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 10^1/250, or the 250th root of 10.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	15.945
2	31.891
3	47.836
4	63.781	28/27
5	79.726	22/21
6	95.672	37/35
7	111.617
8	127.562	14/13
9	143.507
10	159.453	34/31
11	175.398
12	191.343
13	207.288	62/55
14	223.234	58/51
15	239.179
16	255.124
17	271.069	76/65
18	287.015
19	302.96
20	318.905
21	334.85
22	350.796	49/40, 60/49
23	366.741	68/55
24	382.686
25	398.631
26	414.577	47/37
27	430.522
28	446.467
29	462.412
30	478.358
31	494.303
32	510.248	47/35, 51/38
33	526.193
34	542.139
35	558.084
36	574.029	39/28
37	589.974
38	605.92
39	621.865	63/44
40	637.81
41	653.755
42	669.701
43	685.646	55/37
44	701.591	3/2
45	717.536
46	733.482
47	749.427
48	765.372	14/9
49	781.317
50	797.263	65/41
51	813.208
52	829.153
53	845.099	44/27, 57/35
54	861.044	51/31, 74/45
55	876.989
56	892.934	62/37
57	908.88
58	924.825	29/17
59	940.77
60	956.715
61	972.661
62	988.606
63	1004.551
64	1020.496
65	1036.442
66	1052.387
67	1068.332	76/41
68	1084.277	58/31
69	1100.223
70	1116.168	40/21
71	1132.113
72	1148.058
73	1164.004
74	1179.949
75	1195.894
76	1211.839
77	1227.785
78	1243.73	80/39
79	1259.675
80	1275.62
81	1291.566
82	1307.511
83	1323.456
84	1339.401	13/6
85	1355.347
86	1371.292
87	1387.237
88	1403.182	9/4
89	1419.128
90	1435.073
91	1451.018
92	1466.963	7/3
93	1482.909
94	1498.854
95	1514.799
96	1530.744
97	1546.69	22/9
98	1562.635	37/15
99	1578.58
100	1594.525
101	1610.471
102	1626.416
103	1642.361
104	1658.307
105	1674.252
106	1690.197	69/26
107	1706.142
108	1722.088
109	1738.033
110	1753.978
111	1769.923
112	1785.869
113	1801.814
114	1817.759	20/7
115	1833.704
116	1849.65
117	1865.595
118	1881.54
119	1897.485
120	1913.431
121	1929.376
122	1945.321	40/13
123	1961.266
124	1977.212	47/15
125	1993.157
126	2009.102
127	2025.047
128	2040.993	13/4
129	2056.938
130	2072.883
131	2088.828
132	2104.774
133	2120.719
134	2136.664
135	2152.609
136	2168.555	7/2
137	2184.5
138	2200.445	82/23
139	2216.39
140	2232.336
141	2248.281
142	2264.226	37/10
143	2280.171
144	2296.117
145	2312.062
146	2328.007
147	2343.952
148	2359.898	43/11
149	2375.843
150	2391.788
151	2407.733
152	2423.679
153	2439.624	45/11
154	2455.569
155	2471.515
156	2487.46
157	2503.405
158	2519.35	30/7
159	2535.296
160	2551.241
161	2567.186
162	2583.131	40/9
163	2599.077
164	2615.022
165	2630.967
166	2646.912	60/13
167	2662.858
168	2678.803	47/10
169	2694.748
170	2710.693
171	2726.639
172	2742.584	39/8
173	2758.529
174	2774.474
175	2790.42
176	2806.365
177	2822.31
178	2838.255
179	2854.201
180	2870.146	21/4
181	2886.091
182	2902.036
183	2917.982
184	2933.927	49/9
185	2949.872
186	2965.817
187	2981.763
188	2997.708
189	3013.653	57/10
190	3029.598
191	3045.544
192	3061.489
193	3077.434
194	3093.379
195	3109.325
196	3125.27
197	3141.215
198	3157.16
199	3173.106
200	3189.051	82/13
201	3204.996
202	3220.941	45/7
203	3236.887
204	3252.832
205	3268.777
206	3284.723	20/3
207	3300.668	74/11
208	3316.613
209	3332.558
210	3348.504
211	3364.449
212	3380.394
213	3396.339
214	3412.285
215	3428.23
216	3444.175
217	3460.12
218	3476.066
219	3492.011
220	3507.956
221	3523.901
222	3539.847
223	3555.792
224	3571.737
225	3587.682
226	3603.628
227	3619.573
228	3635.518	49/6
229	3651.463
230	3667.409
231	3683.354
232	3699.299
233	3715.244
234	3731.19
235	3747.135
236	3763.08
237	3779.025
238	3794.971
239	3810.916
240	3826.861
241	3842.806
242	3858.752	65/7
243	3874.697
244	3890.642
245	3906.587
246	3922.533
247	3938.478
248	3954.423
249	3970.368
250	3986.314	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)