201ed12
201 equal divisions of the 12th harmonic (abbreviated 201ed12) is a nonoctave tuning system that divides the interval of 12/1 into 201 equal parts of about 21.4 ¢ each. Each step represents a frequency ratio of 121/201, or the 201st root of 12.
Theory
201ed12 acts as a compressed version of 56edo. It improves primes 3 and 11, but at the cost of 2, 5, 7, 13, 17, and 19. Thus, most would consider this amount of compression as too much.
The main reason one would want to use this much compression is if they are using the 56d val, which most notably supports pajara. This significantly improves the 3rd, 7th, and 11th harmonics, while not damaging prime 5 too much.
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.45 | +2.89 | -2.89 | -3.95 | +1.45 | -8.59 | -4.34 | +5.78 | -5.40 | +0.82 | +0.00 |
| Relative (%) | -6.8 | +13.5 | -13.5 | -18.5 | +6.8 | -40.1 | -20.3 | +27.0 | -25.2 | +3.8 | +0.0 | |
| Steps (reduced) |
56 (56) |
89 (89) |
112 (112) |
130 (130) |
145 (145) |
157 (157) |
168 (168) |
178 (178) |
186 (186) |
194 (194) |
201 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -10.16 | -10.04 | -1.06 | -5.78 | -3.72 | +4.34 | -3.66 | -6.85 | -5.70 | -0.63 | +8.03 |
| Relative (%) | -47.5 | -46.9 | -5.0 | -27.0 | -17.4 | +20.3 | -17.1 | -32.0 | -26.6 | -2.9 | +37.5 | |
| Steps (reduced) |
207 (6) |
213 (12) |
219 (18) |
224 (23) |
229 (28) |
234 (33) |
238 (37) |
242 (41) |
246 (45) |
250 (49) |
254 (53) | |
Intervals
| Steps | Cents | Approximate ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 21.4 | |
| 2 | 42.81 | 40/39, 41/40, 42/41 |
| 3 | 64.21 | |
| 4 | 85.61 | 41/39 |
| 5 | 107.01 | 50/47 |
| 6 | 128.42 | 14/13 |
| 7 | 149.82 | 12/11 |
| 8 | 171.22 | 32/29 |
| 9 | 192.62 | 19/17 |
| 10 | 214.03 | 43/38 |
| 11 | 235.43 | 47/41, 55/48, 63/55 |
| 12 | 256.83 | 29/25 |
| 13 | 278.24 | 27/23, 47/40 |
| 14 | 299.64 | 44/37 |
| 15 | 321.04 | |
| 16 | 342.44 | 39/32 |
| 17 | 363.85 | 37/30, 58/47 |
| 18 | 385.25 | 5/4 |
| 19 | 406.65 | 43/34 |
| 20 | 428.06 | 32/25, 41/32 |
| 21 | 449.46 | |
| 22 | 470.86 | 21/16 |
| 23 | 492.26 | |
| 24 | 513.67 | 35/26, 39/29 |
| 25 | 535.07 | 64/47 |
| 26 | 556.47 | 40/29, 51/37 |
| 27 | 577.87 | |
| 28 | 599.28 | 41/29 |
| 29 | 620.68 | 63/44 |
| 30 | 642.08 | 42/29 |
| 31 | 663.49 | 22/15 |
| 32 | 684.89 | 52/35 |
| 33 | 706.29 | |
| 34 | 727.69 | |
| 35 | 749.1 | 37/24, 57/37 |
| 36 | 770.5 | 39/25, 64/41 |
| 37 | 791.9 | |
| 38 | 813.3 | 8/5 |
| 39 | 834.71 | 34/21 |
| 40 | 856.11 | 41/25 |
| 41 | 877.51 | |
| 42 | 898.92 | 42/25 |
| 43 | 920.32 | 63/37 |
| 44 | 941.72 | 31/18 |
| 45 | 963.12 | 68/39 |
| 46 | 984.53 | |
| 47 | 1005.93 | |
| 48 | 1027.33 | 38/21 |
| 49 | 1048.74 | 11/6 |
| 50 | 1070.14 | |
| 51 | 1091.54 | 62/33 |
| 52 | 1112.94 | |
| 53 | 1134.35 | |
| 54 | 1155.75 | 39/20 |
| 55 | 1177.15 | |
| 56 | 1198.55 | |
| 57 | 1219.96 | |
| 58 | 1241.36 | 43/21 |
| 59 | 1262.76 | |
| 60 | 1284.17 | 21/10 |
| 61 | 1305.57 | 17/8 |
| 62 | 1326.97 | |
