250ed10
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Prime factorization
2 × 53
Step size
15.9453 ¢
Octave
75\250ed10 (1195.89 ¢) (→ 3\10ed10)
Twelfth
119\250ed10 (1897.49 ¢)
Consistency limit
3
Distinct consistency limit
3
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← 249ed10 | 250ed10 | 251ed10 → |
250 equal divisions of the 10th harmonic (abbreviated 250ed10) is a nonoctave tuning system that divides the interval of 10/1 into 250 equal parts of about 15.9 ¢ each. Each step represents a frequency ratio of 101/250, or the 250th root of 10.
Intervals
Steps | Cents | Approximate ratios |
---|---|---|
0 | 0 | 1/1 |
1 | 15.95 | |
2 | 31.89 | |
3 | 47.84 | |
4 | 63.78 | 28/27 |
5 | 79.73 | 22/21 |
6 | 95.67 | 37/35 |
7 | 111.62 | |
8 | 127.56 | 14/13 |
9 | 143.51 | |
10 | 159.45 | 34/31 |
11 | 175.4 | |
12 | 191.34 | |
13 | 207.29 | 62/55 |
14 | 223.23 | 58/51 |
15 | 239.18 | |
16 | 255.12 | |
17 | 271.07 | 76/65 |
18 | 287.01 | |
19 | 302.96 | |
20 | 318.91 | |
21 | 334.85 | |
22 | 350.8 | 49/40, 60/49 |
23 | 366.74 | 68/55 |
24 | 382.69 | |
25 | 398.63 | |
26 | 414.58 | 47/37 |
27 | 430.52 | |
28 | 446.47 | |
29 | 462.41 | |
30 | 478.36 | |
31 | 494.3 | |
32 | 510.25 | 47/35, 51/38 |
33 | 526.19 | |
34 | 542.14 | |
35 | 558.08 | |
36 | 574.03 | 39/28 |
37 | 589.97 | |
38 | 605.92 | |
39 | 621.86 | 63/44 |
40 | 637.81 | |
41 | 653.76 | |
42 | 669.7 | |
43 | 685.65 | 55/37 |
44 | 701.59 | 3/2 |
45 | 717.54 | |
46 | 733.48 | |
47 | 749.43 | |
48 | 765.37 | 14/9 |
49 | 781.32 | |
50 | 797.26 | 65/41 |
51 | 813.21 | |
52 | 829.15 | |
53 | 845.1 | 44/27, 57/35 |
54 | 861.04 | 51/31, 74/45 |
55 | 876.99 | |
56 | 892.93 | 62/37 |
57 | 908.88 | |
58 | 924.82 | 29/17 |
59 | 940.77 | |
60 | 956.72 | |
61 | 972.66 | |
62 | 988.61 | |
63 | 1004.55 | |
64 | 1020.5 | |
65 | 1036.44 | |
66 | 1052.39 | |
67 | 1068.33 | 76/41 |
68 | 1084.28 | 58/31 |
69 | 1100.22 | |
70 | 1116.17 | 40/21 |
71 | 1132.11 | |
72 | 1148.06 | |
73 | 1164 | |
74 | 1179.95 | |
75 | 1195.89 | |
76 | 1211.84 | |
77 | 1227.78 | |
78 | 1243.73 | 80/39 |
79 | 1259.68 | |
80 | 1275.62 | |
81 | 1291.57 | |
82 | 1307.51 | |
83 | 1323.46 | |
84 | 1339.4 | 13/6 |
85 | 1355.35 | |
86 | 1371.29 | |
87 | 1387.24 | |
88 | 1403.18 | 9/4 |
89 | 1419.13 | |
90 | 1435.07 | |
91 | 1451.02 | |
92 | 1466.96 | 7/3 |
93 | 1482.91 | |
94 | 1498.85 | |
95 | 1514.8 | |
96 | 1530.74 | |
97 | 1546.69 | 22/9 |
98 | 1562.63 | 37/15 |
99 | 1578.58 | |
100 | 1594.53 | |
101 | 1610.47 | |
102 | 1626.42 | |
103 | 1642.36 | |
104 | 1658.31 | |
105 | 1674.25 | |
106 | 1690.2 | 69/26 |
107 | 1706.14 | |
108 | 1722.09 | |
109 | 1738.03 | |
110 | 1753.98 | |
111 | 1769.92 | |
112 | 1785.87 | |
113 | 1801.81 | |
114 | 1817.76 | 20/7 |
115 | 1833.7 | |
116 | 1849.65 | |
117 | 1865.59 | |
118 | 1881.54 | |
119 | 1897.49 | |
120 | 1913.43 | |
121 | 1929.38 | |
122 | 1945.32 | 40/13 |
123 | 1961.27 | |
124 | 1977.21 | 47/15 |
125 | 1993.16 | |
126 | 2009.1 | |
127 | 2025.05 | |
128 | 2040.99 | 13/4 |
129 | 2056.94 | |
130 | 2072.88 | |
131 | 2088.83 | |
