101edo: Difference between revisions

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Replace with the automatic interval table that has ups and downs notation
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== Intervals ==
== Intervals ==
{| class="wikitable mw-collapsible"
{{Interval table}}
!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 ==
== Some important MOS scales ==

Revision as of 03:56, 26 February 2024

← 100edo 101edo 102edo →
Prime factorization 101 (prime)
Step size 11.8812 ¢ 
Fifth 59\101 (700.99 ¢)
Semitones (A1:m2) 9:8 (106.9 ¢ : 95.05 ¢)
Consistency limit 3
Distinct consistency limit 3

Template:EDO intro

101edo 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.

Theory

5-limit commas
32805/32768 ( [-15 8 1⟩ ), 51018336/48828125 ( [5 13 -11⟩ )
7-limit commas
126/125, 32805/32768, 2430/2401
Approximation of prime harmonics in 101edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.96 +5.77 +5.43 -4.78 +3.04 +1.98 -0.48 +1.43 +4.09 -4.44
Relative (%) +0.0 -8.1 +48.5 +45.7 -40.3 +25.6 +16.6 -4.1 +12.0 +34.4 -37.4
Steps
(reduced) 		101
(0) 		160
(59) 		235
(33) 		284
(82) 		349
(46) 		374
(71) 		413
(9) 		429
(25) 		457
(53) 		491
(87) 		500
(96)

Intervals

Steps Cents Approximate ratios Ups and downs notation
0 0 1/1 D
1 11.9 ^D, ^^E♭♭
2 23.8 ^^D, ^3E♭♭
3 35.6 ^3D, ^4E♭♭
4 47.5 37/36, 38/37 ^4D, v4E♭
5 59.4 29/28, 30/29 v4D♯, v3E♭
6 71.3 24/23 v3D♯, vvE♭
7 83.2 21/20, 43/41 vvD♯, vE♭
8 95 19/18 vD♯, E♭
9 106.9 17/16, 33/31 D♯, ^E♭
10 118.8 15/14 ^D♯, ^^E♭
11 130.7 14/13, 41/38 ^^D♯, ^3E♭
12 142.6 ^3D♯, ^4E♭
13 154.5 ^4D♯, v4E
14 166.3 v4D𝄪, v3E
15 178.2 41/37 v3D𝄪, vvE
16 190.1 29/26 vvD𝄪, vE
17 202 9/8 E
18 213.9 26/23, 43/38 ^E, ^^F♭
19 225.7 41/36 ^^E, ^3F♭
20 237.6 31/27, 39/34 ^3E, ^4F♭
21 249.5 15/13, 37/32 ^4E, v4F
22 261.4 43/37 v4E♯, v3F
23 273.3 34/29 v3E♯, vvF
24 285.1 vvE♯, vF
25 297 19/16 F
26 308.9 43/36 ^F, ^^G♭♭
27 320.8 ^^F, ^3G♭♭
28 332.7 23/19 ^3F, ^4G♭♭
29 344.6 39/32 ^4F, v4G♭
30 356.4 27/22 v4F♯, v3G♭
31 368.3 26/21 v3F♯, vvG♭
32 380.2 vvF♯, vG♭
33 392.1 vF♯, G♭
34 404 24/19 F♯, ^G♭
35 415.8 ^F♯, ^^G♭
36 427.7 41/32 ^^F♯, ^3G♭
37 439.6 ^3F♯, ^4G♭
38 451.5 ^4F♯, v4G
39 463.4 17/13 v4F𝄪, v3G
40 475.2 v3F𝄪, vvG
41 487.1 45/34 vvF𝄪, vG
42 499 4/3 G
43 510.9 39/29, 43/32 ^G, ^^A♭♭
44 522.8 23/17 ^^G, ^3A♭♭
45 534.7 ^3G, ^4A♭♭
46 546.5 37/27 ^4G, v4A♭
47 558.4 29/21, 40/29 v4G♯, v3A♭
48 570.3 32/23 v3G♯, vvA♭
49 582.2 7/5 vvG♯, vA♭
50 594.1 31/22, 38/27 vG♯, A♭
51 605.9 27/19, 44/31 G♯, ^A♭
52 617.8 10/7 ^G♯, ^^A♭
53 629.7 23/16 ^^G♯, ^3A♭
54 641.6 29/20, 42/29 ^3G♯, ^4A♭
55 653.5 ^4G♯, v4A
56 665.3 v4G𝄪, v3A
57 677.2 34/23 v3G𝄪, vvA
58 689.1 vvG𝄪, vA
59 701 3/2 A
60 712.9 ^A, ^^B♭♭
61 724.8 41/27 ^^A, ^3B♭♭
62 736.6 26/17 ^3A, ^4B♭♭
63 748.5 37/24 ^4A, v4B♭
64 760.4 45/29 v4A♯, v3B♭
65 772.3 v3A♯, vvB♭
66 784.2 vvA♯, vB♭
67 796 19/12 vA♯, B♭
68 807.9 43/27 A♯, ^B♭
69 819.8 45/28 ^A♯, ^^B♭
70 831.7 21/13 ^^A♯, ^3B♭
71 843.6 44/27 ^3A♯, ^4B♭
72 855.4 ^4A♯, v4B
73 867.3 38/23 v4A𝄪, v3B
74 879.2 v3A𝄪, vvB
75 891.1 vvA𝄪, vB
76 903 32/19 B
77 914.9 39/23 ^B, ^^C♭
78 926.7 29/17, 41/24 ^^B, ^3C♭
79 938.6 ^3B, ^4C♭
80 950.5 26/15, 45/26 ^4B, v4C
81 962.4 v4B♯, v3C
82 974.3 v3B♯, vvC
83 986.1 23/13 vvB♯, vC
84 998 16/9 C
85 1009.9 43/24 ^C, ^^D♭♭
86 1021.8 ^^C, ^3D♭♭
87 1033.7 ^3C, ^4D♭♭
88 1045.5 ^4C, v4D♭
89 1057.4 v4C♯, v3D♭
90 1069.3 13/7 v3C♯, vvD♭
91 1081.2 28/15, 43/23 vvC♯, vD♭
92 1093.1 32/17 vC♯, D♭
93 1105 36/19 C♯, ^D♭
94 1116.8 40/21 ^C♯, ^^D♭
95 1128.7 23/12 ^^C♯, ^3D♭
96 1140.6 29/15 ^3C♯, ^4D♭
97 1152.5 37/19 ^4C♯, v4D
98 1164.4 45/23 v4C𝄪, v3D
99 1176.2 v3C𝄪, vvD
100 1188.1 vvC𝄪, vD
101 1200 2/1 D

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=137185"