170ed11

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170ed11

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Prime factorization	2 × 5 × 17
Step size	24.4195¢
Octave	49\170ed11 (1196.56¢)
Twelfth	78\170ed11 (1904.72¢) (→39\85ed11)
Consistency limit	7
Distinct consistency limit	7

170 equal divisions of the 11th harmonic (abbreviated 170ed11) is a nonoctave tuning system that divides the interval of 11/1 into 170 equal parts of about 24.4 ¢ each. Each step represents a frequency ratio of 11^1/170, or the 170th root of 11.

170ed11 is like 49edo, but with 11/1 instead of 2/1 being just. It helps improve the qualities of harmonics 3, 5 and 7 at the expense of 2.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	24.42
2	48.839	36/35
3	73.259	24/23, 49/47
4	97.678	18/17, 55/52
5	122.098	44/41
6	146.517	37/34, 49/45
7	170.937
8	195.356	28/25, 47/42
9	219.776	42/37
10	244.195	38/33
11	268.615
12	293.034	45/38, 58/49
13	317.454
14	341.873	28/23
15	366.293	21/17
16	390.712
17	415.132	47/37
18	439.551	49/38, 58/45
19	463.971	17/13
20	488.39	57/43
21	512.81	39/29
22	537.229	15/11
23	561.649	47/34
24	586.068
25	610.488	37/26
26	634.907
27	659.327	41/28, 60/41
28	683.746	46/31, 49/33
29	708.166
30	732.586	29/19, 55/36
31	757.005	48/31
32	781.425	11/7
33	805.844	43/27
34	830.264	21/13
35	854.683
36	879.103
37	903.522
38	927.942	41/24
39	952.361	26/15
40	976.781	51/29, 58/33
41	1001.2	41/23
42	1025.62	38/21, 47/26
43	1050.039	11/6
44	1074.459
45	1098.878
46	1123.298	44/23
47	1147.717	33/17
48	1172.137
49	1196.556
50	1220.976
51	1245.395	39/19
52	1269.815	25/12
53	1294.234	19/9
54	1318.654	15/7
55	1343.073	50/23
56	1367.493
57	1391.912	38/17
58	1416.332	34/15
59	1440.752	23/10
60	1465.171
61	1489.591	26/11
62	1514.01
63	1538.43
64	1562.849	37/15
65	1587.269	5/2
66	1611.688	33/13
67	1636.108	18/7
68	1660.527	47/18, 60/23
69	1684.947	45/17
70	1709.366	51/19
71	1733.786	49/18
72	1758.205	58/21
73	1782.625	14/5
74	1807.044	54/19
75	1831.464	49/17
76	1855.883	38/13
77	1880.303
78	1904.722
79	1929.142
80	1953.561	34/11
81	1977.981	47/15
82	2002.4
83	2026.82	29/9
84	2051.239
85	2075.659
86	2100.078	37/11
87	2124.498	58/17
88	2148.918	45/13
89	2173.337
90	2197.757
91	2222.176
92	2246.596
93	2271.015	26/7
94	2295.435
95	2319.854	42/11
96	2344.274	31/8
97	2368.693	55/14
98	2393.113
99	2417.532
100	2441.952	41/10
101	2466.371	54/13
102	2490.791
103	2515.21	47/11
104	2539.63	13/3
105	2564.049	22/5
106	2588.469	58/13
107	2612.888
108	2637.308
109	2661.727
110	2686.147
111	2710.566
112	2734.986	34/7
113	2759.405
114	2783.825
115	2808.244
116	2832.664
117	2857.084
118	2881.503	37/7
119	2905.923
120	2930.342
121	2954.762
122	2979.181
123	3003.601	17/3
124	3028.02	23/4
125	3052.44	35/6
126	3076.859
127	3101.279	6/1
128	3125.698
129	3150.118	37/6
130	3174.537
131	3198.957
132	3223.376
133	3247.796
134	3272.215
135	3296.635	47/7
136	3321.054
137	3345.474
138	3369.893	7/1
139	3394.313
140	3418.732	36/5
141	3443.152
142	3467.571
143	3491.991
144	3516.41
145	3540.83
146	3565.25
147	3589.669
148	3614.089
149	3638.508
150	3662.928
151	3687.347
152	3711.767
153	3736.186
154	3760.606
155	3785.025
156	3809.445
157	3833.864
158	3858.284
159	3882.703
160	3907.123
161	3931.542
162	3955.962
163	3980.381
164	4004.801
165	4029.22	41/4
166	4053.64	52/5
167	4078.059
168	4102.479
169	4126.898
170	4151.318	11/1

Harmonics

Approximation of harmonics in 170ed11

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-3.4	+2.8	-6.9	-2.5	-0.7	+1.1	-10.3	+5.5	-5.9	+0.0	-4.1
	Relative (%)	-14.1	+11.3	-28.2	-10.2	-2.8	+4.4	-42.3	+22.7	-24.3	+0.0	-16.9
Steps (reduced)		49 (49)	78 (78)	98 (98)	114 (114)	127 (127)	138 (138)	147 (147)	156 (156)	163 (163)	170 (0)	176 (6)

Approximation of harmonics in 170ed11

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.8	-2.4	+0.3	+10.6	+3.4	+2.1	+6.2	-9.4	+3.8	-3.4	-7.1
	Relative (%)	+15.7	-9.7	+1.1	+43.6	+13.8	+8.6	+25.3	-38.4	+15.7	-14.1	-29.2
Steps (reduced)		182 (12)	187 (17)	192 (22)	197 (27)	201 (31)	205 (35)	209 (39)	212 (42)	216 (46)	219 (49)	222 (52)