173edt

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173edt

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Prime factorization	173 (prime)
Step size	10.994 ¢
Octave	109\173edt (1198.34 ¢)
Consistency limit	9
Distinct consistency limit	9

173 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 173edt or 173ed3), is a nonoctave tuning system that divides the interval of 3/1 into 173 equal parts of about 11 ¢ each. Each step represents a frequency ratio of 3^1/173, or the 173rd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.99	7.51
2	21.99	15.03
3	32.98	22.54	52/51, 55/54
4	43.98	30.06	39/38
5	54.97	37.57
6	65.96	45.09	27/26
7	76.96	52.6	23/22
8	87.95	60.12
9	98.95	67.63	18/17
10	109.94	75.14
11	120.93	82.66
12	131.93	90.17	41/38, 55/51
13	142.92	97.69	63/58
14	153.92	105.2	35/32, 47/43
15	164.91	112.72
16	175.9	120.23	52/47
17	186.9	127.75
18	197.89	135.26	37/33
19	208.89	142.77	44/39
20	219.88	150.29
21	230.87	157.8	8/7
22	241.87	165.32
23	252.86	172.83	22/19
24	263.86	180.35
25	274.85	187.86	34/29
26	285.84	195.38	46/39
27	296.84	202.89
28	307.83	210.4	43/36
29	318.82	217.92
30	329.82	225.43	23/19, 52/43
31	340.81	232.95
32	351.81	240.46	38/31, 49/40, 60/49
33	362.8	247.98	58/47
34	373.79	255.49	36/29
35	384.79	263.01
36	395.78	270.52
37	406.78	278.03	43/34
38	417.77	285.55
39	428.76	293.06
40	439.76	300.58	58/45
41	450.75	308.09
42	461.75	315.61	47/36
43	472.74	323.12
44	483.73	330.64	41/31
45	494.73	338.15
46	505.72	345.66
47	516.72	353.18	31/23
48	527.71	360.69
49	538.7	368.21
50	549.7	375.72
51	560.69	383.24	47/34
52	571.69	390.75	57/41
53	582.68	398.27	7/5
54	593.67	405.78	31/22
55	604.67	413.29
56	615.66	420.81
57	626.66	428.32
58	637.65	435.84	13/9
59	648.64	443.35
60	659.64	450.87
61	670.63	458.38
62	681.63	465.9	43/29
63	692.62	473.41
64	703.61	480.92
65	714.61	488.44
66	725.6	495.95
67	736.6	503.47	26/17, 49/32
68	747.59	510.98	57/37
69	758.58	518.5
70	769.58	526.01
71	780.57	533.53
72	791.57	541.04
73	802.56	548.55	62/39
74	813.55	556.07	8/5
75	824.55	563.58	29/18
76	835.54	571.1	47/29
77	846.53	578.61	31/19, 44/27
78	857.53	586.13
79	868.52	593.64	38/23
80	879.52	601.16
81	890.51	608.67
82	901.5	616.18
83	912.5	623.7
84	923.49	631.21	29/17, 46/27
85	934.49	638.73
86	945.48	646.24	19/11
87	956.47	653.76	33/19
88	967.47	661.27
89	978.46	668.79	51/29
90	989.46	676.3
91	1000.45	683.82	41/23
92	1011.44	691.33	52/29
93	1022.44	698.84
94	1033.43	706.36
95	1044.43	713.87
96	1055.42	721.39	57/31
97	1066.41	728.9
98	1077.41	736.42	41/22, 54/29
99	1088.4	743.93	15/8
100	1099.4	751.45
101	1110.39	758.96
102	1121.38	766.47
103	1132.38	773.99
104	1143.37	781.5
105	1154.37	789.02	37/19
106	1165.36	796.53	49/25, 51/26
107	1176.35	804.05
108	1187.35	811.56
109	1198.34	819.08
110	1209.34	826.59
111	1220.33	834.1
112	1231.32	841.62	55/27
113	1242.32	849.13
114	1253.31	856.65
115	1264.31	864.16	27/13
116	1275.3	871.68
117	1286.29	879.19
118	1297.29	886.71	55/26
119	1308.28	894.22
120	1319.28	901.73	15/7
121	1330.27	909.25	41/19
122	1341.26	916.76
123	1352.26	924.28
124	1363.25	931.79
125	1374.24	939.31
126	1385.24	946.82
127	1396.23	954.34	56/25
128	1407.23	961.85
129	1418.22	969.36
130	1429.21	976.88
131	1440.21	984.39	62/27
132	1451.2	991.91
133	1462.2	999.42
134	1473.19	1006.94
135	1484.18	1014.45
136	1495.18	1021.97
137	1506.17	1029.48
138	1517.17	1036.99
139	1528.16	1044.51	29/12
140	1539.15	1052.02
141	1550.15	1059.54	49/20
142	1561.14	1067.05
143	1572.14	1074.57	57/23
144	1583.13	1082.08
145	1594.12	1089.6
146	1605.12	1097.11
147	1616.11	1104.62
148	1627.11	1112.14
149	1638.1	1119.65
150	1649.09	1127.17	57/22
151	1660.09	1134.68
152	1671.08	1142.2	21/8
153	1682.08	1149.71
154	1693.07	1157.23
155	1704.06	1164.74
156	1715.06	1172.25
157	1726.05	1179.77
158	1737.05	1187.28
159	1748.04	1194.8
160	1759.03	1202.31	58/21
161	1770.03	1209.83
162	1781.02	1217.34
163	1792.02	1224.86
164	1803.01	1232.37	17/6
165	1814	1239.88
166	1825	1247.4
167	1835.99	1254.91	26/9
168	1846.99	1262.43
169	1857.98	1269.94	38/13
170	1868.97	1277.46
171	1879.97	1284.97
172	1890.96	1292.49
173	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 173edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.66	+0.00	-3.32	-4.84	-1.66	-4.67	-4.98	+0.00	+4.49	+4.40	-3.32
	Relative (%)	-15.1	+0.0	-30.2	-44.0	-15.1	-42.5	-45.3	+0.0	+40.9	+40.0	-30.2
Steps (reduced)		109 (109)	173 (0)	218 (45)	253 (80)	282 (109)	306 (133)	327 (154)	346 (0)	363 (17)	378 (32)	391 (45)

Approximation of harmonics in 173edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+1.03	+4.66	-4.84	+4.36	-1.65	-1.66	+3.68	+2.84	-4.67	+2.74	+2.74
	Relative (%)	+9.4	+42.4	-44.0	+39.7	-15.0	-15.1	+33.5	+25.8	-42.5	+24.9	+24.9
Steps (reduced)		404 (58)	416 (70)	426 (80)	437 (91)	446 (100)	455 (109)	464 (118)	472 (126)	479 (133)	487 (141)	494 (148)