26edo: Difference between revisions
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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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{{Catrel|26edo tracks}} | {{Catrel|26edo tracks}} | ||
=== Modern renderings === | === 26 equal divisions of the octave (26edo proper) === | ||
==== Modern renderings ==== | |||
; {{W|Johann Sebastian Bach}} | ; {{W|Johann Sebastian Bach}} | ||
* [https://www.youtube.com/watch?v=LUNOFjiyZ0Y ''Contrapunctus 4'' from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024) | * [https://www.youtube.com/watch?v=LUNOFjiyZ0Y ''Contrapunctus 4'' from ''The Art of Fugue'', BWV 1080] (1742–1749) – rendered by Claudi Meneghin (2024) | ||
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* [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024) | * [https://www.youtube.com/watch?v=-EVO5ntuoSM ''Prelude in E Minor "The Little"''] – rendered by Claudi Meneghin (2024) | ||
=== 21st century === | ==== 21st century ==== | ||
; [[Abnormality]] | ; [[Abnormality]] | ||
* [https://www.youtube.com/watch?v=Tl-AN2zQeAI ''Break''] (2024) | * [https://www.youtube.com/watch?v=Tl-AN2zQeAI ''Break''] (2024) | ||
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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]] | ||
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; [[YoVariable]] | ; [[YoVariable]] | ||
* [https://www.youtube.com/watch?v=01w70PbbT3o ''Jingle Bells (26edo microtonal Lumatone cover + Mystery Song)''] (2025) | * [https://www.youtube.com/watch?v=01w70PbbT3o ''Jingle Bells (26edo microtonal Lumatone cover + Mystery Song)''] (2025) | ||
=== Unequal Derivatives of 26edo === | |||
; [[Bryan Deister]] | |||
* [https://www.youtube.com/shorts/mzUGcki6H0Y ''<nowiki>Daisy Bell - Harry Dacre (microtonal cover in unequal 26ish tone [displaced from 26edo in dozens])</nowiki>''] (2026) — from Bryan Deister's video comments, "displacement in cents roughly: 0, -8, -3, -12, 14, 5, 18, 3, -12, 13, -15, 10" (these repeat every 12 notes, NOT every 13 note semi-octave, thus causing each octave to be different) | |||
[[Category:Listen]] | [[Category:Listen]] | ||