163edt

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163edt

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Prime factorization	163 (prime)
Step size	11.6684 ¢
Octave	103\163edt (1201.85 ¢)
Consistency limit	15
Distinct consistency limit	15

163 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 163edt or 163ed3), is a nonoctave tuning system that divides the interval of 3/1 into 163 equal parts of about 11.7 ¢ each. Each step represents a frequency ratio of 3^1/163, or the 163rd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.67	7.98
2	23.34	15.95
3	35.01	23.93	49/48, 50/49
4	46.67	31.9	37/36, 38/37
5	58.34	39.88	30/29
6	70.01	47.85	25/24
7	81.68	55.83	22/21, 43/41
8	93.35	63.8	19/18, 58/55
9	105.02	71.78
10	116.68	79.75	46/43
11	128.35	87.73	14/13
12	140.02	95.71	51/47
13	151.69	103.68	12/11
14	163.36	111.66
15	175.03	119.63
16	186.69	127.61	39/35, 49/44
17	198.36	135.58	37/33, 46/41
18	210.03	143.56	44/39
19	221.7	151.53	25/22
20	233.37	159.51
21	245.04	167.48	38/33
22	256.71	175.46	29/25
23	268.37	183.44
24	280.04	191.41
25	291.71	199.39	45/38, 58/49
26	303.38	207.36
27	315.05	215.34	6/5
28	326.72	223.31	29/24, 35/29
29	338.38	231.29	45/37
30	350.05	239.26	49/40, 60/49
31	361.72	247.24	37/30
32	373.39	255.21	36/29
33	385.06	263.19	5/4
34	396.73	271.17	44/35
35	408.4	279.14	19/15
36	420.06	287.12
37	431.73	295.09
38	443.4	303.07
39	455.07	311.04	13/10
40	466.74	319.02	38/29, 55/42
41	478.41	326.99	29/22
42	490.07	334.97
43	501.74	342.94
44	513.41	350.92	35/26, 39/29
45	525.08	358.9
46	536.75	366.87	15/11
47	548.42	374.85
48	560.08	382.82	29/21, 47/34
49	571.75	390.8	57/41
50	583.42	398.77	7/5
51	595.09	406.75	55/39
52	606.76	414.72
53	618.43	422.7	10/7
54	630.1	430.67	36/25
55	641.76	438.65	42/29
56	653.43	446.63	35/24, 54/37
57	665.1	454.6
58	676.77	462.58	34/23
59	688.44	470.55	58/39
60	700.11	478.53
61	711.77	486.5
62	723.44	494.48	41/27
63	735.11	502.45	55/36
64	746.78	510.43	20/13, 57/37
65	758.45	518.4
66	770.12	526.38	39/25
67	781.79	534.36	11/7
68	793.45	542.33
69	805.12	550.31	35/22, 43/27
70	816.79	558.28
71	828.46	566.26
72	840.13	574.23	13/8
73	851.8	582.21	18/11
74	863.46	590.18
75	875.13	598.16	58/35
76	886.8	606.13
77	898.47	614.11	42/25
78	910.14	622.09	22/13
79	921.81	630.06	46/27
80	933.47	638.04	12/7
81	945.14	646.01	19/11
82	956.81	653.99	33/19
83	968.48	661.96	7/4
84	980.15	669.94	37/21
85	991.82	677.91	39/22
86	1003.49	685.89	25/14
87	1015.15	693.87
88	1026.82	701.84	38/21
89	1038.49	709.82
90	1050.16	717.79	11/6
91	1061.83	725.77	24/13
92	1073.5	733.74
93	1085.16	741.72
94	1096.83	749.69	49/26
95	1108.5	757.67	55/29
96	1120.17	765.64	21/11
97	1131.84	773.62	25/13
98	1143.51	781.6
99	1155.18	789.57	37/19, 39/20
100	1166.84	797.55
101	1178.51	805.52
102	1190.18	813.5
103	1201.85	821.47
104	1213.52	829.45
105	1225.19	837.42
106	1236.85	845.4	47/23, 49/24
107	1248.52	853.37	37/18
108	1260.19	861.35	29/14
109	1271.86	869.33	25/12
110	1283.53	877.3	21/10
111	1295.2	885.28
112	1306.86	893.25
113	1318.53	901.23	15/7
114	1330.2	909.2	41/19
115	1341.87	917.18
116	1353.54	925.15
117	1365.21	933.13	11/5
118	1376.88	941.1
119	1388.54	949.08	29/13
120	1400.21	957.06
121	1411.88	965.03
122	1423.55	973.01
123	1435.22	980.98	55/24
124	1446.89	988.96	30/13
125	1458.55	996.93
126	1470.22	1004.91
127	1481.89	1012.88
128	1493.56	1020.86	45/19
129	1505.23	1028.83
130	1516.9	1036.81	12/5
131	1528.57	1044.79	29/12
132	1540.23	1052.76
133	1551.9	1060.74	49/20
134	1563.57	1068.71	37/15
135	1575.24	1076.69
136	1586.91	1084.66	5/2
137	1598.58	1092.64
138	1610.24	1100.61	38/15
139	1621.91	1108.59
140	1633.58	1116.56
141	1645.25	1124.54
142	1656.92	1132.52
143	1668.59	1140.49
144	1680.25	1148.47
145	1691.92	1156.44
146	1703.59	1164.42
147	1715.26	1172.39	35/13
148	1726.93	1180.37
149	1738.6	1188.34
150	1750.27	1196.32	11/4
151	1761.93	1204.29	47/17
152	1773.6	1212.27	39/14
153	1785.27	1220.25
154	1796.94	1228.22
155	1808.61	1236.2	54/19
156	1820.28	1244.17
157	1831.94	1252.15
158	1843.61	1260.12	29/10
159	1855.28	1268.1
160	1866.95	1276.07
161	1878.62	1284.05
162	1890.29	1292.02
163	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 163edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+1.85	+0.00	+3.70	+2.44	+1.85	+3.35	+5.55	+0.00	+4.29	+2.65	+3.70
	Relative (%)	+15.8	+0.0	+31.7	+20.9	+15.8	+28.7	+47.5	+0.0	+36.8	+22.7	+31.7
Steps (reduced)		103 (103)	163 (0)	206 (43)	239 (76)	266 (103)	289 (126)	309 (146)	326 (0)	342 (16)	356 (30)	369 (43)

Approximation of harmonics in 163edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.15	+5.20	+2.44	-4.27	-4.21	+1.85	+1.59	-5.53	+3.35	+4.49	-2.45
	Relative (%)	+44.1	+44.6	+20.9	-36.6	-36.1	+15.8	+13.7	-47.4	+28.7	+38.5	-21.0
Steps (reduced)		381 (55)	392 (66)	402 (76)	411 (85)	420 (94)	429 (103)	437 (111)	444 (118)	452 (126)	459 (133)	465 (139)