316edt

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316edt

317edt →

Prime factorization	22 × 79
Step size	6.01884¢
Octave	199\316edt (1197.75¢)
Consistency limit	2
Distinct consistency limit	2

316 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 316edt or 316ed3), is a nonoctave tuning system that divides the interval of 3/1 into 316 equal parts of about 6.02 ¢ each. Each step represents a frequency ratio of 3^1/316, or the 316th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	6.019
2	12.038
3	18.057	99/98
4	24.075
5	30.094	58/57
6	36.113
7	42.132	42/41
8	48.151
9	54.17	65/63, 98/95
10	60.188
11	66.207
12	72.226
13	78.245	45/43, 91/87
14	84.264
15	90.283	98/93
16	96.302	37/35
17	102.32	35/33
18	108.339	33/31
19	114.358	47/44
20	120.377
21	126.396
22	132.415
23	138.433
24	144.452	25/23
25	150.471
26	156.49	81/74
27	162.509
28	168.528	43/39
29	174.547	52/47
30	180.565
31	186.584
32	192.603	19/17
33	198.622	37/33, 46/41
34	204.641
35	210.66	35/31
36	216.678	17/15
37	222.697	58/51
38	228.716
39	234.735	63/55
40	240.754	54/47
41	246.773	98/85
42	252.791	81/70
43	258.81
44	264.829
45	270.848
46	276.867
47	282.886
48	288.905	13/11
49	294.923	51/43
50	300.942	69/58
51	306.961
52	312.98
53	318.999
54	325.018	35/29
55	331.036	23/19
56	337.055
57	343.074	50/41
58	349.093
59	355.112	27/22, 70/57
60	361.131	85/69
61	367.15
62	373.168
63	379.187
64	385.206
65	391.225
66	397.244	39/31
67	403.263
68	409.281	19/15
69	415.3
70	421.319	37/29
71	427.338
72	433.357
73	439.376	58/45
74	445.395	75/58
75	451.413	74/57
76	457.432
77	463.451	98/75
78	469.47
79	475.489	25/19
80	481.508
81	487.526	57/43
82	493.545
83	499.564
84	505.583
85	511.602
86	517.621	58/43
87	523.64	23/17
88	529.658
89	535.677
90	541.696
91	547.715	70/51
92	553.734	95/69
93	559.753
94	565.771
95	571.79
96	577.809	81/58
97	583.828
98	589.847
99	595.866
100	601.884
101	607.903	27/19, 98/69
102	613.922
103	619.941	93/65
104	625.96
105	631.979
106	637.998
107	644.016	74/51
108	650.035
109	656.054
110	662.073	85/58
111	668.092	25/17
112	674.111	31/21
113	680.129
114	686.148	55/37
115	692.167	85/57
116	698.186
117	704.205
118	710.224	98/65
119	716.243	62/41
120	722.261
121	728.28	99/65
122	734.299
123	740.318	23/15
124	746.337
125	752.356
126	758.374
127	764.393	14/9
128	770.412	39/25
129	776.431
130	782.45	11/7
131	788.469	41/26
132	794.488	87/55
133	800.506	27/17
134	806.525
135	812.544
136	818.563	69/43
137	824.582	66/41
138	830.601	21/13
139	836.619
140	842.638
141	848.657
142	854.676	95/58
143	860.695	74/45
144	866.714
145	872.733
146	878.751
147	884.77	5/3
148	890.789
149	896.808	47/28
150	902.827
151	908.846	93/55
152	914.864
153	920.883	63/37
154	926.902
155	932.921
156	938.94	43/25
157	944.959
158	950.978
159	956.996
160	963.015	75/43, 82/47
161	969.034
162	975.053	65/37
163	981.072	37/21
164	987.091
165	993.109	55/31
166	999.128
167	1005.147	84/47
168	1011.166
169	1017.185	9/5
170	1023.204
171	1029.222
172	1035.241
173	1041.26
174	1047.279
175	1053.298
176	1059.317
177	1065.336
178	1071.354	13/7
179	1077.373	41/22, 95/51
180	1083.392	43/23
181	1089.411
182	1095.43
183	1101.449	17/9
184	1107.467	55/29
185	1113.486	78/41
186	1119.505	21/11
187	1125.524
188	1131.543	25/13
189	1137.562	27/14
190	1143.581
191	1149.599
192	1155.618
193	1161.637	45/23
194	1167.656
195	1173.675	65/33
196	1179.694	85/43
197	1185.712
198	1191.731
199	1197.75
200	1203.769
201	1209.788
202	1215.807
203	1221.826
204	1227.844	63/31
205	1233.863	51/25
206	1239.882
207	1245.901
208	1251.92
209	1257.939
210	1263.957
211	1269.976
212	1275.995
213	1282.014	65/31, 86/41
214	1288.033
215	1294.052	19/9
216	1300.071
217	1306.089
218	1312.108
219	1318.127
220	1324.146	58/27
221	1330.165
222	1336.184
223	1342.202
224	1348.221	85/39
225	1354.24
226	1360.259
227	1366.278
228	1372.297	95/43
229	1378.315	51/23
230	1384.334
231	1390.353
232	1396.372
233	1402.391
234	1408.41
235	1414.429	43/19
236	1420.447
237	1426.466	57/25, 98/43
238	1432.485
239	1438.504
240	1444.523
241	1450.542
242	1456.56	58/25
243	1462.579
244	1468.598
245	1474.617
246	1480.636	87/37
247	1486.655
248	1492.674	45/19
249	1498.692
250	1504.711	31/13
251	1510.73
252	1516.749
253	1522.768
254	1528.787
255	1534.805
256	1540.824	95/39
257	1546.843	22/9
258	1552.862
259	1558.881
260	1564.9
261	1570.919	57/23
262	1576.937	87/35
263	1582.956
264	1588.975
265	1594.994	98/39
266	1601.013	58/23
267	1607.032	43/17
268	1613.05	33/13
269	1619.069
270	1625.088
271	1631.107
272	1637.126
273	1643.145
274	1649.164	70/27
275	1655.182
276	1661.201	47/18
277	1667.22	55/21
278	1673.239
279	1679.258
280	1685.277	45/17
281	1691.295	93/35
282	1697.314
283	1703.333	99/37
284	1709.352	51/19
285	1715.371
286	1721.39
287	1727.408
288	1733.427
289	1739.446
290	1745.465	74/27
291	1751.484
292	1757.503	69/25
293	1763.522
294	1769.54
295	1775.559
296	1781.578
297	1787.597
298	1793.616	31/11
299	1799.635	99/35
300	1805.653
301	1811.672
302	1817.691
303	1823.71	43/15
304	1829.729
305	1835.748
306	1841.767
307	1847.785
308	1853.804
309	1859.823	41/14
310	1865.842
311	1871.861
312	1877.88
313	1883.898	98/33
314	1889.917
315	1895.936
316	1901.955	3/1

