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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.


== Intervals ==
=== Odd harmonics ===
{| class="wikitable"
{{Harmonics in equal|101}}
!Degree
!Cents
|-
|0
|0.000
|-
|1
|11.881
|-
|2
|23.762
|-
|3
|35.644
|-
|4
|47.525
|-
|5
|59.406
|-
|6
|71.287
|-
|7
|83.168
|-
|8
|95.050
|-
|9
|106.931
|-
|10
|118.812
|-
|11
|130.693
|-
|12
|142.574
|-
|13
|154.455
|-
|14
|166.337
|-
|15
|178.218
|-
|16
|190.099
|-
|17
|201.980
|-
|18
|213.861
|-
|19
|225.743
|-
|20
|237.624
|-
|21
|249.505
|-
|22
|261.386
|-
|23
|273.267
|-
|24
|285.149
|-
|25
|297.030
|-
|26
|308.911
|-
|27
|320.792
|-
|28
|332.673
|-
|29
|344.554
|-
|30
|356.436
|-
|31
|368.317
|-
|32
|380.198
|-
|33
|392.079
|-
|34
|403.960
|-
|35
|415.842
|-
|36
|427.723
|-
|37
|439.604
|-
|38
|451.485
|-
|39
|463.366
|-
|40
|475.248
|-
|41
|487.129
|-
|42
|499.010
|-
|43
|510.891
|-
|44
|522.772
|-
|45
|534.653
|-
|46
|546.535
|-
|47
|558.416
|-
|48
|570.297
|-
|49
|582.178
|-
|50
|594.059
|-
|...
|...
|}


== Some important MOS scales ==
=== 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.


'''25 13 25 25 13:''' ''3L2s MOS'' (Pentatonic)
== Intervals ==
 
{{Interval table}}
{| class="wikitable right-all"
! Steps
! Cents
|-
| 25
| 297.030
|-
| 38
| 451.485
|-
| 63
| 748.515
|-
| 88
| 1045.545
|}
 
'''17 17 8 17 17 17 8:''' ''5L2s MOS'' (Diatonic Pythagorean)
 
{| class="wikitable right-all"
! Steps
! Cents
|-
| 17
| 201.980
|-
| 34
| 403.960
|-
| 42
| 499.010
|-
| 59
| 700.990
|-
| 76
| 902.970
|-
| 93
| 1104.950
|}
 
'''13 13 13 13 13 13 13 10:''' ''7L1s MOS'' (Grumpy Octatonic)
 
{| class="wikitable right-all"
! Steps
! Cents
|-
| 13
| 154.455
|-
| 26
| 308.911
|-
| 39
| 463.366
|-
| 52
| 617.822
|-
| 65
| 772.277
|-
| 78
| 926.733
|-
| 91
| 1081.188
|}
 
'''13 13 13 5 13 13 13 13 5:''' ''7L2s MOS'' (Superdiatonic 1/13-tone 13;5 relation)
 
{| class="wikitable right-all"
! Steps
! Cents
|-
| 13
| 154.455
|-
| 26
| 308.911
|-
| 39
| 463.366
|-
| 44
| 522.772
|-
| 57
| 677.228
|-
| 70
| 831.683
|-
| 83
| 986.139
|-
| 96
| 1045.545
|}
 
'''10 10 7 10 10 10 7 10 10 10 7:''' ''8L3s MOS'' (Improper Sensi-11)
 
{| class="wikitable right-all"
! Steps
! Cents
|-
| 10
| 118.812
|-
| 20
| 237.624
|-
| 27
| 320.792
|-
| 37
| 439.604
|-
| 47
| 558.416
|-
| 57
| 677.228
|-
| 64
| 760.396
|-
| 74
| 879.218
|-
| 84
| 998.020
|-
| 94
| 1116.842
|}


'''7 7 7 8 7 7 7 7 8 7 7 7 7 8:''' ''3L11s MOS'' (Anti-Ketradektriatoh)
== 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 right-all"
== Instruments ==
! Steps
* [[Lumatone mapping for 101edo]]
! Cents
|-
| 7
| 83.168
|-
| 14
| 166.337
|-
| 22
| 261.386
|-
| 29
| 344.554
|-
| 36
| 427.723
|-
| 43
| 510.891
|-
| 50
| 594.059
|-
| 58
| 689.119
|-
| 65
| 772.287
|-
| 72
| 855.446
|-
| 79
| 938.614
|-
| 86
| 1021.782
|-
| 93
| 1104.950
|}


== Links ==
== 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]


[http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}}
== External links ==
* [http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}}


[[Category:Armodue]]
[[Category:Armodue]]
[[Category:Equal divisions of the octave]]
[[Category:Grackle]]
[[Category:Grackle]]
[[Category:Prime EDO]]
[[Category:3-limit]]
Retrieved from "https://en.xen.wiki/w/101edo"