101edo: Difference between revisions

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'''''101-EDO''''' divides the [[Octave|octave]] into 101 equal parts of 11.881 [[cent|cent]]s each. It can be used to tune the [[Schismatic_family|grackle temperament]]. It is the 26th [[prime_numbers|prime]] edo. The 101cd val provides an excellent tuning for [[Magic_family#Witchcraft|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|5-limit]] commas: 32805/32768, <5 13 -11|
;[[5-limit]] commas: 32805/32768, <5 13 -11|
;[[7-limit]] commas: 126/125, 32805/32768, 2430/2401


[[7-limit|7-limit]] commas: 126/125, 32805/32768, 2430/2401
== Some important MOS scales ==
 
==<u>Some important MOS scales:</u>==


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


{| class="wikitable"
{| class="wikitable"
! Steps
! Cents
|-
|-
| | 25
| 25
| | 297.03
| 297.03
|-
|-
| | 38
| 38
| | 451.485
| 451.485
|-
|-
| | 63
| 63
| | 748.515
| 748.515
|-
|-
| | 88
| 88
| | 1045.545
| 1045.545
|}
|}
'''17 17 8 17 17 17 8:''' ''5L2s MOS'' (Diatonic Pythagorean)
'''17 17 8 17 17 17 8:''' ''5L2s MOS'' (Diatonic Pythagorean)


{| class="wikitable"
{| class="wikitable"
! Steps
! Cents
|-
|-
| | '''17'''
| '''17'''
| | '''201.98'''
| '''201.98'''
|-
|-
| | 34
| 34
| | 403.96
| 403.96
|-
|-
| | '''42'''
| '''42'''
| | '''499.01'''
| '''499.01'''
|-
|-
| | '''59'''
| '''59'''
| | '''700.99'''
| '''700.99'''
|-
|-
| | '''76'''
| '''76'''
| | '''902.97'''
| '''902.97'''
|-
|-
| | 93
| 93
| | 1104.95
| 1104.95
|}
|}
'''13 13 13 13 13 13 13 10:''' ''7L1s MOS'' (Grumpy Octatonic)
'''13 13 13 13 13 13 13 10:''' ''7L1s MOS'' (Grumpy Octatonic)


{| class="wikitable"
{| class="wikitable"
! Steps
! Cents
|-
|-
| | 13
| 13
| | 154.455
| 154.455
|-
|-
| | 26
| 26
| | 308.911
| 308.911
|-
|-
| | 39
| 39
| | 463.366
| 463.366
|-
|-
| | 52
| 52
| | 617.822
| 617.822
|-
|-
| | 65
| 65
| | 772.277
| 772.277
|-
|-
| | 78
| 78
| | 926.733
| 926.733
|-
|-
| | 91
| 91
| | 1081.188
| 1081.188
|}
|}
'''13 13 13 5 13 13 13 13 5:''' ''7L2s MOS'' (Superdiatonic 1/13-tone 13;5 relation)
'''13 13 13 5 13 13 13 13 5:''' ''7L2s MOS'' (Superdiatonic 1/13-tone 13;5 relation)


{| class="wikitable"
{| class="wikitable"
! Steps
! Cents
|-
|-
| | '''13/101'''
| '''13'''
| | '''154.455'''
| '''154.455'''
|-
|-
| | '''26/101'''
| '''26'''
| | '''308.911'''
| '''308.911'''
|-
|-
| | 39/101
| 39
| | 463.366
| 463.366
|-
|-
| | '''44/101'''
| '''44'''
| | '''522.772'''
| '''522.772'''
|-
|-
| | '''57/101'''
| '''57'''
| | '''677.228'''
| '''677.228'''
|-
|-
| | '''70/101'''
| '''70'''
| | '''831.683'''
| '''831.683'''
|-
|-
| | '''83/101'''
| '''83'''
| | '''986.139'''
| '''986.139'''
|-
|-
| | 96/101
| 96
| | 1045.545
| 1045.545
|}
|}
'''10 10 7 10 10 10 7 10 10 10 7:''' ''8L3s MOS'' (Improper Sensi-11)
'''10 10 7 10 10 10 7 10 10 10 7:''' ''8L3s MOS'' (Improper Sensi-11)


{| class="wikitable"
{| class="wikitable"
! Steps
! Cents
|-
|-
| | '''10'''
| '''10'''
| | '''118.812'''
| '''118.812'''
|-
|-
| | 20
| 20
| | 237.624
| 237.624
|-
|-
| | '''27'''
| '''27'''
| | '''320.792'''
| '''320.792'''
|-
|-
| | '''37'''
| '''37'''
| | '''439.604'''
| '''439.604'''
|-
|-
| | '''47'''
| '''47'''
| | '''558.416'''
| '''558.416'''
|-
|-
| | 57
| 57
| | 677.228
| 677.228
|-
|-
| | '''64'''
| '''64'''
| | '''760.396'''
| '''760.396'''
|-
|-
| | '''74'''
| '''74'''
| | '''879.218'''
| '''879.218'''
|-
|-
| | '''84'''
| '''84'''
| | '''998.03'''
| '''998.03'''
|-
|-
| | 94
| 94
| | 1116.842
| 1116.842
|}
|}
'''7 7 7 8 7 7 7 7 8 7 7 7 7 8:''' ''3L11s 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
! Cents
|-
|-
| | '''7'''
| '''7'''
| | '''83.168'''
| '''83.168'''
|-
|-
| | '''14'''
| '''14'''
| | '''166.337'''
| '''166.337'''
|-
|-
| | 22
| 22
| | 261.386
| 261.386
|-
|-
| | '''29'''
| '''29'''
| | '''344.5545'''
| '''344.5545'''
|-
|-
| | '''36'''
| '''36'''
| | '''427.723'''
| '''427.723'''
|-
|-
| | '''43'''
| '''43'''
| | '''510.891'''
| '''510.891'''
|-
|-
| | '''50'''
| '''50'''
| | '''594.0595'''
| '''594.0595'''
|-
|-
| | 58
| 58
| | 689.119
| 689.119
|-
|-
| | '''65'''
| '''65'''
| | '''772.287'''
| '''772.287'''
|-
|-
| | '''72'''
| '''72'''
| | '''855.4455'''
| '''855.4455'''
|-
|-
| | '''79'''
| '''79'''
| | '''938.614'''
| '''938.614'''
|-
|-
| | '''86'''
| '''86'''
| | '''1021.782'''
| '''1021.782'''
|-
|-
| | 93
| 93
| | 1104.95
| 1104.95
|}
|}


=Links=
== Links ==
[http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal]
[http://tech.groups.yahoo.com/group/tuning-math/message/11157 The Ellis duodene in 101-equal]


Line 183: Line 199:
[[Category:Edo]]
[[Category:Edo]]
[[Category:Grackle]]
[[Category:Grackle]]
[[Category:Prime edo]]
[[Category:Prime EDO]]
[[Category:Pythagorean]]
[[Category:Pythagorean]]
[[Category:Scales]]
[[Category:Scales]]

Revision as of 09:49, 2 November 2018

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, <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
25 297.03
38 451.485
63 748.515
88 1045.545

17 17 8 17 17 17 8: 5L2s MOS (Diatonic Pythagorean)

Steps Cents
17 201.98
34 403.96
42 499.01
59 700.99
76 902.97
93 1104.95

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
84 998.03
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
29 344.5545
36 427.723
43 510.891
50 594.0595
58 689.119
65 772.287
72 855.4455
79 938.614
86 1021.782
93 1104.95

Links

The Ellis duodene in 101-equal

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