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| '''''101-EDO''''' divides the [[octave]] into 101 equal parts of 11.881 [[cent]]s each. It can be used to tune the [[grackle]] temperament. It is the 26th [[prime EDO]]. The 101cd val provides an excellent tuning for [[witchcraft]] temperament, falling between the 13 and 15 limit least squares tuning.
| | {{Infobox ET}} |
| | {{ED intro}} |
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| ;[[5-limit]] commas: 32805/32768 ( {{Monzo| -15 8 1 }} ), 51018336/48828125 ( {{Monzo| 5 13 -11 }} )
| | == Theory == |
| ;[[7-limit]] commas: 126/125, 32805/32768, 2430/2401 | | 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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| == Some important MOS scales == | | === Odd harmonics === |
| | {{Harmonics in equal|101}} |
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| '''25 13 25 25 13:''' ''3L2s MOS'' (Pentatonic)
| | === 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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| {| class="wikitable"
| | == Intervals == |
| ! Steps
| | {{Interval table}} |
| ! Cents
| |
| |-
| |
| | 25
| |
| | 297.030
| |
| |-
| |
| | 38
| |
| | 451.485
| |
| |-
| |
| | 63
| |
| | 748.515
| |
| |-
| |
| | 88
| |
| | 1045.545
| |
| |}
| |
|
| |
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| '''17 17 8 17 17 17 8:''' ''5L2s MOS'' (Diatonic Pythagorean)
| | == Scales == |
| | === Mos scales === |
| | * 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) |
| | * 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) |
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| {| class="wikitable"
| | == Instruments == |
| ! Steps
| | * [[Lumatone mapping for 101edo]] |
| ! Cents
| |
| |-
| |
| | '''17'''
| |
| | '''201.980'''
| |
| |-
| |
| | 34
| |
| | 403.960
| |
| |-
| |
| | '''42'''
| |
| | '''499.010'''
| |
| |-
| |
| | '''59'''
| |
| | '''700.990'''
| |
| |-
| |
| | '''76'''
| |
| | '''902.970'''
| |
| |-
| |
| | 93
| |
| | 1104.950
| |
| |}
| |
|
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| '''13 13 13 13 13 13 13 10:''' ''7L1s MOS'' (Grumpy Octatonic) | | == 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] |
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| {| class="wikitable"
| | == External links == |
| ! Steps
| | * [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}} |
| ! Cents
| |
| |-
| |
| | 13
| |
| | 154.455
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| |-
| |
| | 26
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| | 308.911
| |
| |-
| |
| | 39
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| | 463.366
| |
| |-
| |
| | 52
| |
| | 617.822
| |
| |-
| |
| | 65
| |
| | 772.277
| |
| |-
| |
| | 78
| |
| | 926.733
| |
| |-
| |
| | 91
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| | 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"
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| ! Steps
| |
| ! Cents
| |
| |-
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| | '''13'''
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| | '''154.455'''
| |
| |-
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| | '''26'''
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| | '''308.911'''
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| |-
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| | 39
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| | 463.366
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| |-
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| | '''44'''
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| | '''522.772'''
| |
| |-
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| | '''57'''
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| | '''677.228'''
| |
| |-
| |
| | '''70'''
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| | '''831.683'''
| |
| |-
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| | '''83'''
| |
| | '''986.139'''
| |
| |-
| |
| | 96
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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"
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| ! Steps
| |
| ! Cents
| |
| |-
| |
| | '''10'''
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| | '''118.812'''
| |
| |-
| |
| | 20
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| | 237.624
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| |-
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| | '''27'''
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| | '''320.792'''
| |
| |-
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| | '''37'''
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| | '''439.604'''
| |
| |-
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| | '''47'''
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| | '''558.416'''
| |
| |-
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| | 57
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| | 677.228
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| |-
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| | '''64'''
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| | '''760.396'''
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| |-
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| | '''74'''
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| | '''879.218'''
| |
| |-
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| | '''84'''
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| | '''998.020'''
| |
| |-
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| | 94
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| | 1116.842
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| |}
| |
|
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| '''7 7 7 8 7 7 7 7 8 7 7 7 7 8:''' ''3L11s MOS'' (Anti-Ketradektriatoh)
| |
|
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| {| class="wikitable"
| |
| ! Steps
| |
| ! Cents
| |
| |-
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| | '''7'''
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| | '''83.168'''
| |
| |-
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| | '''14'''
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| | '''166.337'''
| |
| |-
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| | 22
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| | 261.386
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| |-
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| | '''29'''
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| | '''344.554'''
| |
| |-
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| | '''36'''
| |
| | '''427.723'''
| |
| |-
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| | '''43'''
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| | '''510.891'''
| |
| |-
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| | '''50'''
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| | '''594.059'''
| |
| |-
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| | 58
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| | 689.119
| |
| |-
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| | '''65'''
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| | '''772.287'''
| |
| |-
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| | '''72'''
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| | '''855.446'''
| |
| |-
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| | '''79'''
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| | '''938.614'''
| |
| |-
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| | '''86'''
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| | '''1021.782'''
| |
| |-
| |
| | 93
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| | 1104.950
| |
| |}
| |
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| == Links ==
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| [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal]
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| [[Category:101-tone]]
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| [[Category:Armodue]] | | [[Category:Armodue]] |
| [[Category:Edo]]
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| [[Category:Grackle]] | | [[Category:Grackle]] |
| [[Category:Prime EDO]]
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| [[Category:Pythagorean]]
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| [[Category:Scales]]
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| [[Category:todo:improve_layout]]
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