201ed12
| ← 200ed12 | 201ed12 | 202ed12 → |
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 |