| 63 | 1348.37 | |
| 64 | 1369.78 | 64/29 |
| 65 | 1391.18 | |
| 66 | 1412.58 | |
| 67 | 1433.99 | |
| 68 | 1455.39 | 51/22 |
| 69 | 1476.79 | 54/23 |
| 70 | 1498.19 | 19/8 |
| 71 | 1519.6 | |
| 72 | 1541 | |
| 73 | 1562.4 | 37/15 |
| 74 | 1583.8 | |
| 75 | 1605.21 | 48/19 |
| 76 | 1626.61 | 64/25 |
| 77 | 1648.01 | 57/22 |
| 78 | 1669.42 | |
| 79 | 1690.82 | |
| 80 | 1712.22 | 43/16 |
| 81 | 1733.62 | |
| 82 | 1755.03 | |
| 83 | 1776.43 | |
| 84 | 1797.83 | 48/17 |
| 85 | 1819.23 | |
| 86 | 1840.64 | 55/19 |
| 87 | 1862.04 | 44/15 |
| 88 | 1883.44 | |
| 89 | 1904.85 | |
| 90 | 1926.25 | |
| 91 | 1947.65 | |
| 92 | 1969.05 | |
| 93 | 1990.46 | 60/19 |
| 94 | 2011.86 | |
| 95 | 2033.26 | 55/17, 68/21 |
| 96 | 2054.67 | |
| 97 | 2076.07 | 63/19 |
| 98 | 2097.47 | 47/14 |
| 99 | 2118.87 | 17/5 |
| 100 | 2140.28 | 31/9 |
| 101 | 2161.68 | |
| 102 | 2183.08 | 60/17 |
| 103 | 2204.48 | 25/7 |
| 104 | 2225.89 | 47/13 |
| 105 | 2247.29 | |
| 106 | 2268.69 | 63/17 |
| 107 | 2290.1 | |
| 108 | 2311.5 | 19/5 |
| 109 | 2332.9 | 50/13 |
| 110 | 2354.3 | |
| 111 | 2375.71 | |
| 112 | 2397.11 | |
| 113 | 2418.51 | |
| 114 | 2439.91 | 45/11 |
| 115 | 2461.32 | 29/7 |
| 116 | 2482.72 | |
| 117 | 2504.12 | 17/4 |
| 118 | 2525.53 | 43/10 |
| 119 | 2546.93 | |
| 120 | 2568.33 | |
| 121 | 2589.73 | 58/13 |
| 122 | 2611.14 | |
| 123 | 2632.54 | |
| 124 | 2653.94 | |
| 125 | 2675.35 | |
| 126 | 2696.75 | 19/4 |
| 127 | 2718.15 | |
| 128 | 2739.55 | |
| 129 | 2760.96 | |
| 130 | 2782.36 | |
| 131 | 2803.76 | |
| 132 | 2825.16 | 46/9 |
| 133 | 2846.57 | |
| 134 | 2867.97 | |
| 135 | 2889.37 | |
| 136 | 2910.78 | 43/8 |
| 137 | 2932.18 | |
| 138 | 2953.58 | |
| 139 | 2974.98 | |
| 140 | 2996.39 | |
| 141 | 3017.79 | 40/7 |
| 142 | 3039.19 | |
| 143 | 3060.59 | 41/7 |
| 144 | 3082 | |
| 145 | 3103.4 | |
| 146 | 3124.8 | |
| 147 | 3146.21 | |
| 148 | 3167.61 | |
| 149 | 3189.01 | |
| 150 | 3210.41 | |
| 151 | 3231.82 | |
| 152 | 3253.22 | |
| 153 | 3274.62 | |
| 154 | 3296.03 | 47/7 |
| 155 | 3317.43 | |
| 156 | 3338.83 | |
| 157 | 3360.23 | |
| 158 | 3381.64 | |
| 159 | 3403.04 | 50/7 |
| 160 | 3424.44 | |
| 161 | 3445.84 | |
| 162 | 3467.25 | |
| 163 | 3488.65 | 15/2 |
| 164 | 3510.05 | |
| 165 | 3531.46 | |
| 166 | 3552.86 | |
| 167 | 3574.26 | |
| 168 | 3595.66 | |
| 169 | 3617.07 | |
| 170 | 3638.47 | |
| 171 | 3659.87 | 58/7 |
| 172 | 3681.27 | |
| 173 | 3702.68 | |
| 174 | 3724.08 | |
| 175 | 3745.48 | |
| 176 | 3766.89 | |
| 177 | 3788.29 | |
| 178 | 3809.69 | |
| 179 | 3831.09 | 64/7 |
| 180 | 3852.5 | |
| 181 | 3873.9 | |
| 182 | 3895.3 | |
| 183 | 3916.71 | 48/5 |
| 184 | 3938.11 | |
| 185 | 3959.51 | |
| 186 | 3980.91 | |
| 187 | 4002.32 | |
| 188 | 4023.72 | |
| 189 | 4045.12 | |
| 190 | 4066.52 | |
| 191 | 4087.93 | |
| 192 | 4109.33 | |
| 193 | 4130.73 | |
| 194 | 4152.14 | 11/1 |
| 195 | 4173.54 | |
| 196 | 4194.94 | |
| 197 | 4216.34 | |
| 198 | 4237.75 | |
| 199 | 4259.15 | |
| 200 | 4280.55 | |
| 201 | 4301.96 | 12/1 |