26edo: Difference between revisions
→Intervals: add 26/21, 64/49, and complements |
→Instruments: Add ''A rough introduction to 26edo on the Lumatone'' by YoVariable (2026) |
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| de = 26-EDO | | de = 26-EDO | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
26edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing the 2.9.5.21.11.13.17.19-subgroup with 26edo. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics. [[104edo]] is a notable dual- | 26edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing the 2.9.5.21.11.13.17.19-subgroup with 26edo. | ||
26edo tempers out [[Fynn's comma]], which sets ~7/4 to 21\26. This is shared by several notable superset edos. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics. [[104edo]] is a notable dual-5's system. [[130edo]], [[364edo]], [[494edo]], and [[624edo]] do well in approximating JI, though they are more complex. | |||
== Intervals == | == Intervals == | ||
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== Approximation to irrational intervals == | == Approximation to irrational intervals == | ||
26edo approximates both [[acoustic phi]] (the [[golden ratio]]) and [[pi]] quite accurately. Not until 1076edo do we find a better edo in terms of relative error on these intervals. | 26edo approximates both [[acoustic phi]] (the [[golden ratio]]) and [[pi]] quite accurately. Not until 1076edo do we find a better edo in terms of relative error on these intervals{{Clarify}}. | ||
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* [[Lumatone mapping for 26edo]] | * [[Lumatone mapping for 26edo]] | ||
* [https://www.youtube.com/watch?v=HrZ-PoUXGTg ''A rough introduction to 26edo on the Lumatone''] by [[YoVariable]] (2026) | |||
== Literature == | == Literature == | ||
[http://www.ronsword.com Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.] | [http://www.ronsword.com Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.] | ||
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* [https://www.youtube.com/shorts/1aCl6tuVS0c ''Happy Together - The Turtles (microtonal cover in 26edo)''] (2026) | * [https://www.youtube.com/shorts/1aCl6tuVS0c ''Happy Together - The Turtles (microtonal cover in 26edo)''] (2026) | ||
* ''My Violet - 26edo'' (2026) | * ''My Violet - 26edo'' (2026) | ||
** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki> | ** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>] (Lumatone view) | ||
** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki> | ** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>] (Lumatone view) | ||
** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006) | |||
* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026) | * [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026) | ||