101edo: Difference between revisions

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== Theory ==

101edo is in[[consistent]] in the [[5-odd-limit]], with [[harmonic]]s [[5/1|5]] and [[7/1|7]] falling about halfway between its steps. As such, {{val| 101 160 '''235''' '''284''' }} ([[patent val]]) and {{val| 101 160 '''234''' '''283''' }} (101cd) are about as viable. Using the patent val, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and 51018336/48828125 in the 5-limit; [[126/125]] and [[2430/2401]] in the [[7-limit]]. It can be used to tune the [[grackle]] temperament. The 101cd val provides an excellent tuning for [[witchcraft]] temperament, falling between the 13- and 15-odd-limit least squares tuning. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~

101edo is in[[consistent]] in the [[5-odd-limit]], with [[harmonic]]s [[5/1|5]] and [[7/1|7]] falling about halfway between its steps. As such, {{val| 101 160 '''235''' '''284''' }} ([[patent val]]) and {{val| 101 160 '''234''' '''283''' }} (101cd) are about as viable. Using the patent val, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and 51018336/48828125 in the 5-limit; [[126/125]] and [[2430/2401]] in the [[7-limit]]. It can be used to tune the [[grackle]] temperament. The 101cd val provides an excellent tuning for [[witchcraft]] temperament, falling between the 13- and 15-odd-limit least squares tuning.

=== Odd harmonics ===

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* 3L 2s: 25 13 25 25 13 ((25 38 63 88 101)\101){{clarify}}

* Grackle[7] 5L 2s: 17 17 8 17 17 17 8 ((17 34 42 59 76 93)\101)

* ~~Grumpy Octatonic~~ 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101)

* Pine 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101)

* Superdiatonic 1/13-tone 13;5 relation: 13 13 13 5 13 13 13 13 5 ((13 26 39 44 57 70 83 96 101)\101)

* Sensi[11] 8L 3s: 10 10 7 10 10 10 7 10 10 10 7 ((10 20 27 37 47 57 64 74 84 94)\101){{clarify}}

* Anti-Ketradektriatoh 3L 11s: 7 7 7 8 7 7 7 7 8 7 7 7 7 8 ((7 14 22 29 36 43 50 58 65 72 79 86 93 101)\101)

== Instruments ==

* [[Lumatone mapping for 101edo]]

== Music ==

; [[Francium]]

* "Eggclent" from ''Eggs'' (2025) – [https://open.spotify.com/track/4S0BTeb9yDdMUuT1QJy26H Spotify] | [https://francium223.bandcamp.com/track/eggclent Bandcamp] | [https://www.youtube.com/watch?v=FAe4O71Mvj0 YouTube]

== External links ==

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 == Theory ==
-edo is in[[consistent]] in the [[5-odd-limit]], with [[harmonic]]s [[5/1|5]] and [[7/1|7]] falling about halfway between its steps. As such, {{val| 101 160 '''235''' '''284''' }} ([[patent val]]) and {{val| 101 160 '''234''' '''283''' }} (101cd) are about as viable. Using the patent val, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and 51018336/48828125 in the 5-limit; [[126/125]] and [[2430/2401]] in the [[7-limit]]. It can be used to tune the [[grackle]] temperament. The 101cd val provides an excellent tuning for [[witchcraft]] temperament, falling between the 13- and 15-odd-limit least squares tuning. (''See [[regular temperament]] for more about what all this means and how to use it.'')
+edo is in[[consistent]] in the [[5-odd-limit]], with [[harmonic]]s [[5/1|5]] and [[7/1|7]] falling about halfway between its steps. As such, {{val| 101 160 '''235''' '''284''' }} ([[patent val]]) and {{val| 101 160 '''234''' '''283''' }} (101cd) are about as viable. Using the patent val, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) and 51018336/48828125 in the 5-limit; [[126/125]] and [[2430/2401]] in the [[7-limit]]. It can be used to tune the [[grackle]] temperament. The 101cd val provides an excellent tuning for [[witchcraft]] temperament, falling between the 13- and 15-odd-limit least squares tuning.
 === Odd harmonics ===
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 * 3L 2s: 25 13 25 25 13 ((25 38 63 88 101)\101){{clarify}} <!-- why is this significant? -->
 * Grackle[7] 5L 2s: 17 17 8 17 17 17 8 ((17 34 42 59 76 93)\101)
-* Grumpy Octatonic 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101)
+* Pine 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101)
 * Superdiatonic 1/13-tone 13;5 relation: 13 13 13 5 13 13 13 13 5 ((13 26 39 44 57 70 83 96 101)\101)
 * Sensi[11] 8L 3s: 10 10 7 10 10 10 7 10 10 10 7 ((10 20 27 37 47 57 64 74 84 94)\101){{clarify}} <!-- which val? -->
 * Anti-Ketradektriatoh 3L 11s: 7 7 7 8 7 7 7 7 8 7 7 7 7 8 ((7 14 22 29 36 43 50 58 65 72 79 86 93 101)\101)
+== Instruments ==
+* [[Lumatone mapping for 101edo]]
+== Music ==
+; [[Francium]]
+* "Eggclent" from ''Eggs'' (2025) – [https://open.spotify.com/track/4S0BTeb9yDdMUuT1QJy26H Spotify] | [https://francium223.bandcamp.com/track/eggclent Bandcamp] | [https://www.youtube.com/watch?v=FAe4O71Mvj0 YouTube]
 == External links ==