169edt

← 168edt 169edt 170edt →
Prime factorization	132
Step size	11.2542 ¢
Octave	107\169edt (1204.2 ¢)
Consistency limit	3
Distinct consistency limit	3

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

169 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 169edt or 169ed3), is a nonoctave tuning system that divides the interval of 3/1 into 169 equal parts of about 11.3 ¢ each. Each step represents a frequency ratio of 3^1/169, or the 169th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.25	7.69
2	22.51	15.38
3	33.76	23.08
4	45.02	30.77	39/38
5	56.27	38.46
6	67.53	46.15	26/25
7	78.78	53.85	45/43
8	90.03	61.54
9	101.29	69.23	35/33
10	112.54	76.92
11	123.8	84.62	29/27
12	135.05	92.31
13	146.3	100	62/57
14	157.56	107.69	23/21
15	168.81	115.38	43/39
16	180.07	123.08
17	191.32	130.77	19/17
18	202.58	138.46
19	213.83	146.15	43/38
20	225.08	153.85
21	236.34	161.54	39/34, 47/41
22	247.59	169.23	15/13
23	258.85	176.92
24	270.1	184.62
25	281.35	192.31
26	292.61	200	45/38
27	303.86	207.69
28	315.12	215.38	6/5
29	326.37	223.08	35/29
30	337.63	230.77	62/51
31	348.88	238.46
32	360.13	246.15
33	371.39	253.85	57/46
34	382.64	261.54
35	393.9	269.23	54/43
36	405.15	276.92
37	416.4	284.62	14/11
38	427.66	292.31
39	438.91	300	58/45
40	450.17	307.69	35/27
41	461.42	315.38
42	472.68	323.08	46/35
43	483.93	330.77	41/31, 45/34
44	495.18	338.46
45	506.44	346.15
46	517.69	353.85	31/23, 58/43
47	528.95	361.54	19/14
48	540.2	369.23
49	551.45	376.92
50	562.71	384.62	18/13
51	573.96	392.31	39/28, 46/33
52	585.22	400
53	596.47	407.69	55/39
54	607.73	415.38	27/19
55	618.98	423.08
56	630.23	430.77	36/25
57	641.49	438.46	42/29
58	652.74	446.15	51/35
59	664	453.85	22/15
60	675.25	461.54	31/21
61	686.5	469.23	58/39
62	697.76	476.92
63	709.01	484.62
64	720.27	492.31	47/31
65	731.52	500	29/19
66	742.78	507.69	43/28
67	754.03	515.38	17/11
68	765.28	523.08	14/9
69	776.54	530.77
70	787.79	538.46
71	799.05	546.15	46/29
72	810.3	553.85
73	821.55	561.54	45/28
74	832.81	569.23	55/34
75	844.06	576.92	57/35
76	855.32	584.62
77	866.57	592.31
78	877.83	600
79	889.08	607.69
80	900.33	615.38
81	911.59	623.08	22/13
82	922.84	630.77	46/27
83	934.1	638.46
84	945.35	646.15	19/11
85	956.6	653.85	33/19
86	967.86	661.54
87	979.11	669.23	44/25
88	990.37	676.92	39/22, 62/35
89	1001.62	684.62	41/23
90	1012.88	692.31
91	1024.13	700
92	1035.38	707.69
93	1046.64	715.38
94	1057.89	723.08	35/19
95	1069.15	730.77
96	1080.4	738.46	28/15
97	1091.65	746.15	62/33
98	1102.91	753.85
99	1114.16	761.54
100	1125.42	769.23
101	1136.67	776.92	27/14
102	1147.93	784.62	33/17
103	1159.18	792.31	41/21, 43/22
104	1170.43	800	57/29
105	1181.69	807.69
106	1192.94	815.38
107	1204.2	823.08
108	1215.45	830.77
109	1226.7	838.46
110	1237.96	846.15	45/22, 47/23
111	1249.21	853.85	35/17
112	1260.47	861.54	29/14
113	1271.72	869.23	25/12
114	1282.98	876.92
115	1294.23	884.62	19/9
116	1305.48	892.31
117	1316.74	900	62/29
118	1327.99	907.69	28/13
119	1339.25	915.38	13/6
120	1350.5	923.08
121	1361.75	930.77
122	1373.01	938.46	42/19
123	1384.26	946.15
124	1395.52	953.85	47/21, 56/25
125	1406.77	961.54
126	1418.03	969.23	34/15
127	1429.28	976.92
128	1440.53	984.62
129	1451.79	992.31
130	1463.04	1000
131	1474.3	1007.69
132	1485.55	1015.38	33/14
133	1496.8	1023.08
134	1508.06	1030.77	43/18
135	1519.31	1038.46
136	1530.57	1046.15	46/19
137	1541.82	1053.85
138	1553.08	1061.54
139	1564.33	1069.23
140	1575.58	1076.92
141	1586.84	1084.62	5/2
142	1598.09	1092.31
143	1609.35	1100	38/15
144	1620.6	1107.69
145	1631.85	1115.38
146	1643.11	1123.08
147	1654.36	1130.77	13/5
148	1665.62	1138.46	34/13
149	1676.87	1146.15
150	1688.13	1153.85
151	1699.38	1161.54
152	1710.63	1169.23	51/19
153	1721.89	1176.92
154	1733.14	1184.62
155	1744.4	1192.31
156	1755.65	1200
157	1766.9	1207.69
158	1778.16	1215.38
159	1789.41	1223.08
160	1800.67	1230.77
161	1811.92	1238.46
162	1823.18	1246.15	43/15
163	1834.43	1253.85
164	1845.68	1261.54
165	1856.94	1269.23	38/13
166	1868.19	1276.92
167	1879.45	1284.62
168	1890.7	1292.31
169	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 169edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.20	+0.00	-2.86	+4.72	+4.20	-3.83	+1.33	+0.00	-2.34	+1.47	-2.86
Error	Relative (%)	+37.3	+0.0	-25.4	+41.9	+37.3	-34.0	+11.9	+0.0	-20.8	+13.1	-25.4
Steps (reduced)		107 (107)	169 (0)	213 (44)	248 (79)	276 (107)	299 (130)	320 (151)	338 (0)	354 (16)	369 (31)	382 (44)

Approximation of harmonics in 169edt
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.87	+0.37	+4.72	+5.53	+1.86	+4.20	+0.63	+1.86	-3.83	-5.59	-3.76
Error	Relative (%)	+43.3	+3.3	+41.9	+49.1	+16.6	+37.3	+5.6	+16.5	-34.0	-49.6	-33.4
Steps (reduced)		395 (57)	406 (68)	417 (79)	427 (89)	436 (98)	445 (107)	453 (115)	461 (123)	468 (130)	475 (137)	482 (144)