177edt

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177edt

178edt →

Prime factorization	3 × 59
Step size	10.7455 ¢
Octave	112\177edt (1203.5 ¢)
Consistency limit	3
Distinct consistency limit	3

177 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 177edt or 177ed3), is a nonoctave tuning system that divides the interval of 3/1 into 177 equal parts of about 10.7 ¢ each. Each step represents a frequency ratio of 3^1/177, or the 177th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.75	7.34
2	21.49	14.69
3	32.24	22.03
4	42.98	29.38
5	53.73	36.72
6	64.47	44.07	27/26
7	75.22	51.41	47/45
8	85.96	58.76	41/39
9	96.71	66.1	37/35
10	107.46	73.45	33/31, 50/47
11	118.2	80.79
12	128.95	88.14
13	139.69	95.48
14	150.44	102.82
15	161.18	110.17	34/31, 45/41
16	171.93	117.51
17	182.67	124.86	10/9
18	193.42	132.2	19/17
19	204.16	139.55
20	214.91	146.89	43/38
21	225.66	154.24	57/50
22	236.4	161.58	39/34, 47/41
23	247.15	168.93	15/13
24	257.89	176.27
25	268.64	183.62
26	279.38	190.96
27	290.13	198.31	13/11
28	300.87	205.65	44/37
29	311.62	212.99
30	322.37	220.34	47/39
31	333.11	227.68	57/47, 63/52
32	343.86	235.03	50/41
33	354.6	242.37	27/22
34	365.35	249.72
35	376.09	257.06	41/33, 46/37
36	386.84	264.41
37	397.58	271.75	39/31
38	408.33	279.1	19/15
39	419.07	286.44
40	429.82	293.79	50/39
41	440.57	301.13
42	451.31	308.47
43	462.06	315.82
44	472.8	323.16	46/35
45	483.55	330.51	41/31
46	494.29	337.85
47	505.04	345.2
48	515.78	352.54	31/23, 35/26
49	526.53	359.89
50	537.28	367.23	15/11
51	548.02	374.58
52	558.77	381.92	29/21
53	569.51	389.27	57/41
54	580.26	396.61
55	591	403.95	38/27
56	601.75	411.3
57	612.49	418.64	47/33
58	623.24	425.99	43/30
59	633.99	433.33	62/43
60	644.73	440.68	45/31
61	655.48	448.02	54/37
62	666.22	455.37
63	676.97	462.71	34/23
64	687.71	470.06
65	698.46	477.4
66	709.2	484.75
67	719.95	492.09	47/31, 50/33
68	730.69	499.44
69	741.44	506.78
70	752.19	514.12
71	762.93	521.47
72	773.68	528.81
73	784.42	536.16
74	795.17	543.5
75	805.91	550.85	43/27
76	816.66	558.19
77	827.4	565.54	50/31
78	838.15	572.88	60/37
79	848.9	580.23
80	859.64	587.57
81	870.39	594.92	38/23, 43/26
82	881.13	602.26
83	891.88	609.6
84	902.62	616.95
85	913.37	624.29	39/23
86	924.11	631.64
87	934.86	638.98
88	945.6	646.33	19/11
89	956.35	653.67	33/19
90	967.1	661.02
91	977.84	668.36
92	988.59	675.71	23/13
93	999.33	683.05
94	1010.08	690.4	52/29
95	1020.82	697.74
96	1031.57	705.08
97	1042.31	712.43
98	1053.06	719.77
99	1063.81	727.12	37/20
100	1074.55	734.46
101	1085.3	741.81
102	1096.04	749.15
103	1106.79	756.5
104	1117.53	763.84
105	1128.28	771.19
106	1139.02	778.53
107	1149.77	785.88
108	1160.51	793.22	43/22
109	1171.26	800.56
110	1182.01	807.91
111	1192.75	815.25
112	1203.5	822.6
113	1214.24	829.94
114	1224.99	837.29
115	1235.73	844.63	49/24
116	1246.48	851.98	37/18
117	1257.22	859.32	31/15
118	1267.97	866.67
119	1278.72	874.01
120	1289.46	881.36
121	1300.21	888.7
122	1310.95	896.05
123	1321.7	903.39
124	1332.44	910.73	41/19
125	1343.19	918.08	50/23, 63/29
126	1353.93	925.42
127	1364.68	932.77	11/5
128	1375.43	940.11
129	1386.17	947.46
130	1396.92	954.8
131	1407.66	962.15
132	1418.41	969.49
133	1429.15	976.84
134	1439.9	984.18	62/27
135	1450.64	991.53
136	1461.39	998.87
137	1472.13	1006.21
138	1482.88	1013.56
139	1493.63	1020.9	45/19
140	1504.37	1028.25	31/13
141	1515.12	1035.59
142	1525.86	1042.94
143	1536.61	1050.28
144	1547.35	1057.63	22/9
145	1558.1	1064.97
146	1568.84	1072.32	47/19, 52/21
147	1579.59	1079.66
148	1590.34	1087.01
149	1601.08	1094.35
150	1611.83	1101.69	33/13
151	1622.57	1109.04
152	1633.32	1116.38
153	1644.06	1123.73
154	1654.81	1131.07	13/5
155	1665.55	1138.42	34/13
156	1676.3	1145.76	50/19
157	1687.04	1153.11
158	1697.79	1160.45
159	1708.54	1167.8	51/19
160	1719.28	1175.14	27/10
161	1730.03	1182.49
162	1740.77	1189.83	41/15
163	1751.52	1197.18
164	1762.26	1204.52
165	1773.01	1211.86
166	1783.75	1219.21
167	1794.5	1226.55	31/11
168	1805.25	1233.9
169	1815.99	1241.24
170	1826.74	1248.59
171	1837.48	1255.93	26/9
172	1848.23	1263.28
173	1858.97	1270.62
174	1869.72	1277.97
175	1880.46	1285.31
176	1891.21	1292.66
177	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 177edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.50	+0.00	-3.75	-3.23	+3.50	+5.26	-0.25	+0.00	+0.27	-3.55	-3.75
	Relative (%)	+32.5	+0.0	-34.9	-30.0	+32.5	+49.0	-2.4	+0.0	+2.5	-33.1	-34.9
Steps (reduced)		112 (112)	177 (0)	223 (46)	259 (82)	289 (112)	314 (137)	335 (158)	354 (0)	371 (17)	386 (32)	400 (46)

Approximation of harmonics in 177edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-1.98	-3.23	+3.24	-5.00	+3.50	-4.14	+3.77	+5.26	-0.05	-1.79
	Relative (%)	-24.5	-18.5	-30.0	+30.2	-46.6	+32.5	-38.5	+35.1	+49.0	-0.5	-16.7
Steps (reduced)		413 (59)	425 (71)	436 (82)	447 (93)	456 (102)	466 (112)	474 (120)	483 (129)	491 (137)	498 (144)	505 (151)