42edo: Difference between revisions
→Theory: →Subsets and supersets: Add 84edo as superset. |
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 42 factors into {{factorization|42}}, 42edo contains subset edos {{EDOs| 2, 3, 6, 7, 14, and 21 }}. | Since 42 factors into {{factorization|42}}, 42edo contains subset edos {{EDOs| 2, 3, 6, 7, 14, and 21 }}. Doubling it produces [[84edo]], which has excellent corrections for the 3rd, 5th, 13th, and 19th harmonics, as well as a partial correction to the 17th harmonic. | ||
== Intervals == | == Intervals == | ||
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In this table, dup is equivalent to quidsharp, trup is equivalent to quudsharp, trudsharp is equivalent to quup, dudsharp is equivalent to quip, etc. | In this table, dup is equivalent to quidsharp, trup is equivalent to quudsharp, trudsharp is equivalent to quup, dudsharp is equivalent to quip, etc. | ||
{{sharpness | {{Ups and downs sharpness}} | ||
Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used: | Alternatively, sharps and flats with arrows borrowed from [[Helmholtz–Ellis notation]] can be used: | ||
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== Scales == | == Scales == | ||
; [[MOS scale]]s | |||
{{main|List of MOS scales in 42edo}} | {{main|List of MOS scales in 42edo}} | ||
* Eugene/Tritikleismic[9]: '''3 8 3 3 8 3 3 8 3''' | * Eugene/Tritikleismic[9]: '''3 8 3 3 8 3 3 8 3''' | ||
* Eugene/Tritikleismic[15]: '''3 3 2 3 3 3 3 2 3 3 3 3 2 3 3''' | * Eugene/Tritikleismic[15]: '''3 3 2 3 3 3 3 2 3 3 3 3 2 3 3''' | ||
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* 7-tone pelog: 4 5 9 6 3 10 5 | * 7-tone pelog: 4 5 9 6 3 10 5 | ||
* 5-tone slendro: 8 9 8 9 8 | * 5-tone slendro: 8 9 8 9 8 | ||
; Other scales | |||
* 12-tone 6&7edo scale: 6 1 5 2 4 3 3 4 2 5 1 6 | |||
== Instruments == | == Instruments == | ||
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* [https://www.youtube.com/watch?v=PJw8gZyNPjg ''improv 42edo''] (2023) | * [https://www.youtube.com/watch?v=PJw8gZyNPjg ''improv 42edo''] (2023) | ||
* [https://www.youtube.com/watch?v=ljaSpsQP2qc ''Improvisation in 42edo''] (2023), transcribed by [[Stephen Weigel]] (2024) | * [https://www.youtube.com/watch?v=ljaSpsQP2qc ''Improvisation in 42edo''] (2023), transcribed by [[Stephen Weigel]] (2024) | ||
* [https://www.youtube.com/watch?v=cL6CY3U9mHM ''42edo groove''] (2025) | |||
* ''A Hunger Awakes - 42edo'' (2026) | |||
** [https://www.youtube.com/shorts/B90JT_SxSSE <nowiki>[short]</nowiki>] (Lumatone view) | |||
** [https://www.youtube.com/watch?v=VwHqWffglj4 <nowiki>[full version]</nowiki>] (music video with stop-motion by [[Jelly Eyes]]) | |||
* ''Waltz in 42edo'' (2026) | |||
** [https://www.youtube.com/shorts/D_YgzRJFg8I <nowiki>[short]</nowiki>] (Lumatone view) | |||
** [https://www.youtube.com/watch?v=QyglWQ_0bIk <nowiki>[full version]</nowiki>] | |||
; [[James Kukula]] | ; [[James Kukula]] | ||
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* [https://www.youtube.com/watch?v=ORy7nv6SnN8 ''Glory of Them''] (2024) | * [https://www.youtube.com/watch?v=ORy7nv6SnN8 ''Glory of Them''] (2024) | ||
[[Category: | ; [[Stephen Weigel]] | ||
* [https://www.youtube.com/watch?v=tLmaQK10aYM ''Ĥ̶̩̠̐Ä̶̝͙́̓Ȑ̸̢͒K̷̥̩͌͑!̵̙͆̄ THE BIBLICALLY ACCURATE ANGELS SING!''] (2025; mostly in 42edo, but also some in 40edo) | |||
** [https://www.youtube.com/watch?v=NE77rwCsGHw live performance of the above in Munich, Germany] (2026) | |||
[[Category:Augmented]] | |||
{{Todo|review|add rank 2 temperaments table}} | {{Todo|review|add rank 2 temperaments table}} | ||