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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.
'''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.


;[[5-limit]] commas: 32805/32768 ( {{monzo| -15 8 1 }} ), 51018336/48828125 ( {{monzo| 5 13 -11 }} )
; [[5-limit]] commas: 32805/32768 ( {{monzo| -15 8 1 }} ), 51018336/48828125 ( {{monzo| 5 13 -11 }} )
;[[7-limit]] commas: 126/125, 32805/32768, 2430/2401
; [[7-limit]] commas: 126/125, 32805/32768, 2430/2401


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


'''13 12 13 13 12 13 12 13:''' ''5L3s MOS'' (Oneirotonic, an 8-tone circulating temperament)
'''25 13 25 25 13:''' ''3L2s MOS'' (Pentatonic)


{| class="wikitable"
{| class="wikitable right-all"
! Steps
! Steps
! Cents
! Cents
!Difference from 8edo
|-
|-
|13
| 25
|154.455
| 297.030
| +4.455¢
|-
|-
|'''25'''
| 38
|'''297.030'''
| 451.485
| -2.97¢
|-
|-
|'''38'''
| 63
|'''451.485'''
| 748.515
| +1.485¢
|-
|-
|51
| 88
|605.9405
| 1045.545
| +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)
'''17 17 8 17 17 17 8:''' ''5L2s MOS'' (Diatonic Pythagorean)


{| class="wikitable"
{| class="wikitable"
!Steps
! Steps
!Cents
! Cents
!Difference from 12edo
|-
|-
|9
| 17
|106.059
| 201.980
| +6.059¢
|-
|-
|'''17'''
| 34
|'''201.980'''
| 403.960
| +1.98¢
|-
|26
| 308.911
| +8.911¢
|-
|-
|'''34'''
| 42
|'''403.960'''
| 499.010
| +3.96¢
|-
|-
|'''42'''
| 59
|'''499.010'''
| 700.990
| -.99¢
|-
|-
|51
| 76
|605.9405
| 902.970
| +5.9405¢
|-
|-
|'''59'''
| 93
|'''700.990'''
| 1104.950
| +.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)
'''13 13 13 13 13 13 13 10:''' ''7L1s MOS'' (Grumpy Octatonic)


{| class="wikitable"
{| class="wikitable"
!Steps
! Steps
!Cents
! Cents
|-
|-
|10
| 13
|118.812
| 154.455
|-
|-
|'''13'''
| 26
|'''154.455'''
| 308.911
|-
|23
|273.267
|-
|'''26'''
|'''308.911'''
|-
|-
|36
| 39
|427.723
| 463.366
|-
|-
|'''39'''
| 52
|'''463.366'''
| 617.822
|-
|-
|49
| 65
|582.178
| 772.277
|-
|-
|'''52'''
| 78
|'''617.822'''
| 926.733
|-
|-
|62
| 91
|736.337
| 1081.188
|-
|'''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)
'''13 13 13 5 13 13 13 13 5:''' ''7L2s MOS'' (Superdiatonic 1/13-tone 13;5 relation)


{| class="wikitable"
{| class="wikitable"
!Steps
! Steps
!Cents
! Cents
|-
|-
|8
| 13
|95.0495
| 154.455
|-
|-
|'''13'''
| 26
|'''154.455'''
| 308.911
|-
|-
|21
| 39
|249.505
| 463.366
|-
|-
|'''26'''
| 44
|'''308.911'''
| 522.772
|-
|-
|34
| 57
| 403.960
| 677.228
|-
|-
|'''39'''
| 70
|'''463.366'''
| 831.683
|-
|-
|'''44'''
| 83
|'''522.772'''
| 986.139
|-
|-
|52
| 96
|617.822
| 1045.545
|-
|'''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)
'''10 10 7 10 10 10 7 10 10 10 7:''' ''8L3s MOS'' (Improper Sensi-11)


{| class="wikitable"
{| class="wikitable"
!Steps
! Steps
!Cents
! 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
| 10
|368.317
| 118.812
| +8.317¢
|-
|-
|'''34'''
| 20
|'''403.960'''
| 237.624
| +3.96¢
|-
|-
|'''37'''
| 27
|'''439.604'''
| 320.792
| -.396¢
|-
|-
|41
| 37
|487.129
| 439.604
| +7.129¢
|-
|-
|'''44'''
| 47
|'''527.772'''
| 558.416
| +7.772¢
|-
|-
|'''47'''
| 57
|'''558.416'''
| 677.228
| +8.416¢
|-
|-
|51
| 64
|605.9405
| 760.396
| +5.9405¢
|-
|-
|'''54'''
| 74
| '''641.584'''
| 879.218
| +1.584¢
|-
|-
|'''57'''
| 84
|'''677.228'''
| 998.020
| +7.228¢
|-
|-
|61
| 94
|724.7525
| 1116.842
| +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)
'''7 7 7 8 7 7 7 7 8 7 7 7 7 8:''' ''3L11s MOS'' (Anti-Ketradektriatoh)


{| class="wikitable"
{| class="wikitable"
!Steps
! Steps
!Cents
! 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 or allows one to use an MOS scale with 50 or more large steps 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
|[[3L 11s]]
|-
|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
| 7
|17L 11s
| 83.168
|-
|-
|29
| 14
|14L 15s
| 166.337
|-
|-
|30
| 22
|11L 19s
| 261.386
|-
|-
|31
| 29
|8L 23s
| 344.554
|-
|-
|32
| 36
|5L 27s
| 427.723
|-
|-
|33
| 43
|2L 31s
| 510.891
|-
|-
|34
| 50
|33L 1s
| 594.059
| rowspan="17" |3:2
|-
|-
|35
| 58
|31L 4s
| 689.119
|-
|-
|36
| 65
|29L 7s
| 772.287
|-
|-
|37
| 72
|27L 10s
| 855.446
|-
|-
|38
| 79
|25L 13s
| 938.614
|-
|-
|39
| 86
|23L 16s
| 1021.782
|-
|-
|40
| 93
|21L 19s
| 1104.950
|-
|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]
== Links ==
 
[http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal] {{dead link}}


[[Category:101-tone]]
[[Category:101-tone]]
Line 633: Line 203:
[[Category:Pythagorean]]
[[Category:Pythagorean]]
[[Category:Scales]]
[[Category:Scales]]
{{todo|improve_layout|unify precision}}

Revision as of 14:33, 5 June 2021

101 EDO divides the octave into 101 equal parts of 11.881 cents 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.

5-limit commas
32805/32768 ( [-15 8 1⟩ ), 51018336/48828125 ( [5 13 -11⟩ )
7-limit commas
126/125, 32805/32768, 2430/2401

Some important MOS scales

25 13 25 25 13: 3L2s MOS (Pentatonic)

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)

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)

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)

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)

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)

Steps 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

The Ellis duodene in 101-equal [dead link]

Retrieved from "https://en.xen.wiki/index.php?title=101edo&oldid=71938"