26edo: Difference between revisions
→Music: Split into 26edo proper and unequal derivatives of 26edo, starting with Bryan Deister's Daisy Bell - Harry Dacre (microtonal cover in unequal 26ish tone [displaced from 26edo in dozens]) (2026) |
Move Fynn's comma to subsets and supersets section |
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{{ | {{Interwiki | ||
| en = 26edo | |||
| de = 26-EDO | | de = 26-EDO | ||
| es = | | es = | ||
| ja = | | ja = | ||
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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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| 8 | | 8 | ||
| 369.23 | | 369.23 | ||
| [[5/4]], [[11/9]], [[16/13]] | | [[5/4]], [[11/9]], [[16/13]], [[26/21]] | ||
| M3 | | M3 | ||
| F# | | F# | ||
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| 10 | | 10 | ||
| 461.54 | | 461.54 | ||
| [[21/16]], [[13/10]] | | [[21/16]], [[13/10]], [[64/49]] | ||
| d4 | | d4 | ||
| Gb | | Gb | ||
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| 16 | | 16 | ||
| 738.46 | | 738.46 | ||
| [[32/21]], [[20/13]] | | [[32/21]], [[20/13]], [[49/32]] | ||
| A5 | | A5 | ||
| A# | | A# | ||
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| 18 | | 18 | ||
| 830.77 | | 830.77 | ||
| [[13/8]], [[ | | [[8/5]], [[13/8]], [[21/13]] | ||
| m6 | | m6 | ||
| Bb | | Bb | ||
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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}}. | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
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** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>''] | ** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>''] | ||
** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>''] | ** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>''] | ||
* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026) | |||
; [[User:Eboone|Ebooone]] | ; [[User:Eboone|Ebooone]] | ||