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| '''''101-EDO''''' divides the [[Octave|octave]] into 101 equal parts of 11.881 [[cent|cent]]s each. It can be used to tune the [[Schismatic_family|grackle temperament]]. It is the 26th [[prime_numbers|prime]] edo. The 101cd val provides an excellent tuning for [[Magic_family#Witchcraft|witchcraft temperament]], falling between the 13 and 15 limit least squares tuning.
| | {{Infobox ET}} |
| | {{ED intro}} |
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| [[5-limit|5-limit]] commas: 32805/32768, <5 13 -11| | | == 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. |
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| [[7-limit|7-limit]] commas: 126/125, 32805/32768, 2430/2401
| | === Odd harmonics === |
| | {{Harmonics in equal|101}} |
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| ==<u>Some important MOS scales:</u>== | | === Subsets and supersets === |
| | 101edo is the 26th [[prime edo]], following [[97edo]] and before [[103edo]]. [[202edo]], which doubles it, provides a good correction to the 5th, 7th, and 11th harmonics. |
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| '''25 13 25 25 13:''' ''3L2s MOS'' (Pentatonic)
| | == Intervals == |
| | {{Interval table}} |
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| |
|
| {| class="wikitable"
| | == Scales == |
| |-
| | === Mos scales === |
| | | 25
| | * 3L 2s: 25 13 25 25 13 ((25 38 63 88 101)\101){{clarify}} <!-- why is this significant? --> |
| | | 297.03
| | * Grackle[7] 5L 2s: 17 17 8 17 17 17 8 ((17 34 42 59 76 93)\101) |
| |-
| | * Pine 7L 1s: 13 13 13 13 13 13 13 10 ((13 26 39 52 65 78 91 101)\101) |
| | | 38
| | * 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) |
| | | 451.485
| | * 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) |
| | | 63
| |
| | | 748.515
| |
| |-
| |
| | | 88
| |
| | | 1045.545
| |
| |}
| |
| '''17 17 8 17 17 17 8:''' ''5L2s MOS'' (Diatonic Pythagorean)
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|
| |
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| {| class="wikitable"
| | == Instruments == |
| |-
| | * [[Lumatone mapping for 101edo]] |
| | | '''17'''
| |
| | | '''201.98'''
| |
| |-
| |
| | | 34
| |
| | | 403.96
| |
| |-
| |
| | | '''42'''
| |
| | | '''499.01'''
| |
| |-
| |
| | | '''59'''
| |
| | | '''700.99'''
| |
| |-
| |
| | | '''76'''
| |
| | | '''902.97'''
| |
| |-
| |
| | | 93
| |
| | | 1104.95
| |
| |}
| |
| '''13 13 13 13 13 13 13 10:''' ''7L1s MOS'' (Grumpy Octatonic)
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| {| class="wikitable"
| | == Music == |
| |-
| | ; [[Francium]] |
| | | 13
| | * "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] |
| | | 154.455
| |
| |-
| |
| | | 26
| |
| | | 308.911
| |
| |- | |
| | | 39
| |
| | | 463.366
| |
| |-
| |
| | | 52
| |
| | | 617.822
| |
| |- | |
| | | 65
| |
| | | 772.277
| |
| |-
| |
| | | 78
| |
| | | 926.733
| |
| |-
| |
| | | 91
| |
| | | 1081.188
| |
| |}
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| '''13 13 13 5 13 13 13 13 5:''' ''7L2s MOS'' (Superdiatonic 1/13-tone 13;5 relation)
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| {| class="wikitable"
| | == External links == |
| |-
| | * [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}} |
| | | '''13/101'''
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| | | '''154.455'''
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| |-
| |
| | | '''26/101'''
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| | | '''308.911'''
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| |-
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| | | 39/101
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| | | 463.366
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| |-
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| | | '''44/101'''
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| | | '''522.772'''
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| |-
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| | | '''57/101'''
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| | | '''677.228'''
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| |-
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| | | '''70/101'''
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| | | '''831.683'''
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| |-
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| | | '''83/101'''
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| | | '''986.139'''
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| |-
| |
| | | 96/101
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| | | 1045.545
| |
| |}
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| '''10 10 7 10 10 10 7 10 10 10 7:''' ''8L3s MOS'' (Improper Sensi-11)
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|
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|
| {| class="wikitable"
| | [[Category:Armodue]] |
| |-
| | [[Category:Grackle]] |
| | | '''10'''
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| | | '''118.812'''
| |
| |-
| |
| | | 20
| |
| | | 237.624
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| |-
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| | | '''27'''
| |
| | | '''320.792'''
| |
| |-
| |
| | | '''37'''
| |
| | | '''439.604'''
| |
| |-
| |
| | | '''47'''
| |
| | | '''558.416'''
| |
| |-
| |
| | | 57
| |
| | | 677.228
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| |-
| |
| | | '''64'''
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| | | '''760.396'''
| |
| |-
| |
| | | '''74'''
| |
| | | '''879.218'''
| |
| |-
| |
| | | '''84'''
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| | | '''998.03'''
| |
| |-
| |
| | | 94
| |
| | | 1116.842
| |
| |}
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| '''7 7 7 8 7 7 7 7 8 7 7 7 7 8:''' ''3L11s MOS'' (Anti-Ketradektriatoh)
| |
| | |
| {| class="wikitable"
| |
| |-
| |
| | | '''7'''
| |
| | | '''83.168'''
| |
| |-
| |
| | | '''14'''
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| | | '''166.337'''
| |
| |-
| |
| | | 22
| |
| | | 261.386
| |
| |-
| |
| | | '''29'''
| |
| | | '''344.5545'''
| |
| |-
| |
| | | '''36'''
| |
| | | '''427.723'''
| |
| |-
| |
| | | '''43'''
| |
| | | '''510.891'''
| |
| |-
| |
| | | '''50'''
| |
| | | '''594.0595'''
| |
| |-
| |
| | | 58
| |
| | | 689.119
| |
| |-
| |
| | | '''65'''
| |
| | | '''772.287'''
| |
| |-
| |
| | | '''72'''
| |
| | | '''855.4455'''
| |
| |-
| |
| | | '''79'''
| |
| | | '''938.614'''
| |
| |-
| |
| | | '''86'''
| |
| | | '''1021.782'''
| |
| |-
| |
| | | 93
| |
| | | 1104.95
| |
| |}
| |
| | |
| =Links=
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| [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] [[Category:101-tone]]
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| [[Category:101edo]] | |
| [[Category:armodue]]
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| [[Category:edo]]
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| [[Category:equal]]
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| [[Category:grackle]]
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| [[Category:prime_edo]]
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| [[Category:pythagorean]]
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| [[Category:scales]]
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| [[Category:todo:improve_leayout]]
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| [[Category:todo:unify_precision]]
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