201edt

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← 200edt

201edt

202edt →

Prime factorization

3 × 67

Step size

9.46246 ¢

Octave

127\201edt (1201.73 ¢)

Consistency limit

4

Distinct consistency limit

4

201 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 201edt or 201ed3), is a nonoctave tuning system that divides the interval of 3/1 into 201 equal parts of about 9.46 ¢ each. Each step represents a frequency ratio of 3^1/201, or the 201st root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.46	6.47
2	18.92	12.94
3	28.39	19.4	63/62
4	37.85	25.87
5	47.31	32.34	37/36
6	56.77	38.81	31/30
7	66.24	45.27	27/26
8	75.7	51.74	47/45
9	85.16	58.21	21/20
10	94.62	64.68	19/18
11	104.09	71.14
12	113.55	77.61
13	123.01	84.08	29/27
14	132.47	90.55	68/63
15	141.94	97.01	51/47
16	151.4	103.48	12/11
17	160.86	109.95	34/31, 45/41
18	170.32	116.42
19	179.79	122.89
20	189.25	129.35	29/26
21	198.71	135.82	37/33
22	208.17	142.29	62/55
23	217.64	148.76	17/15
24	227.1	155.22	49/43
25	236.56	161.69	39/34, 47/41
26	246.02	168.16
27	255.49	174.63
28	264.95	181.09
29	274.41	187.56	34/29, 41/35
30	283.87	194.03	33/28
31	293.34	200.5
32	302.8	206.97
33	312.26	213.43
34	321.72	219.9
35	331.19	226.37	23/19, 63/52
36	340.65	232.84	28/23
37	350.11	239.3	60/49
38	359.57	245.77
39	369.04	252.24	26/21
40	378.5	258.71	51/41
41	387.96	265.17
42	397.42	271.64	39/31
43	406.89	278.11	43/34, 62/49
44	416.35	284.58
45	425.81	291.04	55/43
46	435.27	297.51	9/7
47	444.74	303.98
48	454.2	310.45	13/10
49	463.66	316.92	17/13
50	473.12	323.38
51	482.59	329.85	37/28
52	492.05	336.32
53	501.51	342.79
54	510.97	349.25	47/35
55	520.44	355.72	27/20
56	529.9	362.19
57	539.36	368.66
58	548.82	375.12	70/51
59	558.29	381.59	29/21
60	567.75	388.06	68/49
61	577.21	394.53	60/43
62	586.67	401
63	596.14	407.46	55/39
64	605.6	413.93
65	615.06	420.4
66	624.52	426.87	33/23
67	633.99	433.33	62/43
68	643.45	439.8	29/20
69	652.91	446.27
70	662.37	452.74
71	671.83	459.2	28/19
72	681.3	465.67	40/27, 43/29
73	690.76	472.14
74	700.22	478.61
75	709.68	485.07
76	719.15	491.54
77	728.61	498.01
78	738.07	504.48
79	747.53	510.95	57/37
80	757	517.41
81	766.46	523.88
82	775.92	530.35	36/23
83	785.38	536.82	63/40
84	794.85	543.28	19/12
85	804.31	549.75
86	813.77	556.22
87	823.23	562.69	37/23
88	832.7	569.15	55/34
89	842.16	575.62
90	851.62	582.09	18/11
91	861.08	588.56	51/31
92	870.55	595.02	43/26
93	880.01	601.49
94	889.47	607.96
95	898.93	614.43	37/22
96	908.4	620.9	49/29
97	917.86	627.36	17/10
98	927.32	633.83
99	936.78	640.3
100	946.25	646.77	19/11
101	955.71	653.23	33/19
102	965.17	659.7
103	974.63	666.17
104	984.1	672.64	30/17
105	993.56	679.1	55/31
106	1003.02	685.57	66/37
107	1012.48	692.04	70/39
108	1021.95	698.51
109	1031.41	704.98	49/27
