201ed12

201 equal divisions of the 12th harmonic (abbreviated 201ed12) is a nonoctave tuning system that divides the interval of 12/1 into 201 equal parts of about 21.4 ¢ each. Each step represents a frequency ratio of 12^1/201, or the 201st root of 12.

← 200ed12

201ed12

202ed12 →

Prime factorization	3 × 67
Step size	21.4028 ¢
Octave	56\201ed12 (1198.55 ¢)
Twelfth	89\201ed12 (1904.85 ¢)
Consistency limit	6
Distinct consistency limit	6

Theory

201ed12 acts as a compressed version of 56edo.

Approximation of harmonics in 201ed12

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.45	+2.89	-2.89	-3.95	+1.45	-8.59	-4.34	+5.78	-5.40	+0.82	+0.00
	Relative (%)	-6.8	+13.5	-13.5	-18.5	+6.8	-40.1	-20.3	+27.0	-25.2	+3.8	+0.0
Steps (reduced)		56 (56)	89 (89)	112 (112)	130 (130)	145 (145)	157 (157)	168 (168)	178 (178)	186 (186)	194 (194)	201 (0)

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	21.4
2	42.81	40/39, 41/40, 42/41
3	64.21
4	85.61	41/39
5	107.01	50/47
6	128.42	14/13
7	149.82	12/11
8	171.22	32/29
9	192.62	19/17
10	214.03	43/38
11	235.43	47/41, 55/48, 63/55
12	256.83	29/25
13	278.24	27/23, 47/40
14	299.64	44/37
15	321.04
16	342.44	39/32
17	363.85	37/30, 58/47
18	385.25	5/4
19	406.65	43/34
20	428.06	32/25, 41/32
21	449.46
22	470.86	21/16
23	492.26
24	513.67	35/26, 39/29
25	535.07	64/47
26	556.47	40/29, 51/37
27	577.87
28	599.28	41/29
29	620.68	63/44
30	642.08	42/29
31	663.49	22/15
32	684.89	52/35
33	706.29
34	727.69
35	749.1	37/24, 57/37
36	770.5	39/25, 64/41
37	791.9
38	813.3	8/5
39	834.71	34/21
40	856.11	41/25
41	877.51
42	898.92	42/25
43	920.32	63/37
44	941.72	31/18
45	963.12	68/39
46	984.53
47	1005.93
48	1027.33	38/21
49	1048.74	11/6
50	1070.14
51	1091.54	62/33
52	1112.94
53	1134.35
54	1155.75	39/20
55	1177.15
56	1198.55
57	1219.96
58	1241.36	43/21
59	1262.76
60	1284.17	21/10
61	1305.57	17/8
62	1326.97
63	1348.37
64	1369.78	64/29
65	1391.18
66	1412.58
67	1433.99
68	1455.39	51/22
69	1476.79	54/23
70	1498.19	19/8
71	1519.6
72	1541
73	1562.4	37/15
74	1583.8
75	1605.21	48/19
76	1626.61	64/25
77	1648.01	57/22
78	1669.42
79	1690.82
80	1712.22	43/16
81	1733.62
82	1755.03
83	1776.43
84	1797.83	48/17
85	1819.23
86	1840.64	55/19
87	1862.04	44/15
88	1883.44
89	1904.85
90	1926.25
91	1947.65
92	1969.05
93	1990.46	60/19
94	2011.86
95	2033.26	55/17, 68/21
96	2054.67
97	2076.07	63/19
98	2097.47	47/14
99	2118.87	17/5
100	2140.28	31/9
101	2161.68
102	2183.08	60/17
103	2204.48	25/7
104	2225.89	47/13
105	2247.29
106	2268.69	63/17
107	2290.1
108	2311.5	19/5
109	2332.9	50/13
110	2354.3
111	2375.71
112	2397.11
113	2418.51
114	2439.91	45/11
115	2461.32	29/7
116	2482.72
117	2504.12	17/4
118	2525.53	43/10
119	2546.93
120	2568.33
121	2589.73	58/13
122	2611.14
123	2632.54
124	2653.94
125	2675.35
126	2696.75	19/4
127	2718.15
128	2739.55
129	2760.96
130	2782.36
131	2803.76
132	2825.16	46/9
133	2846.57
134	2867.97
135	2889.37
136	2910.78	43/8
137	2932.18
138	2953.58
139	2974.98
140	2996.39
141	3017.79	40/7
142	3039.19
143	3060.59	41/7
144	3082
145	3103.4
146	3124.8
147	3146.21
148	3167.61
149	3189.01
150	3210.41
151	3231.82
152	3253.22
153	3274.62
154	3296.03	47/7
155	3317.43
156	3338.83
157	3360.23
158	3381.64
159	3403.04	50/7
160	3424.44
161	3445.84
162	3467.25
163	3488.65	15/2
164	3510.05
165	3531.46
166	3552.86
167	3574.26
168	3595.66
169	3617.07
170	3638.47
171	3659.87	58/7
172	3681.27
173	3702.68
174	3724.08
175	3745.48
176	3766.89
177	3788.29
178	3809.69
179	3831.09	64/7
180	3852.5
181	3873.9
182	3895.3
183	3916.71	48/5
184	3938.11
185	3959.51
186	3980.91
187	4002.32
188	4023.72
189	4045.12
190	4066.52
191	4087.93
192	4109.33
193	4130.73
194	4152.14	11/1
195	4173.54
196	4194.94
197	4216.34
198	4237.75
199	4259.15
200	4280.55
201	4301.96	12/1

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