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	48.84	36/35
3	73.26	24/23, 49/47
4	97.68	18/17, 55/52
5	122.1	44/41
6	146.52	37/34, 49/45
7	170.94
8	195.36	28/25, 47/42
9	219.78	42/37
10	244.2	38/33
11	268.61
12	293.03	45/38, 58/49
13	317.45
14	341.87	28/23
15	366.29	21/17
16	390.71
17	415.13	47/37
18	439.55	49/38, 58/45
19	463.97	17/13
20	488.39	57/43
21	512.81	39/29
22	537.23	15/11
23	561.65	47/34
24	586.07
25	610.49	37/26
26	634.91
27	659.33	41/28, 60/41
28	683.75	46/31, 49/33
29	708.17
30	732.59	29/19, 55/36
31	757.01	48/31
32	781.42	11/7
33	805.84	43/27
34	830.26	21/13
35	854.68
36	879.1
37	903.52
38	927.94	41/24
39	952.36	26/15
40	976.78	51/29, 58/33
41	1001.2	41/23
42	1025.62	38/21, 47/26
43	1050.04	11/6
44	1074.46
45	1098.88
46	1123.3	44/23
47	1147.72	33/17
48	1172.14
49	1196.56
50	1220.98
51	1245.4	39/19
52	1269.81	25/12
53	1294.23	19/9
54	1318.65	15/7
55	1343.07	50/23
56	1367.49
57	1391.91	38/17
58	1416.33	34/15
59	1440.75	23/10
60	1465.17
61	1489.59	26/11
62	1514.01
63	1538.43
64	1562.85	37/15
65	1587.27	5/2
66	1611.69	33/13
67	1636.11	18/7
68	1660.53	47/18, 60/23
69	1684.95	45/17
70	1709.37	51/19
71	1733.79	49/18
72	1758.21	58/21
73	1782.62	14/5
74	1807.04	54/19
75	1831.46	49/17
76	1855.88	38/13
77	1880.3
78	1904.72
79	1929.14
80	1953.56	34/11
81	1977.98	47/15
82	2002.4
83	2026.82	29/9
84	2051.24
85	2075.66
86	2100.08	37/11
87	2124.5	58/17
88	2148.92	45/13
89	2173.34
90	2197.76
91	2222.18
92	2246.6
93	2271.02	26/7
94	2295.43
95	2319.85	42/11
96	2344.27	31/8
97	2368.69	55/14
98	2393.11
99	2417.53
100	2441.95	41/10
101	2466.37	54/13
102	2490.79
103	2515.21	47/11
104	2539.63	13/3
105	2564.05	22/5
106	2588.47	58/13
107	2612.89
108	2637.31
109	2661.73
110	2686.15
111	2710.57
112	2734.99	34/7
113	2759.41
114	2783.82
115	2808.24
116	2832.66
117	2857.08
118	2881.5	37/7
119	2905.92
120	2930.34
121	2954.76
122	2979.18
123	3003.6	17/3
124	3028.02	23/4
125	3052.44	35/6
126	3076.86
127	3101.28	6/1
128	3125.7
129	3150.12	37/6
130	3174.54
131	3198.96
132	3223.38
133	3247.8
134	3272.22
135	3296.63	47/7
136	3321.05
137	3345.47
138	3369.89	7/1
139	3394.31
140	3418.73	36/5
141	3443.15
142	3467.57
143	3491.99
144	3516.41
145	3540.83
146	3565.25
147	3589.67
148	3614.09
149	3638.51
150	3662.93
151	3687.35
152	3711.77
153	3736.19
154	3760.61
155	3785.03
156	3809.44
157	3833.86
158	3858.28
159	3882.7
160	3907.12
161	3931.54
162	3955.96
163	3980.38
164	4004.8
165	4029.22	41/4
166	4053.64	52/5
167	4078.06
168	4102.48
169	4126.9
170	4151.32	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)