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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
!Difference from 8edo
|-
|13
|154.455
| +4.455¢
|-
|'''25'''
|'''297.030'''
| -2.97¢
|-
|'''38'''
|'''451.485'''
| +1.485¢
|-
|51
|605.9405
| +5.9405¢
|-
|'''63'''
|'''748.515'''
| -1.485¢
|-
|75
|891.089
| -8.911¢
|-
|'''88'''
| '''1045.5445'''
| -4.5555¢
|}


'''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
!Difference from 12edo
|-
|9
|106.059
| +6.059¢
|-
|'''17'''
|'''201.980'''
| +1.98¢
|-
|26
| 308.911
| +8.911¢
|-
|'''34'''
|'''403.960'''
| +3.96¢
|-
|'''42'''
|'''499.010'''
| -.99¢
|-
|51
|605.9405
| +5.9405¢
|-
|'''59'''
|'''700.990'''
| +.99¢
|-
|68
|807.921
| +7.921¢
|-
|'''76'''
|'''902.970'''
| +2.97¢
|-
| 85
|1009.901
| +9.901¢
|-
| '''93'''
|'''1104.950'''
| +4.95¢
|}


'''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'''
|}
'''4 3 3 4 3 3 4 3 4 3 3 4 3 3 4 3 3 4 3 4 3 3 4 3 3 4 3 3 4 3:''' ''11L19s MOS'' (Improper Sensi-30, a 30-tone circulating temperament)
{| class="wikitable"
!Steps
!Cents
!Difference from 30edo
|-
|4
|47.525
| +7.525¢
|-
|'''7'''
|'''83.168'''
| +3.168¢
|-
|'''10'''
|'''118.812'''
| -1.188¢
|-
|14
|166.336
| +6.336¢
|-
|'''17'''
| '''201.980'''
| +1.98¢
|-
|'''20'''
|'''237.624'''
| +7.624¢
|-
|'''24'''
|'''285.1485'''
| +5.1485¢
|-
|'''27'''
|'''320.792'''
| +.792¢
|-
|31
|368.317
| +8.317¢
|-
|'''34'''
|'''403.960'''
| +3.96¢
|-
|'''37'''
|'''439.604'''
| -.396¢
|-
|41
|487.129
| +7.129¢
|-
|'''44'''
|'''527.772'''
| +7.772¢
|-
|'''47'''
|'''558.416'''
| +8.416¢
|-
|51
|605.9405
| +5.9405¢
|-
|'''54'''
| '''641.584'''
| +1.584¢
|-
|'''57'''
|'''677.228'''
| +7.228¢
|-
|61
|724.7525
| +4.7525¢
|-
|'''64'''
|'''760.396'''
| +.396¢
|-
|68
|807.921
| +7.921¢
|-
|'''71'''
|'''843.564'''
| +3.564¢
|-
|'''74'''
|'''879.218'''
| -.792¢
|-
|78
|926.733
| +6.733¢
|-
|'''81'''
|'''962.376'''
| +2.376¢
|-
|'''84'''
|'''998.020'''
| -1.98¢
|-
|88
|1045.5445
| +5.5445¢
|-
|'''91'''
|'''1081.188'''
| +1.188¢
|-
|'''94'''
|'''1116.842'''
| -3.158¢
|-
|98
|1164.3564
| +4.356¢
|}
'''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
|}Since 101edo has a step of 11.881 cents, it also allows one to use its MOS scales as circulating temperaments. It is the first edo which truly allows one to use an 80 tone or larger MOS scale as a circulating temperament.
{| class="wikitable"
|+Circulating temperaments in 101edo
!Tones
!Pattern
!L:s
|-
|5
|[[1L 4s]]
|21:20
|-
|6
|[[5L 1s]]
|17:16
|-
|7
|[[3L 4s]]
|15:14
|-
|8
|[[5L 3s]]
|13:12
|-
|9
|[[2L 7s]]
|12:11
|-
|10
|[[1L 9s]]
|11:10
|-
|11
|[[2L 9s]]
|10:9
|-
|12
|[[5L 7s]]
|9:8
|-
|13
|[[10L 3s]]
| rowspan="2" |8:7
|-
|14
|[[2L 12s]]
|-
|15
|[[11L 4s]]
| rowspan="2" |7:6
|-
|16
|[[5L 11s]]
|-
|17
|16L 1s
| rowspan="4" |6:5
|-
|18
|11L 7s
|-
|19
|[[6L 13s]]
|-
|20
|1L 19s
|-
|21
|17L 4s
| rowspan="5" |5:4
|-
|22
|13L 9s
|-
|23
|9L 14s
|-
|24
|[[5L 19s]]
|-
|25
|1L 24s
|-
|26
|23L 3s
| rowspan="8" |4:3
|-
|27
|20L 7s
|-
|28
|17L 11s
|-
|29
|14L 15s
|-
|30
|11L 19s
|-
|31
|8L 23s
|-
|32
|5L 27s
|-
|33
|2L 31s
|-
|34
|33L 1s
| rowspan="17" |3:2
|-
|35
|31L 4s
|-
|36
|29L 7s
|-
|37
|27L 10s
|-
|38
|25L 13s
|-
|39
|23L 16s
|-
|40
|21L 19s
|-
|41
|19L 22s
|-
|42
|17L 25s
|-
|43
|15L 28s
|-
|44
|13L 31s
|-
|45
|11L 34s
|-
|46
|9L 37s
|-
|47
|7L 40s
|-
|48
|5L 43s
|-
|49
|3L 49s
|-
|50
|1L 49s
|-
|51
|50L 1s
| rowspan="30" |2:1
|-
|52
|49L 3s
|-
|53
|48L 5s
|-
|54
|47L 7s
|-
|55
|46L 9s
|-
|56
|45L 11s
|-
|57
|44L 13s
|-
|58
|43L 15s
|-
|59
|42L 17s
|-
|60
|41L 19s
|-
|61
|40L 21s
|-
|62
|39L 23s
|-
|63
|38L 25s
|-
|64
|37L 27s
|-
|65
|36L 29s
|-
|66
|35L 31s
|-
|67
|34L 33s
|-
|68
|33L 35s
|-
|69
|32L 37s
|-
|70
|31L 39s
|-
|71
|30L 41s
|-
|72
|29L 43s
|-
|73
|28L 45s
|-
|74
|27L 47s
|-
|75
|26L 49s
|-
|76
|25L 51s
|-
|77
|24L 53s
|-
|78
|23L 55s
|-
|79
|22L 57s
|-
|80
|21L 59s
|}
==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]]
{{todo|improve_layout|unify precision}}
Retrieved from "https://en.xen.wiki/w/101edo"