172edt

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172edt

173edt →

Prime factorization	22 × 43
Step size	11.0579 ¢
Octave	109\172edt (1205.31 ¢)
Consistency limit	3
Distinct consistency limit	3

172 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 172edt or 172ed3), is a nonoctave tuning system that divides the interval of 3/1 into 172 equal parts of about 11.1 ¢ each. Each step represents a frequency ratio of 3^1/172, or the 172nd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.06	7.56
2	22.12	15.12
3	33.17	22.67	51/50
4	44.23	30.23	39/38
5	55.29	37.79
6	66.35	45.35
7	77.41	52.91	23/22, 45/43
8	88.46	60.47
9	99.52	68.02	18/17
10	110.58	75.58	49/46
11	121.64	83.14
12	132.69	90.7	27/25
13	143.75	98.26	25/23, 63/58
14	154.81	105.81	47/43
15	165.87	113.37
16	176.93	120.93	41/37
17	187.98	128.49	39/35
18	199.04	136.05	37/33
19	210.1	143.6	35/31, 44/39
20	221.16	151.16	25/22
21	232.22	158.72
22	243.27	166.28
23	254.33	173.84	22/19, 51/44
24	265.39	181.4
25	276.45	188.95	27/23
26	287.5	196.51
27	298.56	204.07
28	309.62	211.63
29	320.68	219.19
30	331.74	226.74	23/19
31	342.79	234.3
32	353.85	241.86	27/22
33	364.91	249.42	21/17, 58/47
34	375.97	256.98	41/33
35	387.03	264.53
36	398.08	272.09	39/31
37	409.14	279.65	19/15
38	420.2	287.21
39	431.26	294.77	50/39
40	442.32	302.33
41	453.37	309.88	13/10
42	464.43	317.44	17/13
43	475.49	325	25/19
44	486.55	332.56
45	497.6	340.12
46	508.66	347.67	51/38, 55/41
47	519.72	355.23
48	530.78	362.79
49	541.84	370.35
50	552.89	377.91
51	563.95	385.47	18/13
52	575.01	393.02
53	586.07	400.58
54	597.13	408.14
55	608.18	415.7	27/19
56	619.24	423.26
57	630.3	430.81
58	641.36	438.37
59	652.41	445.93	51/35
60	663.47	453.49	22/15
61	674.53	461.05	31/21
62	685.59	468.6	55/37
63	696.65	476.16
64	707.7	483.72
65	718.76	491.28
66	729.82	498.84
67	740.88	506.4	23/15
68	751.94	513.95	54/35
69	762.99	521.51
70	774.05	529.07
71	785.11	536.63
72	796.17	544.19
73	807.23	551.74
74	818.28	559.3
75	829.34	566.86	21/13
76	840.4	574.42
77	851.46	581.98
78	862.51	589.53	51/31
79	873.57	597.09	58/35
80	884.63	604.65	5/3
81	895.69	612.21
82	906.75	619.77
83	917.8	627.33	17/10
84	928.86	634.88
85	939.92	642.44	31/18, 43/25
86	950.98	650
87	962.04	657.56	54/31
88	973.09	665.12
89	984.15	672.67	30/17
90	995.21	680.23
91	1006.27	687.79
92	1017.32	695.35	9/5
93	1028.38	702.91
94	1039.44	710.47	31/17
95	1050.5	718.02
96	1061.56	725.58
97	1072.61	733.14	13/7
98	1083.67	740.7	43/23, 58/31
99	1094.73	748.26
100	1105.79	755.81
101	1116.85	763.37
102	1127.9	770.93
103	1138.96	778.49
104	1150.02	786.05	35/18
105	1161.08	793.6	43/22, 45/23
106	1172.14	801.16
107	1183.19	808.72
108	1194.25	816.28
109	1205.31	823.84
110	1216.37	831.4
111	1227.42	838.95	63/31
112	1238.48	846.51	45/22, 47/23
113	1249.54	854.07	35/17
114	1260.6	861.63
115	1271.66	869.19
116	1282.71	876.74
117	1293.77	884.3	19/9
118	1304.83	891.86
119	1315.89	899.42
120	1326.95	906.98
121	1338	914.53	13/6
122	1349.06	922.09
123	1360.12	929.65
124	1371.18	937.21
125	1382.23	944.77
126	1393.29	952.33	38/17
127	1404.35	959.88
128	1415.41	967.44
129	1426.47	975	57/25
130	1437.52	982.56	39/17
131	1448.58	990.12	30/13
132	1459.64	997.67
133	1470.7	1005.23
134	1481.76	1012.79
135	1492.81	1020.35	45/19
136	1503.87	1027.91	31/13
137	1514.93	1035.47
138	1525.99	1043.02
139	1537.05	1050.58	17/7
140	1548.1	1058.14	22/9
141	1559.16	1065.7
142	1570.22	1073.26	57/23
143	1581.28	1080.81
144	1592.33	1088.37
145	1603.39	1095.93
146	1614.45	1103.49
147	1625.51	1111.05	23/9
148	1636.57	1118.6
149	1647.62	1126.16	44/17, 57/22
150	1658.68	1133.72
151	1669.74	1141.28
152	1680.8	1148.84
153	1691.86	1156.4
154	1702.91	1163.95
155	1713.97	1171.51	35/13
156	1725.03	1179.07
157	1736.09	1186.63
158	1747.14	1194.19
159	1758.2	1201.74	58/21
160	1769.26	1209.3	25/9
161	1780.32	1216.86
162	1791.38	1224.42
163	1802.43	1231.98	17/6
164	1813.49	1239.53
165	1824.55	1247.09	43/15
166	1835.61	1254.65
167	1846.67	1262.21
168	1857.72	1269.77	38/13
169	1868.78	1277.33	50/17
170	1879.84	1284.88
171	1890.9	1292.44
172	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 172edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+5.31	+0.00	-0.44	+0.27	+5.31	+3.83	+4.87	+0.00	-5.48	-4.61	-0.44
	Relative (%)	+48.0	+0.0	-4.0	+2.5	+48.0	+34.6	+44.0	+0.0	-49.5	-41.7	-4.0
Steps (reduced)		109 (109)	172 (0)	217 (45)	252 (80)	281 (109)	305 (133)	326 (154)	344 (0)	360 (16)	375 (31)	389 (45)

Approximation of harmonics in 172edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.74	-1.92	+0.27	-0.88	+4.74	+5.31	+0.17	-0.17	+3.83	+0.69	+1.14
	Relative (%)	+42.9	-17.4	+2.5	-8.0	+42.9	+48.0	+1.5	-1.5	+34.6	+6.3	+10.3
Steps (reduced)		402 (58)	413 (69)	424 (80)	434 (90)	444 (100)	453 (109)	461 (117)	469 (125)	477 (133)	484 (140)	491 (147)