171edt

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171edt

172edt →

Prime factorization	32 × 19
Step size	11.1225 ¢
Octave	108\171edt (1201.23 ¢) (→ 12\19edt)
Consistency limit	9
Distinct consistency limit	9

171 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 171edt or 171ed3), is a nonoctave tuning system that divides the interval of 3/1 into 171 equal parts of about 11.1 ¢ each. Each step represents a frequency ratio of 3^1/171, or the 171st root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.12	7.6
2	22.25	15.2
3	33.37	22.81	52/51
4	44.49	30.41	39/38
5	55.61	38.01	31/30, 32/31
6	66.74	45.61
7	77.86	53.22	23/22
8	88.98	60.82
9	100.1	68.42	18/17
10	111.23	76.02	16/15
11	122.35	83.63	44/41
12	133.47	91.23
13	144.59	98.83
14	155.72	106.43	35/32
15	166.84	114.04
16	177.96	121.64	41/37, 51/46
17	189.08	129.24	29/26
18	200.21	136.84	46/41, 55/49
19	211.33	144.44	26/23, 35/31
20	222.45	152.05	33/29, 58/51
21	233.57	159.65
22	244.7	167.25	38/33
23	255.82	174.85	51/44
24	266.94	182.46	7/6
25	278.06	190.06	27/23
26	289.19	197.66	13/11
27	300.31	205.26	44/37
28	311.43	212.87
29	322.55	220.47	47/39
30	333.68	228.07	57/47
31	344.8	235.67
32	355.92	243.27
33	367.04	250.88	21/17, 47/38
34	378.17	258.48	46/37, 51/41, 56/45
35	389.29	266.08
36	400.41	273.68	29/23, 34/27
37	411.53	281.29	33/26, 52/41
38	422.66	288.89	37/29
39	433.78	296.49	9/7
40	444.9	304.09
41	456.02	311.7
42	467.15	319.3	38/29, 55/42
43	478.27	326.9	29/22
44	489.39	334.5
45	500.51	342.11
46	511.64	349.71	39/29
47	522.76	357.31	23/17
48	533.88	364.91	49/36
49	545	372.51	37/27
50	556.13	380.12	51/37, 62/45
51	567.25	387.72
52	578.37	395.32
53	589.49	402.92	45/32, 52/37
54	600.62	410.53	41/29, 58/41
55	611.74	418.13	37/26, 47/33
56	622.86	425.73
57	633.99	433.33	49/34
58	645.11	440.94	45/31
59	656.23	448.54	19/13
60	667.35	456.14
61	678.48	463.74
62	689.6	471.35
63	700.72	478.95	3/2
64	711.84	486.55
65	722.97	494.15	41/27, 44/29
66	734.09	501.75	55/36
67	745.21	509.36
68	756.33	516.96	48/31
69	767.46	524.56
70	778.58	532.16	58/37
71	789.7	539.77	41/26
72	800.82	547.37	27/17
73	811.95	554.97
74	823.07	562.57	37/23
75	834.19	570.18	34/21
76	845.31	577.78	44/27
77	856.44	585.38
78	867.56	592.98
79	878.68	600.58
80	889.8	608.19
81	900.93	615.79	37/22
82	912.05	623.39	22/13
83	923.17	630.99	46/27
84	934.29	638.6	12/7
85	945.42	646.2	19/11
86	956.54	653.8	33/19
87	967.66	661.4	7/4
88	978.78	669.01
89	989.91	676.61	39/22, 62/35
90	1001.03	684.21	41/23
91	1012.15	691.81	52/29
92	1023.27	699.42	56/31
93	1034.4	707.02
94	1045.52	714.62
95	1056.64	722.22
96	1067.76	729.82
97	1078.89	737.43	41/22
98	1090.01	745.03
99	1101.13	752.63	17/9
100	1112.25	760.23
101	1123.38	767.84	44/23
102	1134.5	775.44	52/27
103	1145.62	783.04	31/16
104	1156.74	790.64
105	1167.87	798.25	55/28
106	1178.99	805.85
107	1190.11	813.45
108	1201.23	821.05	2/1
109	1212.36	828.65
110	1223.48	836.26
111	1234.6	843.86	49/24
112	1245.72	851.46	39/19
113	1256.85	859.06	31/15
114	1267.97	866.67
115	1279.09	874.27
116	1290.22	881.87
117	1301.34	889.47
118	1312.46	897.08	32/15
119	1323.58	904.68	58/27
120	1334.71	912.28
121	1345.83	919.88	37/17
122	1356.95	927.49	46/21
123	1368.07	935.09
124	1379.2	942.69	51/23
125	1390.32	950.29	29/13
126	1401.44	957.89
127	1412.56	965.5	52/23
128	1423.69	973.1
129	1434.81	980.7	55/24
130	1445.93	988.3
131	1457.05	995.91
132	1468.18	1003.51	7/3
133	1479.3	1011.11
134	1490.42	1018.71	26/11
135	1501.54	1026.32
136	1512.67	1033.92
137	1523.79	1041.52	41/17
138	1534.91	1049.12	17/7
139	1546.03	1056.73
140	1557.16	1064.33
141	1568.28	1071.93	47/19
142	1579.4	1079.53
143	1590.52	1087.13
144	1601.65	1094.74	58/23
145	1612.77	1102.34	33/13
146	1623.89	1109.94	23/9
147	1635.01	1117.54	18/7
148	1646.14	1125.15	44/17
149	1657.26	1132.75
150	1668.38	1140.35
151	1679.5	1147.95	29/11
152	1690.63	1155.56
153	1701.75	1163.16
154	1712.87	1170.76
155	1723.99	1178.36	46/17
156	1735.12	1185.96
157	1746.24	1193.57
158	1757.36	1201.17
159	1768.48	1208.77
160	1779.61	1216.37
161	1790.73	1223.98	45/16
162	1801.85	1231.58	17/6
163	1812.97	1239.18
164	1824.1	1246.78
165	1835.22	1254.39
166	1846.34	1261.99
167	1857.46	1269.59	38/13
168	1868.59	1277.19
169	1879.71	1284.8
170	1890.83	1292.4
171	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 171edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.23	+0.00	+2.47	+5.44	+1.23	+1.30	+3.70	+0.00	-4.44	-2.61	+2.47
	Relative (%)	+11.1	+0.0	+22.2	+49.0	+11.1	+11.7	+33.3	+0.0	-39.9	-23.5	+22.2
Steps (reduced)		108 (108)	171 (0)	216 (45)	251 (80)	279 (108)	303 (132)	324 (153)	342 (0)	358 (16)	373 (31)	387 (45)

Approximation of harmonics in 171edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+2.54	+5.44	+4.94	+0.09	+1.23	-3.39	-3.21	+1.30	-1.37	-0.47
	Relative (%)	-23.7	+22.8	+49.0	+44.4	+0.8	+11.1	-30.5	-28.8	+11.7	-12.4	-4.3
Steps (reduced)		399 (57)	411 (69)	422 (80)	432 (90)	441 (99)	450 (108)	458 (116)	466 (124)	474 (132)	481 (139)	488 (146)