101edo
← 100edo | 101edo | 102edo → |
101 equal divisions of the octave (abbreviated 101edo), or 101-tone equal temperament (101tet), 101 equal temperament (101et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 101 equal parts of about 11.9 ¢ each. Each step represents a frequency ratio of 21/101, or the 101 root of 2.
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
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 | -8 | +49 | +46 | -40 | +26 | +17 | -4 | +12 | +34 | -37 | |
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 | Ups and downs notation | Approximate ratios |
---|---|---|---|
0 | 0 | D | 1/1 |
1 | 11.8812 | ^D, v7Eb | |
2 | 23.7624 | ^^D, v6Eb | 64/63, 78/77 |
3 | 35.6436 | ^3D, v5Eb | 50/49, 55/54, 56/55 |
4 | 47.5248 | ^4D, v4Eb | 40/39 |
5 | 59.4059 | ^5D, v3Eb | |
6 | 71.2871 | ^6D, vvEb | |
7 | 83.1683 | ^7D, vEb | 21/20, 81/77 |
8 | 95.0495 | ^8D, Eb | 55/52 |
9 | 106.931 | D#, v8E | |
10 | 118.812 | ^D#, v7E | 15/14, 77/72 |
11 | 130.693 | ^^D#, v6E | 14/13 |
12 | 142.574 | ^3D#, v5E | 13/12 |
13 | 154.455 | ^4D#, v4E | 12/11 |
14 | 166.337 | ^5D#, v3E | |
15 | 178.218 | ^6D#, vvE | |
16 | 190.099 | ^7D#, vE | |
17 | 201.98 | E | 9/8 |
18 | 213.861 | ^E, v7F | |
19 | 225.743 | ^^E, v6F | |
20 | 237.624 | ^3E, v5F | 55/48, 63/55 |
21 | 249.505 | ^4E, v4F | 15/13, 52/45 |
22 | 261.386 | ^5E, v3F | 64/55, 65/56 |
23 | 273.267 | ^6E, vvF | |
24 | 285.149 | ^7E, vF | |
25 | 297.03 | F | 32/27 |
26 | 308.911 | ^F, v7Gb | |
27 | 320.792 | ^^F, v6Gb | 77/64 |
28 | 332.673 | ^3F, v5Gb | 63/52 |
29 | 344.554 | ^4F, v4Gb | 11/9, 39/32 |
30 | 356.436 | ^5F, v3Gb | 16/13, 27/22 |
31 | 368.317 | ^6F, vvGb | 26/21 |
32 | 380.198 | ^7F, vGb | 56/45 |
33 | 392.079 | ^8F, Gb | |
34 | 403.96 | F#, v8G | 81/64 |
35 | 415.842 | ^F#, v7G | 80/63 |
36 | 427.723 | ^^F#, v6G | 77/60 |
37 | 439.604 | ^3F#, v5G | |
38 | 451.485 | ^4F#, v4G | 13/10 |
39 | 463.366 | ^5F#, v3G | 55/42, 72/55 |
40 | 475.248 | ^6F#, vvG | 21/16 |
41 | 487.129 | ^7F#, vG | 65/49 |
42 | 499.01 | G | 4/3 |
43 | 510.891 | ^G, v7Ab | |
44 | 522.772 | ^^G, v6Ab | |
45 | 534.653 | ^3G, v5Ab | |
46 | 546.535 | ^4G, v4Ab | |
47 | 558.416 | ^5G, v3Ab | |
48 | 570.297 | ^6G, vvAb | 39/28 |
49 | 582.178 | ^7G, vAb | 7/5 |
50 | 594.059 | ^8G, Ab | 45/32, 55/39 |
51 | 605.941 | G#, v8A | 64/45, 78/55 |
52 | 617.822 | ^G#, v7A | 10/7, 77/54 |
53 | 629.703 | ^^G#, v6A | 56/39 |
54 | 641.584 | ^3G#, v5A | |
55 | 653.465 | ^4G#, v4A | |
56 | 665.347 | ^5G#, v3A | |
57 | 677.228 | ^6G#, vvA | 77/52 |
58 | 689.109 | ^7G#, vA | |
59 | 700.99 | A | 3/2 |
60 | 712.871 | ^A, v7Bb | |
61 | 724.752 | ^^A, v6Bb | 32/21 |
62 | 736.634 | ^3A, v5Bb | 55/36, 75/49 |
63 | 748.515 | ^4A, v4Bb | 20/13 |
64 | 760.396 | ^5A, v3Bb | 65/42 |
65 | 772.277 | ^6A, vvBb | |
66 | 784.158 | ^7A, vBb | 63/40 |
67 | 796.04 | ^8A, Bb | |
68 | 807.921 | A#, v8B | |
69 | 819.802 | ^A#, v7B | 45/28, 77/48 |
70 | 831.683 | ^^A#, v6B | 21/13 |
71 | 843.564 | ^3A#, v5B | 13/8, 44/27 |
72 | 855.446 | ^4A#, v4B | 18/11, 64/39 |
73 | 867.327 | ^5A#, v3B | |
74 | 879.208 | ^6A#, vvB | |
75 | 891.089 | ^7A#, vB | |
76 | 902.97 | B | 27/16 |
77 | 914.851 | ^B, v7C | |
78 | 926.733 | ^^B, v6C | 77/45 |
79 | 938.614 | ^3B, v5C | 55/32 |
80 | 950.495 | ^4B, v4C | 26/15, 45/26 |
81 | 962.376 | ^5B, v3C | |
82 | 974.257 | ^6B, vvC | |
83 | 986.139 | ^7B, vC | |
84 | 998.02 | C | 16/9 |
85 | 1009.9 | ^C, v7Db | |
86 | 1021.78 | ^^C, v6Db | |
87 | 1033.66 | ^3C, v5Db | |
88 | 1045.54 | ^4C, v4Db | 11/6 |
89 | 1057.43 | ^5C, v3Db | 24/13, 81/44 |
90 | 1069.31 | ^6C, vvDb | 13/7 |
91 | 1081.19 | ^7C, vDb | 28/15 |
92 | 1093.07 | ^8C, Db | |
93 | 1104.95 | C#, v8D | |
94 | 1116.83 | ^C#, v7D | 40/21 |
95 | 1128.71 | ^^C#, v6D | |
96 | 1140.59 | ^3C#, v5D | |
97 | 1152.48 | ^4C#, v4D | 39/20 |
98 | 1164.36 | ^5C#, v3D | 49/25, 55/28 |
99 | 1176.24 | ^6C#, vvD | 63/32, 77/39 |
100 | 1188.12 | ^7C#, vD | |
101 | 1200 | D | 2/1 |
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 |