110	1040.87	711.44	31/17
111	1050.33	717.91	11/6
112	1059.8	724.38
113	1069.26	730.85
114	1078.72	737.31	69/37
115	1088.18	743.78
116	1097.65	750.25	49/26
117	1107.11	756.72	36/19, 55/29
118	1116.57	763.18	40/21
119	1126.03	769.65	23/12
120	1135.5	776.12	52/27
121	1144.96	782.59
122	1154.42	789.05	37/19
123	1163.88	795.52
124	1173.35	801.99
125	1182.81	808.46
126	1192.27	814.93
127	1201.73	821.39
128	1211.2	827.86
129	1220.66	834.33
130	1230.12	840.8	57/28
131	1239.58	847.26
132	1249.05	853.73
133	1258.51	860.2	60/29
134	1267.97	866.67
135	1277.43	873.13	23/11
136	1286.89	879.6
137	1296.36	886.07	55/26
138	1305.82	892.54
139	1315.28	899	62/29
140	1324.74	905.47	43/20, 58/27
141	1334.21	911.94
142	1343.67	918.41	63/29
143	1353.13	924.88
144	1362.59	931.34
145	1372.06	937.81
146	1381.52	944.28	20/9
147	1390.98	950.75
148	1400.44	957.21
149	1409.91	963.68	70/31
150	1419.37	970.15
151	1428.83	976.62
152	1438.29	983.08	39/17, 62/27
153	1447.76	989.55	30/13
154	1457.22	996.02
155	1466.68	1002.49	7/3
156	1476.14	1008.96	68/29
157	1485.61	1015.42
158	1495.07	1021.89
159	1504.53	1028.36	31/13
160	1513.99	1034.83
161	1523.46	1041.29	41/17
162	1532.92	1047.76	63/26
163	1542.38	1054.23
164	1551.84	1060.7	49/20
165	1561.31	1067.16	69/28
166	1570.77	1073.63	52/21, 57/23
167	1580.23	1080.1
168	1589.69	1086.57
169	1599.16	1093.03	68/27
170	1608.62	1099.5
171	1618.08	1105.97	28/11
172	1627.54	1112.44
173	1637.01	1118.91
174	1646.47	1125.37
175	1655.93	1131.84
176	1665.39	1138.31	34/13
177	1674.86	1144.78
178	1684.32	1151.24	45/17
179	1693.78	1157.71
180	1703.24	1164.18
181	1712.71	1170.65
182	1722.17	1177.11
183	1731.63	1183.58
184	1741.09	1190.05	41/15
185	1750.56	1196.52	11/4
186	1760.02	1202.99	47/17
187	1769.48	1209.45
188	1778.94	1215.92
189	1788.41	1222.39
190	1797.87	1228.86
191	1807.33	1235.32	54/19
192	1816.79	1241.79	20/7
193	1826.26	1248.26
194	1835.72	1254.73	26/9
195	1845.18	1261.19
196	1854.64	1267.66
197	1864.11	1274.13
198	1873.57	1280.6	62/21
199	1883.03	1287.06
200	1892.49	1293.53
201	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 201edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.73	+0.00	+3.47	-4.35	+1.73	-0.19	-4.26	+0.00	-2.62	+2.70	+3.47
Error	Relative (%)	+18.3	+0.0	+36.6	-46.0	+18.3	-2.0	-45.1	+0.0	-27.7	+28.6	+36.6
Steps (reduced)		127 (127)	201 (0)	254 (53)	294 (93)	328 (127)	356 (155)	380 (179)	402 (0)	421 (19)	439 (37)	455 (53)

Approximation of harmonics in 201edt
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+1.54	-4.35	-2.53	-3.40	+1.73	+2.75	-0.88	-0.19	+4.44	+3.18
Error	Relative (%)	-27.8	+16.3	-46.0	-26.8	-35.9	+18.3	+29.1	-9.3	-2.0	+46.9	+33.6
Steps (reduced)		469 (67)	483 (81)	495 (93)	507 (105)	518 (116)	529 (127)	539 (137)	548 (146)	557 (155)	566 (164)	574 (172)