132 | 2104.77 | |
133 | 2120.72 | |
134 | 2136.66 | |
135 | 2152.61 | |
136 | 2168.55 | 7/2 |
137 | 2184.5 | |
138 | 2200.45 | 82/23 |
139 | 2216.39 | |
140 | 2232.34 | |
141 | 2248.28 | |
142 | 2264.23 | 37/10 |
143 | 2280.17 | |
144 | 2296.12 | |
145 | 2312.06 | |
146 | 2328.01 | |
147 | 2343.95 | |
148 | 2359.9 | 43/11 |
149 | 2375.84 | |
150 | 2391.79 | |
151 | 2407.73 | |
152 | 2423.68 | |
153 | 2439.62 | 45/11 |
154 | 2455.57 | |
155 | 2471.51 | |
156 | 2487.46 | |
157 | 2503.41 | |
158 | 2519.35 | 30/7 |
159 | 2535.3 | |
160 | 2551.24 | |
161 | 2567.19 | |
162 | 2583.13 | 40/9 |
163 | 2599.08 | |
164 | 2615.02 | |
165 | 2630.97 | |
166 | 2646.91 | 60/13 |
167 | 2662.86 | |
168 | 2678.8 | 47/10 |
169 | 2694.75 | |
170 | 2710.69 | |
171 | 2726.64 | |
172 | 2742.58 | 39/8 |
173 | 2758.53 | |
174 | 2774.47 | |
175 | 2790.42 | |
176 | 2806.36 | |
177 | 2822.31 | |
178 | 2838.26 | |
179 | 2854.2 | |
180 | 2870.15 | 21/4 |
181 | 2886.09 | |
182 | 2902.04 | |
183 | 2917.98 | |
184 | 2933.93 | 49/9 |
185 | 2949.87 | |
186 | 2965.82 | |
187 | 2981.76 | |
188 | 2997.71 | |
189 | 3013.65 | 57/10 |
190 | 3029.6 | |
191 | 3045.54 | |
192 | 3061.49 | |
193 | 3077.43 | |
194 | 3093.38 | |
195 | 3109.32 | |
196 | 3125.27 | |
197 | 3141.22 | |
198 | 3157.16 | |
199 | 3173.11 | |
200 | 3189.05 | 82/13 |
201 | 3205 | |
202 | 3220.94 | 45/7 |
203 | 3236.89 | |
204 | 3252.83 | |
205 | 3268.78 | |
206 | 3284.72 | 20/3 |
207 | 3300.67 | 74/11 |
208 | 3316.61 | |
209 | 3332.56 | |
210 | 3348.5 | |
211 | 3364.45 | |
212 | 3380.39 | |
213 | 3396.34 | |
214 | 3412.28 | |
215 | 3428.23 | |
216 | 3444.18 | |
217 | 3460.12 | |
218 | 3476.07 | |
219 | 3492.01 | |
220 | 3507.96 | |
221 | 3523.9 | |
222 | 3539.85 | |
223 | 3555.79 | |
224 | 3571.74 | |
225 | 3587.68 | |
226 | 3603.63 | |
227 | 3619.57 | |
228 | 3635.52 | 49/6 |
229 | 3651.46 | |
230 | 3667.41 | |
231 | 3683.35 | |
232 | 3699.3 | |
233 | 3715.24 | |
234 | 3731.19 | |
235 | 3747.13 | |
236 | 3763.08 | |
237 | 3779.03 | |
238 | 3794.97 | |
239 | 3810.92 | |
240 | 3826.86 | |
241 | 3842.81 | |
242 | 3858.75 | 65/7 |
243 | 3874.7 | |
244 | 3890.64 | |
245 | 3906.59 | |
246 | 3922.53 | |
247 | 3938.48 | |
248 | 3954.42 | |
249 | 3970.37 | |
250 | 3986.31 | 10/1 |
Harmonics
Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -4.11 | -4.47 | +7.73 | +4.11 | +7.37 | -4.38 | +3.63 | +7.01 | +0.00 | -5.55 | +3.26 |
Relative (%) | -25.7 | -28.0 | +48.5 | +25.7 | +46.2 | -27.5 | +22.8 | +43.9 | +0.0 | -34.8 | +20.5 | |
Steps (reduced) |
75 (75) |
119 (119) |
151 (151) |
175 (175) |
195 (195) |
211 (211) |
226 (226) |
239 (239) |
250 (0) |
260 (10) |
270 (20) |
Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Error | Absolute (¢) | -7.75 | +7.46 | -0.36 | -0.48 | +6.18 | +2.90 | +4.97 | -4.11 | +7.10 | +6.29 | -6.89 |
Relative (%) | -48.6 | +46.8 | -2.3 | -3.0 | +38.8 | +18.2 | +31.2 | -25.7 | +44.5 | +39.4 | -43.2 | |
Steps (reduced) |
278 (28) |
287 (37) |
294 (44) |
301 (51) |
308 (58) |
314 (64) |
320 (70) |
325 (75) |
331 (81) |
336 (86) |
340 (90) |