170edt

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170edt

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Prime factorization	2 × 5 × 17
Step size	11.188 ¢
Octave	107\170edt (1197.11 ¢)
Consistency limit	3
Distinct consistency limit	3

170 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 170edt or 170ed3), is a nonoctave tuning system that divides the interval of 3/1 into 170 equal parts of about 11.2 ¢ each. Each step represents a frequency ratio of 3^1/170, or the 170th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.19	7.65
2	22.38	15.29
3	33.56	22.94	51/50, 52/51
4	44.75	30.59	39/38
5	55.94	38.24	31/30
6	67.13	45.88	26/25
7	78.32	53.53	45/43
8	89.5	61.18
9	100.69	68.82	35/33
10	111.88	76.47
11	123.07	84.12	29/27
12	134.26	91.76	27/25
13	145.44	99.41	25/23
14	156.63	107.06	23/21
15	167.82	114.71	43/39, 54/49
16	179.01	122.35	41/37, 51/46
17	190.2	130	29/26
18	201.38	137.65
19	212.57	145.29	26/23
20	223.76	152.94	33/29, 58/51
21	234.95	160.59
22	246.14	168.24
23	257.32	175.88	29/25
24	268.51	183.53
25	279.7	191.18
26	290.89	198.82	58/49
27	302.08	206.47	25/21
28	313.26	214.12
29	324.45	221.76	35/29
30	335.64	229.41	17/14
31	346.83	237.06	11/9
32	358.02	244.71
33	369.2	252.35	26/21, 47/38
34	380.39	260
35	391.58	267.65
36	402.77	275.29
37	413.95	282.94	33/26, 47/37
38	425.14	290.59	23/18, 55/43
39	436.33	298.24	9/7
40	447.52	305.88	22/17
41	458.71	313.53	30/23, 43/33
42	469.89	321.18
43	481.08	328.82	33/25
44	492.27	336.47
45	503.46	344.12
46	514.65	351.76	35/26
47	525.83	359.41	42/31
48	537.02	367.06	15/11
49	548.21	374.71
50	559.4	382.35	29/21
51	570.59	390	57/41
52	581.77	397.65	7/5
53	592.96	405.29	31/22, 38/27
54	604.15	412.94	17/12
55	615.34	420.59
56	626.53	428.24
57	637.71	435.88	13/9
58	648.9	443.53
59	660.09	451.18
60	671.28	458.82
61	682.47	466.47	43/29, 46/31
62	693.65	474.12
63	704.84	481.76
64	716.03	489.41
65	727.22	497.06	35/23
66	738.41	504.71
67	749.59	512.35	54/35
68	760.78	520	45/29
69	771.97	527.65
70	783.16	535.29	11/7
71	794.35	542.94
72	805.53	550.59	43/27
73	816.72	558.24
74	827.91	565.88	50/31
75	839.1	573.53
76	850.29	581.18	49/30
77	861.47	588.82	51/31
78	872.66	596.47
79	883.85	604.12	5/3
80	895.04	611.76	52/31
81	906.23	619.41
82	917.41	627.06	17/10
83	928.6	634.71
84	939.79	642.35	43/25
85	950.98	650	26/15, 45/26
86	962.17	657.65
87	973.35	665.29
88	984.54	672.94	30/17
89	995.73	680.59
90	1006.92	688.24
91	1018.11	695.88	9/5
92	1029.29	703.53
93	1040.48	711.18	31/17
94	1051.67	718.82
95	1062.86	726.47
96	1074.05	734.12
97	1085.23	741.76	58/31
98	1096.42	749.41	49/26
99	1107.61	757.06	55/29
100	1118.8	764.71	21/11
101	1129.99	772.35
102	1141.17	780	29/15
103	1152.36	787.65	35/18
104	1163.55	795.29
105	1174.74	802.94
106	1185.92	810.59
107	1197.11	818.24
108	1208.3	825.88
109	1219.49	833.53
110	1230.68	841.18	55/27
111	1241.86	848.82	43/21
112	1253.05	856.47
113	1264.24	864.12	27/13
114	1275.43	871.76
115	1286.62	879.41
116	1297.8	887.06	36/17, 55/26
117	1308.99	894.71	49/23
118	1320.18	902.35	15/7
119	1331.37	910	41/19
120	1342.56	917.65
121	1353.74	925.29
122	1364.93	932.94	11/5
123	1376.12	940.59	31/14
124	1387.31	948.24	49/22
125	1398.5	955.88
126	1409.68	963.53
127	1420.87	971.18	25/11
128	1432.06	978.82
129	1443.25	986.47	23/10
130	1454.44	994.12	51/22
131	1465.62	1001.76	7/3
132	1476.81	1009.41	54/23
133	1488	1017.06	26/11
134	1499.19	1024.71
135	1510.38	1032.35	55/23
136	1521.56	1040
137	1532.75	1047.65
138	1543.94	1055.29
139	1555.13	1062.94	27/11
140	1566.32	1070.59	42/17
141	1577.5	1078.24
142	1588.69	1085.88
143	1599.88	1093.53
144	1611.07	1101.18
145	1622.26	1108.82
146	1633.44	1116.47
147	1644.63	1124.12
148	1655.82	1131.76
149	1667.01	1139.41	55/21
150	1678.2	1147.06	29/11
151	1689.38	1154.71
152	1700.57	1162.35
153	1711.76	1170
154	1722.95	1177.65	46/17
155	1734.14	1185.29	49/18
156	1745.32	1192.94
157	1756.51	1200.59
158	1767.7	1208.24	25/9
159	1778.89	1215.88
160	1790.08	1223.53
161	1801.26	1231.18
162	1812.45	1238.82
163	1823.64	1246.47	43/15
164	1834.83	1254.12
165	1846.02	1261.76
166	1857.2	1269.41	38/13
167	1868.39	1277.06	50/17
168	1879.58	1284.71
169	1890.77	1292.35
170	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 170edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.89	+0.00	+5.41	-0.51	-2.89	-1.25	+2.53	+0.00	-3.40	-0.58	+5.41
	Relative (%)	-25.8	+0.0	+48.4	-4.5	-25.8	-11.1	+22.6	+0.0	-30.4	-5.2	+48.4
Steps (reduced)		107 (107)	170 (0)	215 (45)	249 (79)	277 (107)	301 (131)	322 (152)	340 (0)	356 (16)	371 (31)	385 (45)

Approximation of harmonics in 170edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.10	-4.13	-0.51	-0.36	-4.62	-2.89	+4.20	+4.90	-1.25	-3.47	-2.11
	Relative (%)	+9.8	-36.9	-4.5	-3.2	-41.3	-25.8	+37.6	+43.8	-11.1	-31.0	-18.8
Steps (reduced)		397 (57)	408 (68)	419 (79)	429 (89)	438 (98)	447 (107)	456 (116)	464 (124)	471 (131)	478 (138)	485 (145)