174edt

← 173edt 174edt 175edt →
Prime factorization	2 × 3 × 29
Step size	10.9308 ¢
Octave	110\174edt (1202.39 ¢) (→ 55\87edt)
Consistency limit	6
Distinct consistency limit	6

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174 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 174edt or 174ed3), is a nonoctave tuning system that divides the interval of 3/1 into 174 equal parts of about 10.9 ¢ each. Each step represents a frequency ratio of 3^1/174, or the 174th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.93	7.47
2	21.86	14.94
3	32.79	22.41	52/51, 55/54
4	43.72	29.89	39/38
5	54.65	37.36
6	65.58	44.83	27/26
7	76.52	52.3	23/22, 47/45
8	87.45	59.77	41/39
9	98.38	67.24	18/17, 55/52
10	109.31	74.71	33/31
11	120.24	82.18	15/14
12	131.17	89.66	41/38, 55/51
13	142.1	97.13	38/35, 51/47, 63/58
14	153.03	104.6	47/43
15	163.96	112.07	11/10
16	174.89	119.54	52/47
17	185.82	127.01
18	196.75	134.48	28/25
19	207.68	141.95	62/55
20	218.62	149.43	42/37
21	229.55	156.9
22	240.48	164.37	54/47
23	251.41	171.84	52/45
24	262.34	179.31	50/43, 57/49
25	273.27	186.78	41/35, 55/47
26	284.2	194.25	33/28
27	295.13	201.72	51/43
28	306.06	209.2	37/31
29	316.99	216.67
30	327.92	224.14	52/43
31	338.85	231.61	45/37, 62/51
32	349.78	239.08
33	360.72	246.55
34	371.65	254.02	31/25
35	382.58	261.49
36	393.51	268.97	54/43
37	404.44	276.44
38	415.37	283.91	47/37
39	426.3	291.38	55/43
40	437.23	298.85
41	448.16	306.32	35/27
42	459.09	313.79	30/23, 43/33
43	470.02	321.26
44	480.95	328.74	33/25
45	491.88	336.21
46	502.82	343.68
47	513.75	351.15	35/26, 39/29
48	524.68	358.62	42/31
49	535.61	366.09
50	546.54	373.56	37/27
51	557.47	381.03
52	568.4	388.51	25/18
53	579.33	395.98
54	590.26	403.45	52/37
55	601.19	410.92	58/41
56	612.12	418.39	47/33
57	623.05	425.86	43/30
58	633.99	433.33	62/43
59	644.92	440.8	45/31
60	655.85	448.28	19/13
61	666.78	455.75	25/17
62	677.71	463.22	34/23, 37/25
63	688.64	470.69
64	699.57	478.16
65	710.5	485.63
66	721.43	493.1	47/31
67	732.36	500.57	29/19
68	743.29	508.05	43/28, 63/41
69	754.22	515.52	17/11
70	765.15	522.99	14/9
71	776.09	530.46	36/23, 47/30
72	787.02	537.93	52/33
73	797.95	545.4
74	808.88	552.87
75	819.81	560.34
76	830.74	567.82	21/13
77	841.67	575.29
78	852.6	582.76	18/11
79	863.53	590.23	28/17
80	874.46	597.7	58/35, 63/38
81	885.39	605.17	5/3
82	896.32	612.64	47/28, 52/31
83	907.25	620.11	49/29
84	918.19	627.59	17/10
85	929.12	635.06
86	940.05	642.53	31/18, 43/25
87	950.98	650	26/15, 45/26
88	961.91	657.47	54/31
89	972.84	664.94
90	983.77	672.41	30/17
91	994.7	679.89
92	1005.63	687.36
93	1016.56	694.83	9/5
94	1027.49	702.3	38/21
95	1038.42	709.77	51/28
96	1049.35	717.24	11/6
97	1060.29	724.71
98	1071.22	732.18	13/7
99	1082.15	739.66	43/23
100	1093.08	747.13	47/25
101	1104.01	754.6
102	1114.94	762.07
103	1125.87	769.54	23/12
104	1136.8	777.01	27/14
105	1147.73	784.48	33/17
106	1158.66	791.95	41/21
107	1169.59	799.43	55/28, 57/29
108	1180.52	806.9
109	1191.45	814.37
110	1202.39	821.84
111	1213.32	829.31
112	1224.25	836.78
113	1235.18	844.25	51/25
114	1246.11	851.72	39/19
115	1257.04	859.2	31/15
116	1267.97	866.67	52/25
117	1278.9	874.14
118	1289.83	881.61
119	1300.76	889.08
120	1311.69	896.55
121	1322.62	904.02	58/27
122	1333.55	911.49	54/25
123	1344.49	918.97	50/23
124	1355.42	926.44
125	1366.35	933.91
126	1377.28	941.38	31/14
127	1388.21	948.85	29/13
128	1399.14	956.32
129	1410.07	963.79
130	1421	971.26	25/11
131	1431.93	978.74
132	1442.86	986.21	23/10
133	1453.79	993.68
134	1464.72	1001.15
135	1475.65	1008.62
136	1486.59	1016.09
137	1497.52	1023.56
138	1508.45	1031.03	43/18, 55/23
139	1519.38	1038.51
140	1530.31	1045.98
141	1541.24	1053.45	56/23
142	1552.17	1060.92
143	1563.1	1068.39	37/15
144	1574.03	1075.86
145	1584.96	1083.33
146	1595.89	1090.8
147	1606.82	1098.28	43/17
148	1617.75	1105.75	28/11
149	1628.69	1113.22
150	1639.62	1120.69	49/19
151	1650.55	1128.16
152	1661.48	1135.63	47/18
153	1672.41	1143.1
154	1683.34	1150.57	37/14
155	1694.27	1158.05
156	1705.2	1165.52
157	1716.13	1172.99	62/23
158	1727.06	1180.46
159	1737.99	1187.93	30/11
160	1748.92	1195.4
161	1759.85	1202.87	47/17, 58/21
162	1770.79	1210.34
163	1781.72	1217.82	14/5
164	1792.65	1225.29	31/11
165	1803.58	1232.76	17/6
166	1814.51	1240.23
167	1825.44	1247.7
168	1836.37	1255.17	26/9
169	1847.3	1262.64
170	1858.23	1270.11	38/13
171	1869.16	1277.59
172	1880.09	1285.06
173	1891.02	1292.53
174	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 174edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.39	+0.00	+4.77	+1.03	+2.39	-2.15	-3.77	+0.00	+3.42	+2.38	+4.77
Error	Relative (%)	+21.8	+0.0	+43.6	+9.5	+21.8	-19.6	-34.5	+0.0	+31.3	+21.7	+43.6
Steps (reduced)		110 (110)	174 (0)	220 (46)	255 (81)	284 (110)	308 (134)	329 (155)	348 (0)	365 (17)	380 (32)	394 (46)

Approximation of harmonics in 174edt
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+0.24	+1.03	-1.39	+2.96	+2.39	-3.77	-5.13	-2.15	+4.76	+4.32
Error	Relative (%)	-24.1	+2.2	+9.5	-12.7	+27.1	+21.8	-34.5	-46.9	-19.6	+43.6	+39.5
Steps (reduced)		406 (58)	418 (70)	429 (81)	439 (91)	449 (101)	458 (110)	466 (118)	474 (126)	482 (134)	490 (142)	497 (149)