179edt

← 178edt 179edt 180edt →
Prime factorization	179 (prime)
Step size	10.6254 ¢
Octave	113\179edt (1200.68 ¢)
Consistency limit	10
Distinct consistency limit	10

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179 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 179edt or 179ed3), is a nonoctave tuning system that divides the interval of 3/1 into 179 equal parts of about 10.6 ¢ each. Each step represents a frequency ratio of 3^1/179, or the 179th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	10.63	7.26
2	21.25	14.53
3	31.88	21.79	55/54, 56/55, 57/56
4	42.5	29.05	41/40, 42/41
5	53.13	36.31	33/32
6	63.75	43.58	28/27
7	74.38	50.84	24/23, 47/45
8	85	58.1	21/20
9	95.63	65.36	37/35
10	106.25	72.63	50/47
11	116.88	79.89	46/43
12	127.51	87.15	14/13
13	138.13	94.41	13/12
14	148.76	101.68
15	159.38	108.94	34/31, 57/52
16	170.01	116.2	32/29, 43/39
17	180.63	123.46
18	191.26	130.73	48/43
19	201.88	137.99
20	212.51	145.25	26/23
21	223.13	152.51	33/29, 58/51
22	233.76	159.78
23	244.39	167.04	38/33
24	255.01	174.3	22/19, 51/44
25	265.64	181.56	7/6
26	276.26	188.83	34/29
27	286.89	196.09	46/39
28	297.51	203.35	19/16
29	308.14	210.61	43/36, 49/41, 55/46
30	318.76	217.88
31	329.39	225.14	52/43
32	340.01	232.4	28/23, 45/37
33	350.64	239.66	49/40, 60/49
34	361.27	246.93
35	371.89	254.19	57/46
36	382.52	261.45
37	393.14	268.72	54/43, 64/51
38	403.77	275.98	24/19
39	414.39	283.24	47/37
40	425.02	290.5	23/18, 55/43
41	435.64	297.77	9/7
42	446.27	305.03	22/17
43	456.89	312.29	56/43
44	467.52	319.55	38/29, 55/42
45	478.15	326.82	29/22
46	488.77	334.08	57/43
47	499.4	341.34
48	510.02	348.6	47/35, 51/38
49	520.65	355.87	27/20, 50/37
50	531.27	363.13
51	541.9	370.39	26/19, 41/30
52	552.52	377.65	11/8
53	563.15	384.92	18/13
54	573.77	392.18	39/28, 46/33
55	584.4	399.44
56	595.03	406.7	55/39
57	605.65	413.97	44/31
58	616.28	421.23	10/7
59	626.9	428.49	56/39
60	637.53	435.75	13/9
61	648.15	443.02	16/11
62	658.78	450.28	60/41
63	669.4	457.54
64	680.03	464.8	40/27
65	690.65	472.07
66	701.28	479.33	3/2
67	711.9	486.59
68	722.53	493.85	41/27, 44/29
69	733.16	501.12	29/19, 55/36
70	743.78	508.38	43/28, 63/41
71	754.41	515.64	17/11
72	765.03	522.91	14/9
73	775.66	530.17	36/23
74	786.28	537.43	52/33, 63/40
75	796.91	544.69
76	807.53	551.96	51/32
77	818.16	559.22
78	828.78	566.48
79	839.41	573.74	13/8
80	850.04	581.01	49/30
81	860.66	588.27	23/14, 51/31
82	871.29	595.53	43/26, 48/29
83	881.91	602.79
84	892.54	610.06
85	903.16	617.32	32/19
86	913.79	624.58	39/23
87	924.41	631.84	29/17
88	935.04	639.11
89	945.66	646.37	19/11
90	956.29	653.63	33/19
91	966.92	660.89
92	977.54	668.16	51/29, 58/33
93	988.17	675.42	23/13
94	998.79	682.68	57/32
95	1009.42	689.94	43/24