Harmonics

Approximation of prime harmonics in 316edt

Harmonic		2	3	5	7	11	13	17	19	23
Error	Absolute (¢)	-2.25	+0.00	+0.41	+1.73	+1.69	+1.38	+0.40	+0.45	+0.72
	Relative (%)	-37.4	+0.0	+6.8	+28.7	+28.0	+22.9	+6.7	+7.5	+12.0
Steps (reduced)		199 (199)	316 (0)	463 (147)	560 (244)	690 (58)	738 (106)	815 (183)	847 (215)	902 (270)

Approximation of odd harmonics in 316edt

Harmonic		25	27	29	31	33	35	37	39	41	43	45	47	49	51	53	55
Error	Absolute (¢)	+0.82	+0.00	+2.68	+1.58	+1.69	+2.14	+2.24	+1.38	-0.94	+0.87	+0.41	-2.65	-2.56	+0.40	+0.02	+2.10
	Relative (%)	+13.7	+0.0	+44.6	+26.3	+28.0	+35.5	+37.1	+22.9	-15.6	+14.5	+6.8	-43.9	-42.6	+6.7	+0.3	+34.8
Steps (reduced)		926 (294)	948 (0)	969 (21)	988 (40)	1006 (58)	1023 (75)	1039 (91)	1054 (106)	1068 (120)	1082 (134)	1095 (147)	1107 (159)	1119 (171)	1131 (183)	1142 (194)	1153 (205)