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	15.95
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)