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


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


{| class="wikitable"
{| class="wikitable"
Line 12: Line 12:
! Cents
! Cents
|-
|-
| 25
|13
| 297.030
|154.455
|-
|-
| 38
| '''25'''
| 451.485
| '''297.030'''
|-
|-
| 63
| '''38'''
| 748.515
| '''451.485'''
|-
|-
| 88
|51
| 1045.545
|605.9405
|-
| '''63'''
| '''748.515'''
|-
|75
|891.089
|-
| '''88'''
| '''1045.545'''
|}
|}


'''17 17 8 17 17 17 8:''' ''5L2s MOS'' (Diatonic Pythagorean)
'''9 8 9 8 8 9 8 9 8 9 8 8:''' ''5L7s MOS'' (Diatonic Pythagorean, a 12-tone circulating temperament)


{| class="wikitable"
{| class="wikitable"
! Steps
! Steps
! Cents
! Cents
|-
|9
|106.059
|-
|-
| '''17'''
| '''17'''
| '''201.980'''
| '''201.980'''
|-
|-
| 34
|26
| 403.960
|308.911
|-
| '''34'''
| '''403.960'''
|-
|-
| '''42'''
| '''42'''
| '''499.010'''
| '''499.010'''
|-
|51
|605.940
|-
|-
| '''59'''
| '''59'''
| '''700.990'''
| '''700.990'''
|-
|68
|807.921
|-
|-
| '''76'''
| '''76'''
| '''902.970'''
| '''902.970'''
|-
|-
| 93
|85
| 1104.950
|1009.901
|-
| '''93'''
| '''1104.950'''
|}
|}


'''13 13 13 13 13 13 13 10:''' ''7L1s MOS'' (Grumpy Octatonic)
'''10 3 10 3 10 3 10 3 10 3 10 3 10 3 10:''' ''8L7s MOS'' (Opossum)


{| class="wikitable"
{| class="wikitable"
Line 56: Line 80:
! Cents
! Cents
|-
|-
| 13
|10
| 154.455
|118.812
|-
| '''13'''
| '''154.455'''
|-
|23
|273.267
|-
| '''26'''
| '''308.911'''
|-
|36
|427.723
|-
|-
| 26
| '''39'''
| 308.911
| '''463.366'''
|-
|-
| 39
|49
| 463.366
|582.178
|-
| '''52'''
| '''617.822'''
|-
|62
|736.337
|-
| '''65'''
| '''772.277'''
|-
|-
| 52
|75
| 617.822
|891.089
|-
|-
| 65
| '''78'''
| 772.277
| '''926.733'''
|-
|-
| 78
|88
| 926.733
|1045.4455
|-
|-
| 91
| '''91'''
| 1081.188
| '''1081.188'''
|}
|}


'''13 13 13 5 13 13 13 13 5:''' ''7L2s MOS'' (Superdiatonic 1/13-tone 13;5 relation)
'''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"
{| class="wikitable"
! Steps
! Steps
! Cents
! Cents
|-
|8
|95.0495
|-
|-
| '''13'''
| '''13'''
| '''154.455'''
| '''154.455'''
|-
|21
|249.505
|-
|-
| '''26'''
| '''26'''
| '''308.911'''
| '''308.911'''
|-
|-
| 39
|34
| 463.366
|403.960
|-
| '''39'''
| '''463.366'''
|-
|-
| '''44'''
| '''44'''
| '''522.772'''
| '''522.772'''
|-
|52
|617.822
|-
|-
| '''57'''
| '''57'''
| '''677.228'''
| '''677.228'''
|-
|65
|772.277
|-
|-
| '''70'''
| '''70'''
| '''831.683'''
| '''831.683'''
|-
|78
|926.733
|-
|-
| '''83'''
| '''83'''
| '''986.139'''
| '''986.139'''
|-
|-
| 96
|91
| 1045.545
|1081.188
|-
| '''96'''
| '''1045.545'''
|}
|}


'''10 10 7 10 10 10 7 10 10 10 7:''' ''8L3s MOS'' (Improper Sensi-11)
'''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"
{| class="wikitable"
! Steps
! Steps
! Cents
! Cents
|-
|7
|83.168
|-
|-
| '''10'''
| '''10'''
| '''118.812'''
| '''118.812'''
|-
|-
| 20
|17
| 237.624
|201.980
|-
| '''20'''
| '''237.624'''
|-
|-
| '''27'''
| '''27'''
| '''320.792'''
| '''320.792'''
|-
|34
|403.960
|-
|-
| '''37'''
| '''37'''
| '''439.604'''
| '''439.604'''
|-
|44
|527.772
|-
|-
| '''47'''
| '''47'''
| '''558.416'''
| '''558.416'''
|-
|-
| 57
|54
| 677.228
|641.584
|-
| '''57'''
| '''677.228'''
|-
|-
| '''64'''
| '''64'''
| '''760.396'''
| '''760.396'''
|-
|71
|843.564
|-
|-
| '''74'''
| '''74'''
| '''879.218'''
| '''879.218'''
|-
|81
|962.376
|-
|-
| '''84'''
| '''84'''
| '''998.020'''
| '''998.020'''
|-
|-
| 94
|91
| 1116.842
|1081.188
|-
| '''94'''
| '''1116.842'''
|}
|}


'''7 7 7 8 7 7 7 7 8 7 7 7 7 8:''' ''3L11s MOS'' (Anti-Ketradektriatoh)
'''7 7 7 7 1 7 7 7 7 7 1 7 7 7 7 7 1:''' ''14L3s MOS'' (Anti-Ketradektriatoh)


{| class="wikitable"
{| class="wikitable"
Line 158: Line 248:
| '''166.337'''
| '''166.337'''
|-
|-
| 22
|21
| 261.386
|249.505
|-
| '''22'''
| '''261.386'''
|-
|-
| '''29'''
| '''29'''
Line 173: Line 266:
| '''594.059'''
| '''594.059'''
|-
|-
| 58
|57
| 689.119
|677.278
|-
| '''58'''
| '''689.119'''
|-
|-
| '''65'''
| '''65'''
Line 188: Line 284:
| '''1021.782'''
| '''1021.782'''
|-
|-
| 93
| '''93'''
| 1104.950
| '''1104.950'''
|-
|100
|1188.119
|}
|}


Revision as of 20:08, 14 April 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

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

Steps Cents
13 154.455
25 297.030
38 451.485
51 605.9405
63 748.515
75 891.089
88 1045.545

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

Steps 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)

Steps 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 1045.4455
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)

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)

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)

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

The Ellis duodene in 101-equal

Retrieved from "https://en.xen.wiki/index.php?title=101edo&oldid=67307"