176edt

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176edt

177edt →

Prime factorization	24 × 11
Step size	10.8066 ¢
Octave	111\176edt (1199.53 ¢)
Consistency limit	22
Distinct consistency limit	16

176 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 176edt or 176ed3), is a nonoctave tuning system that divides the interval of 3/1 into 176 equal parts of about 10.8 ¢ each. Each step represents a frequency ratio of 3^1/176, or the 176th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.81	7.39
2	21.61	14.77
3	32.42	22.16	52/51, 55/54, 56/55
4	43.23	29.55	40/39, 41/40
5	54.03	36.93	32/31, 33/32
6	64.84	44.32	27/26
7	75.65	51.7	47/45
8	86.45	59.09	41/39
9	97.26	66.48	55/52
10	108.07	73.86	33/31, 50/47
11	118.87	81.25	15/14
12	129.68	88.64	55/51
13	140.49	96.02	51/47
14	151.29	103.41	12/11
15	162.1	110.8	45/41, 56/51
16	172.91	118.18	21/19
17	183.71	125.57
18	194.52	132.95	47/42
19	205.32	140.34
20	216.13	147.73	17/15
21	226.94	155.11	49/43, 57/50
22	237.74	162.5	39/34
23	248.55	169.89	15/13
24	259.36	177.27	36/31
25	270.16	184.66
26	280.97	192.05	20/17
27	291.78	199.43	45/38
28	302.58	206.82	25/21, 56/47
29	313.39	214.2
30	324.2	221.59	41/34, 47/39
31	335	228.98	17/14, 57/47
32	345.81	236.36
33	356.62	243.75	43/35
34	367.42	251.14	47/38
35	378.23	258.52	51/41, 56/45
36	389.04	265.91
37	399.84	273.3	34/27, 63/50
38	410.65	280.68	52/41
39	421.46	288.07	37/29, 51/40
40	432.26	295.45
41	443.07	302.84	31/24
42	453.88	310.23	13/10
43	464.68	317.61	17/13
44	475.49	325	25/19
45	486.3	332.39	45/34
46	497.1	339.77	4/3
47	507.91	347.16	55/41, 63/47
48	518.72	354.55	27/20
49	529.52	361.93	19/14
50	540.33	369.32	41/30, 56/41
51	551.13	376.7	11/8
52	561.94	384.09
53	572.75	391.48	32/23, 39/28
54	583.55	398.86	7/5
55	594.36	406.25	31/22, 55/39
56	605.17	413.64	44/31
57	615.97	421.02
58	626.78	428.41	56/39
59	637.59	435.8	13/9
60	648.39	443.18	16/11
61	659.2	450.57	41/28, 60/41
62	670.01	457.95
63	680.81	465.34	40/27
64	691.62	472.73
65	702.43	480.11	3/2
66	713.23	487.5
67	724.04	494.89	38/25, 41/27
68	734.85	502.27	26/17, 55/36
69	745.65	509.66	20/13
70	756.46	517.05	48/31
71	767.27	524.43
72	778.07	531.82	47/30, 58/37
73	788.88	539.2	41/26
74	799.69	546.59	27/17, 46/29
75	810.49	553.98
76	821.3	561.36	45/28
77	832.11	568.75	55/34
78	842.91	576.14
79	853.72	583.52	18/11
80	864.53	590.91	28/17
81	875.33	598.3	63/38
82	886.14	605.68
83	896.94	613.07	42/25, 47/28
84	907.75	620.45
85	918.56	627.84	17/10
86	929.36	635.23
87	940.17	642.61	31/18, 43/25
88	950.98	650	26/15, 45/26
89	961.78	657.39	54/31
90	972.59	664.77
91	983.4	672.16	30/17
92	994.2	679.55
93	1005.01	686.93	25/14
94	1015.82	694.32
95	1026.62	701.7	38/21
96	1037.43	709.09	51/28
97	1048.24	716.48	11/6
98	1059.04	723.86
99	1069.85	731.25
100	1080.66	738.64	28/15
101	1091.46	746.02	62/33
102	1102.27	753.41	17/9
103	1113.08	760.8
104	1123.88	768.18	44/23
105	1134.69	775.57	52/27
106	1145.5	782.95	31/16, 64/33
107	1156.3	790.34	39/20
108	1167.11	797.73	51/26
109	1177.92	805.11
110	1188.72	812.5
111	1199.53	819.89	2/1
112	1210.34	827.27
113	1221.14	834.66
114	1231.95	842.05	55/27
115	1242.75	849.43	41/20
116	1253.56	856.82	33/16
117	1264.37	864.2	27/13
118	1275.17	871.59
119	1285.98	878.98
120	1296.79	886.36	55/26
121	1307.59	893.75
122	1318.4	901.14	15/7
123	1329.21	908.52	28/13
124	1340.01	915.91
125	1350.82	923.3	24/11
126	1361.63	930.68
127	1372.43	938.07	42/19
128	1383.24	945.45	20/9
129	1394.05	952.84	47/21
130	1404.85	960.23	9/4
131	1415.66	967.61	34/15
132	1426.47	975	57/25
133	1437.27	982.39	39/17
134	1448.08	989.77	30/13
135	1458.89	997.16
136	1469.69	1004.55
137	1480.5	1011.93	40/17
138	1491.31	1019.32
139	1502.11	1026.7	50/21
140	1512.92	1034.09
141	1523.73	1041.48	41/17
142	1534.53	1048.86
143	1545.34	1056.25
144	1556.15	1063.64
145	1566.95	1071.02	42/17, 47/19
146	1577.76	1078.41
147	1588.56	1085.8
148	1599.37	1093.18	63/25
149	1610.18	1100.57	38/15
150	1620.98	1107.95	51/20
151	1631.79	1115.34
152	1642.6	1122.73	31/12
153	1653.4	1130.11	13/5
154	1664.21	1137.5	34/13
155	1675.02	1144.89	50/19
156	1685.82	1152.27	45/17
157	1696.63	1159.66
158	1707.44	1167.05
159	1718.24	1174.43
160	1729.05	1181.82	19/7
161	1739.86	1189.2	41/15
162	1750.66	1196.59	11/4
163	1761.47	1203.98	47/17
164	1772.28	1211.36	64/23
165	1783.08	1218.75	14/5
166	1793.89	1226.14	31/11
167	1804.7	1233.52
168	1815.5	1240.91
169	1826.31	1248.3
170	1837.12	1255.68	26/9
171	1847.92	1263.07	32/11
172	1858.73	1270.45
173	1869.54	1277.84
174	1880.34	1285.23
175	1891.15	1292.61
176	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 176edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.47	+0.00	-0.94	+1.78	-0.47	+2.82	-1.41	+0.00	+1.31	-1.60	-0.94
	Relative (%)	-4.4	+0.0	-8.7	+16.5	-4.4	+26.1	-13.1	+0.0	+12.1	-14.8	-8.7
Steps (reduced)		111 (111)	176 (0)	222 (46)	258 (82)	287 (111)	312 (136)	333 (157)	352 (0)	369 (17)	384 (32)	398 (46)

Approximation of harmonics in 176edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.97	+2.35	+1.78	-1.89	+1.22	-0.47	+3.18	+0.84	+2.82	-2.07	-3.38
	Relative (%)	+9.0	+21.7	+16.5	-17.5	+11.3	-4.4	+29.5	+7.7	+26.1	-19.2	-31.3
Steps (reduced)		411 (59)	423 (71)	434 (82)	444 (92)	454 (102)	463 (111)	472 (120)	480 (128)	488 (136)	495 (143)	502 (150)