cents, is a good generator for [[Triple BP]]. | ||
== Approximation to irrational intervals == | == Approximation to irrational intervals == | ||
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; [[Mercury Amalgam]] | ; [[Mercury Amalgam]] | ||
* [https://www.youtube.com/watch?v=c_kzhcMMHWM&pp=ygUFNDllZG8%3D ''Wrong Generation (Demo, January 2022)''] (2023) | * [https://www.youtube.com/watch?v=c_kzhcMMHWM&pp=ygUFNDllZG8%3D ''Wrong Generation (Demo, January 2022)''] (2023) | ||
; [[Cam Taylor]] | |||
* [https://www.youtube.com/watch?v=fns6688IRpg ''49-equal: 7-equal meets superpyth''] (2023) | |||
; [[Bryan Deister]] | ; [[Bryan Deister]] | ||
* [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune – ''Man'' (cover)] (2023) | * [https://www.youtube.com/watch?v=7pK-JcIrd18 Deltarune – ''Man'' (cover)] (2023) | ||
; [[YoVariable]] | |||
* [https://www.youtube.com/watch?v=GHslu-ZWspk The Cure - ''Boys Don't Cry'' (cover)] (2025) | |||
[[Category:Archytas]] | [[Category:Archytas]] | ||