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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}}


;[[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.


== Some important MOS scales ==
=== Odd harmonics ===
{{Harmonics in equal|101}}


'''13 12 13 13 12 13 12 13:''' ''5L3s MOS'' (Oneirotonic, an 8-tone circulating temperament)
=== 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.


{| class="wikitable"
== Intervals ==
! Steps
{{Interval table}}
! Cents
|-
|13
|154.455
|-
| '''25'''
| '''297.030'''
|-
| '''38'''
| '''451.485'''
|-
|51
|605.9405
|-
| '''63'''
| '''748.515'''
|-
|75
|891.089
|-
| '''88'''
| '''1045.5445'''
|}


'''9 8 9 8 8 9 8 9 8 9 8 8:''' ''5L7s MOS'' (Diatonic Pythagorean, a 12-tone circulating temperament)
== 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)


{| class="wikitable"
== Instruments ==
! Steps
* [[Lumatone mapping for 101edo]]
! Cents
|-
|9
|106.059
|-
| '''17'''
| '''201.980'''
|-
|26
|308.911
|-
| '''34'''
| '''403.960'''
|-
| '''42'''
| '''499.010'''
|-
|51
|605.940
|-
| '''59'''
| '''700.990'''
|-
|68
|807.921
|-
| '''76'''
| '''902.970'''
|-
|85
|1009.901
|-
| '''93'''
| '''1104.950'''
|}


'''10 3 10 3 10 3 10 3 10 3 10 3 10 3 10:''' ''8L7s MOS'' (Opossum)
== 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]


{| class="wikitable"
== External links ==
! Steps
* [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}}
! Cents
|-
|10
|118.812
|-
| '''13'''
| '''154.455'''
|-
|23
|273.267
|-
| '''26'''
| '''308.911'''
|-
|36
|427.723
|-
| '''39'''
| '''463.366'''
|-
|49
|582.178
|-
| '''52'''
| '''617.822'''
|-
|62
|736.337
|-
| '''65'''
| '''772.277'''
|-
|75
|891.089
|-
| '''78'''
| '''926.733'''
|-
|88
|1045.5445
|-
| '''91'''
| '''1081.188'''
|}


'''8 5 8 5 8 5 5 8 5 8 5 8 5 8 5 5:''' ''7L9s MOS'' (Golden Mavila chromatic 1/13-tone)
{| class="wikitable"
! Steps
! Cents
|-
|8
|95.0495
|-
| '''13'''
| '''154.455'''
|-
|21
|249.505
|-
| '''26'''
| '''308.911'''
|-
|34
|403.960
|-
| '''39'''
| '''463.366'''
|-
| '''44'''
| '''522.772'''
|-
|52
|617.822
|-
| '''57'''
| '''677.228'''
|-
|65
|772.277
|-
| '''70'''
| '''831.683'''
|-
|78
|926.733
|-
| '''83'''
| '''986.139'''
|-
|91
|1081.188
|-
| '''96'''
| '''1045.545'''
|}
'''7 3 7 3 7 7 3 7 3 7 3 7 7 3 7 3 7 3 7:''' ''8L3s MOS'' (Improper Sensi-11)
{| class="wikitable"
! Steps
! Cents
|-
|7
|83.168
|-
| '''10'''
| '''118.812'''
|-
|17
|201.980
|-
| '''20'''
| '''237.624'''
|-
| '''27'''
| '''320.792'''
|-
|34
|403.960
|-
| '''37'''
| '''439.604'''
|-
|44
|527.772
|-
| '''47'''
| '''558.416'''
|-
|54
|641.584
|-
| '''57'''
| '''677.228'''
|-
| '''64'''
| '''760.396'''
|-
|71
|843.564
|-
| '''74'''
| '''879.218'''
|-
|81
|962.376
|-
| '''84'''
| '''998.020'''
|-
|91
|1081.188
|-
| '''94'''
| '''1116.842'''
|}
'''7 7 7 7 1 7 7 7 7 7 1 7 7 7 7 7 1:''' ''14L3s MOS'' (Anti-Ketradektriatoh)
{| class="wikitable"
! Steps
! Cents
|-
| '''7'''
| '''83.168'''
|-
| '''14'''
| '''166.337'''
|-
|21
|249.505
|-
| '''22'''
| '''261.386'''
|-
| '''29'''
| '''344.554'''
|-
| '''36'''
| '''427.723'''
|-
| '''43'''
| '''510.891'''
|-
| '''50'''
| '''594.059'''
|-
|57
|677.278
|-
| '''58'''
| '''689.119'''
|-
| '''65'''
| '''772.287'''
|-
| '''72'''
| '''855.446'''
|-
| '''79'''
| '''938.614'''
|-
| '''86'''
| '''1021.782'''
|-
| '''93'''
| '''1104.950'''
|-
|100
|1188.119
|}
== Links ==
[http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal]
[[Category:101-tone]]
[[Category:Armodue]]
[[Category:Armodue]]
[[Category:Equal divisions of the octave]]
[[Category:Grackle]]
[[Category:Grackle]]
[[Category:Prime EDO]]
[[Category:Pythagorean]]
[[Category:Scales]]
[[Category:todo:improve_layout]]
Retrieved from "https://en.xen.wiki/w/101edo"