96	1020.04	697.21
97	1030.67	704.47	29/16, 49/27
98	1041.29	711.73	31/17, 42/23
99	1051.92	718.99
100	1062.54	726.26	24/13
101	1073.17	733.52
102	1083.8	740.78	43/23, 58/31
103	1094.42	748.04	32/17
104	1105.05	755.31
105	1115.67	762.57	40/21
106	1126.3	769.83	23/12
107	1136.92	777.09	27/14
108	1147.55	784.36	33/17, 64/33
109	1158.17	791.62	41/21
110	1168.8	798.88	55/28, 57/29
111	1179.42	806.15
112	1190.05	813.41
113	1200.68	820.67	2/1
114	1211.3	827.93
115	1221.93	835.2
116	1232.55	842.46	55/27
117	1243.18	849.72	41/20
118	1253.8	856.98	33/16, 64/31
119	1264.43	864.25	27/13
120	1275.05	871.51
121	1285.68	878.77	21/10
122	1296.3	886.03	55/26
123	1306.93	893.3
124	1317.56	900.56
125	1328.18	907.82	28/13
126	1338.81	915.08	13/6
127	1349.43	922.35	24/11
128	1360.06	929.61	57/26
129	1370.68	936.87	64/29
130	1381.31	944.13	20/9
131	1391.93	951.4	38/17
132	1402.56	958.66
133	1413.18	965.92	43/19, 52/23
134	1423.81	973.18
135	1434.44	980.45	55/24
136	1445.06	987.71
137	1455.69	994.97	51/22
138	1466.31	1002.23	7/3
139	1476.94	1009.5	54/23
140	1487.56	1016.76
141	1498.19	1024.02	19/8
142	1508.81	1031.28	43/18, 55/23
143	1519.44	1038.55
144	1530.06	1045.81	46/19
145	1540.69	1053.07	56/23
146	1551.32	1060.34	49/20
147	1561.94	1067.6	37/15
148	1572.57	1074.86
149	1583.19	1082.12
150	1593.82	1089.39
151	1604.44	1096.65	48/19
152	1615.07	1103.91
153	1625.69	1111.17
154	1636.32	1118.44	18/7
155	1646.94	1125.7	44/17, 57/22
156	1657.57	1132.96
157	1668.2	1140.22
158	1678.82	1147.49	29/11
159	1689.45	1154.75
160	1700.07	1162.01
161	1710.7	1169.27	43/16
162	1721.32	1176.54
163	1731.95	1183.8
164	1742.57	1191.06	52/19
165	1753.2	1198.32
166	1763.82	1205.59	36/13
167	1774.45	1212.85	39/14
168	1785.08	1220.11
169	1795.7	1227.37
170	1806.33	1234.64
171	1816.95	1241.9	20/7
172	1827.58	1249.16	23/8
173	1838.2	1256.42
174	1848.83	1263.69	32/11
175	1859.45	1270.95	41/14
176	1870.08	1278.21	56/19
177	1880.7	1285.47
178	1891.33	1292.74
179	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 179edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.68	+0.00	+1.35	-2.45	+0.68	-0.56	+2.03	+0.00	-1.77	+3.23	+1.35
Error	Relative (%)	+6.4	+0.0	+12.7	-23.0	+6.4	-5.3	+19.1	+0.0	-16.7	+30.4	+12.7
Steps (reduced)		113 (113)	179 (0)	226 (47)	262 (83)	292 (113)	317 (138)	339 (160)	358 (0)	375 (17)	391 (33)	405 (47)

Approximation of harmonics in 179edt
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.91	+0.12	-2.45	+2.70	+4.00	+0.68	+2.70	-1.10	-0.56	+3.91	+1.33
Error	Relative (%)	+8.6	+1.1	-23.0	+25.4	+37.7	+6.4	+25.4	-10.3	-5.3	+36.8	+12.5
Steps (reduced)		418 (60)	430 (72)	441 (83)	452 (94)	462 (104)	471 (113)	480 (122)	488 (130)	496 (138)	504 (146)	511 (153)