175edt

← 174edt 175edt 176edt →
Prime factorization	52 × 7
Step size	10.8683 ¢
Octave	110\175edt (1195.51 ¢) (→ 22\35edt)
Consistency limit	3
Distinct consistency limit	3

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175 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 175edt or 175ed3), is a nonoctave tuning system that divides the interval of 3/1 into 175 equal parts of about 10.9 ¢ each. Each step represents a frequency ratio of 3^1/175, or the 175th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.87	7.43
2	21.74	14.86
3	32.6	22.29	52/51, 55/54
4	43.47	29.71
5	54.34	37.14
6	65.21	44.57	27/26
7	76.08	52	23/22, 47/45
8	86.95	59.43	41/39
9	97.81	66.86	18/17, 55/52
10	108.68	74.29	33/31
11	119.55	81.71	15/14
12	130.42	89.14	55/51
13	141.29	96.57	38/35, 51/47
14	152.16	104
15	163.02	111.43
16	173.89	118.86	21/19, 52/47
17	184.76	126.29
18	195.63	133.71	28/25, 47/42
19	206.5	141.14	62/55
20	217.37	148.57	17/15
21	228.23	156
22	239.1	163.43	31/27, 54/47
23	249.97	170.86	52/45
24	260.84	178.29	43/37, 57/49
25	271.71	185.71	55/47
26	282.58	193.14
27	293.44	200.57	45/38
28	304.31	208	31/26
29	315.18	215.43	6/5
30	326.05	222.86	35/29
31	336.92	230.29	17/14, 62/51
32	347.79	237.71	11/9
33	358.65	245.14
34	369.52	252.57	26/21
35	380.39	260
36	391.26	267.43
37	402.13	274.86	29/23
38	413	282.29	33/26, 47/37
39	423.86	289.71	23/18
40	434.73	297.14	9/7
41	445.6	304.57	22/17
42	456.47	312
43	467.34	319.43	38/29, 55/42
44	478.21	326.86	29/22
45	489.07	334.29	57/43
46	499.94	341.71
47	510.81	349.14	47/35
48	521.68	356.57
49	532.55	364	34/25
50	543.42	371.43	26/19
51	554.28	378.86	51/37, 62/45
52	565.15	386.29
53	576.02	393.71
54	586.89	401.14
55	597.76	408.57
56	608.63	416	27/19
57	619.49	423.43
58	630.36	430.86	36/25
59	641.23	438.29	42/29, 55/38
60	652.1	445.71	51/35
61	662.97	453.14	22/15
62	673.84	460.57	31/21
63	684.7	468	49/33, 52/35
64	695.57	475.43
65	706.44	482.86
66	717.31	490.29
67	728.18	497.71
68	739.05	505.14	23/15
69	749.91	512.57	54/35
70	760.78	520	45/29
71	771.65	527.43
72	782.52	534.86	11/7
73	793.39	542.29	49/31
74	804.26	549.71	35/22
75	815.12	557.14
76	825.99	564.57	29/18
77	836.86	572	47/29
78	847.73	579.43	31/19
79	858.6	586.86	23/14
80	869.47	594.29	38/23
81	880.33	601.71
82	891.2	609.14
83	902.07	616.57
84	912.94	624
85	923.81	631.43	29/17
86	934.68	638.86
87	945.54	646.29	19/11
88	956.41	653.71	33/19
89	967.28	661.14
90	978.15	668.57	44/25, 51/29
91	989.02	676	62/35
92	999.88	683.43
93	1010.75	690.86	52/29
94	1021.62	698.29
95	1032.49	705.71	49/27
96	1043.36	713.14	42/23
97	1054.23	720.57	57/31
98	1065.09	728
99	1075.96	735.43	54/29
100	1086.83	742.86
101	1097.7	750.29	49/26
102	1108.57	757.71	55/29
103	1119.44	765.14	21/11
104	1130.3	772.57
105	1141.17	780	29/15
106	1152.04	787.43	35/18
107	1162.91	794.86	45/23
108	1173.78	802.29
109	1184.65	809.71
110	1195.51	817.14
111	1206.38	824.57
112	1217.25	832
113	1228.12	839.43	63/31
114	1238.99	846.86	45/22
115	1249.86	854.29	35/17
116	1260.72	861.71	29/14
117	1271.59	869.14	25/12
118	1282.46	876.57
119	1293.33	884	19/9
120	1304.2	891.43
121	1315.07	898.86	47/22, 62/29
122	1325.93	906.29
123	1336.8	913.71
124	1347.67	921.14	37/17
125	1358.54	928.57	57/26
126	1369.41	936
127	1380.28	943.43
128	1391.14	950.86
129	1402.01	958.29
130	1412.88	965.71	43/19, 52/23
131	1423.75	973.14
132	1434.62	980.57
133	1445.49	988
134	1456.35	995.43	51/22, 58/25
135	1467.22	1002.86	7/3
136	1478.09	1010.29	54/23
137	1488.96	1017.71	26/11
138	1499.83	1025.14
139	1510.7	1032.57
140	1521.56	1040
141	1532.43	1047.43	63/26
142	1543.3	1054.86
143	1554.17	1062.29	27/11
144	1565.04	1069.71	42/17
145	1575.91	1077.14
146	1586.77	1084.57	5/2
147	1597.64	1092
148	1608.51	1099.43	38/15
149	1619.38	1106.86
150	1630.25	1114.29
151	1641.12	1121.71	49/19
152	1651.98	1129.14
153	1662.85	1136.57	47/18
154	1673.72	1144
155	1684.59	1151.43	45/17
156	1695.46	1158.86
157	1706.33	1166.29
158	1717.19	1173.71	62/23
159	1728.06	1181.14	19/7
160	1738.93	1188.57
161	1749.8	1196
162	1760.67	1203.43	47/17
163	1771.54	1210.86
164	1782.4	1218.29	14/5
165	1793.27	1225.71	31/11
166	1804.14	1233.14	17/6
167	1815.01	1240.57
168	1825.88	1248
169	1836.75	1255.43	26/9
170	1847.61	1262.86
171	1858.48	1270.29
172	1869.35	1277.71
173	1880.22	1285.14
174	1891.09	1292.57
175	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 175edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.49	+0.00	+1.90	-4.03	-4.49	+0.35	-2.59	+0.00	+2.36	+0.38	+1.90
Error	Relative (%)	-41.3	+0.0	+17.5	-37.0	-41.3	+3.2	-23.8	+0.0	+21.7	+3.5	+17.5
Steps (reduced)		110 (110)	175 (0)	221 (46)	256 (81)	285 (110)	310 (135)	331 (156)	350 (0)	367 (17)	382 (32)	396 (46)

Approximation of harmonics in 175edt
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.61	-4.13	-4.03	+3.79	-3.35	-4.49	-0.27	-2.13	+0.35	-4.11	-4.99
Error	Relative (%)	+42.4	-38.0	-37.0	+34.9	-30.8	-41.3	-2.5	-19.6	+3.2	-37.8	-45.9
Steps (reduced)		409 (59)	420 (70)	431 (81)	442 (92)	451 (101)	460 (110)	469 (119)	477 (127)	485 (135)	492 (142)	499 (149)