250ed10

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← 249ed10 250ed10 251ed10 →
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

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

Approximation of harmonics in 250ed10
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)
Approximation of harmonics in 250ed10
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)