168edt

← 167edt 168edt 169edt →
Prime factorization	23 × 3 × 7
Step size	11.3212 ¢
Octave	106\168edt (1200.04 ¢) (→ 53\84edt)
Consistency limit	6
Distinct consistency limit	6

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168 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 168edt or 168ed3), is a nonoctave tuning system that divides the interval of 3/1 into 168 equal parts of about 11.3 ¢ each. Each step represents a frequency ratio of 3^1/168, or the 168th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	11.32	7.74
2	22.64	15.48
3	33.96	23.21	51/50, 52/51
4	45.28	30.95	38/37, 39/38
5	56.61	38.69	31/30
6	67.93	46.43	26/25
7	79.25	54.17	22/21, 45/43
8	90.57	61.9	39/37
9	101.89	69.64	35/33
10	113.21	77.38	47/44
11	124.53	85.12	29/27, 43/40
12	135.85	92.86	40/37
13	147.18	100.6	37/34
14	158.5	108.33	57/52
15	169.82	116.07	32/29, 43/39
16	181.14	123.81	10/9
17	192.46	131.55	19/17
18	203.78	139.29	9/8
19	215.1	147.02	43/38
20	226.42	154.76	41/36, 57/50
21	237.74	162.5	39/34, 47/41
22	249.07	170.24	15/13, 52/45
23	260.39	177.98	43/37, 50/43
24	271.71	185.71	48/41, 55/47
25	283.03	193.45
26	294.35	201.19	32/27, 51/43
27	305.67	208.93	31/26, 37/31
28	316.99	216.67	6/5
29	328.31	224.4	29/24, 52/43
30	339.63	232.14	45/37
31	350.96	239.88
32	362.28	247.62	37/30
33	373.6	255.36	31/25, 36/29
34	384.92	263.1
35	396.24	270.83	39/31, 44/35
36	407.56	278.57	43/34
37	418.88	286.31
38	430.2	294.05	41/32, 50/39
39	441.53	301.79	40/31
40	452.85	309.52
41	464.17	317.26	17/13
42	475.49	325	25/19, 54/41
43	486.81	332.74	57/43
44	498.13	340.48	4/3
45	509.45	348.21	47/35, 51/38, 55/41
46	520.77	355.95	27/20, 50/37
47	532.09	363.69	34/25
48	543.42	371.43	26/19
49	554.74	379.17	51/37, 62/45
50	566.06	386.9	43/31
51	577.38	394.64	60/43
52	588.7	402.38	52/37
53	600.02	410.12	41/29, 58/41
54	611.34	417.86	37/26, 47/33
55	622.66	425.6	43/30
56	633.99	433.33	62/43
57	645.31	441.07	45/31
58	656.63	448.81	19/13
59	667.95	456.55	25/17
60	679.27	464.29	37/25, 40/27
61	690.59	472.02
62	701.91	479.76	3/2
63	713.23	487.5
64	724.55	495.24	38/25
65	735.88	502.98	26/17
66	747.2	510.71	57/37
67	758.52	518.45	31/20
68	769.84	526.19	39/25
69	781.16	533.93	11/7
70	792.48	541.67
71	803.8	549.4	35/22, 62/39
72	815.12	557.14
73	826.44	564.88	29/18, 50/31
74	837.77	572.62	60/37
75	849.09	580.36
76	860.41	588.1
77	871.73	595.83	43/26, 48/29
78	883.05	603.57	5/3
79	894.37	611.31	52/31, 57/34, 62/37
80	905.69	619.05	27/16
81	917.01	626.79
82	928.34	634.52	41/24
83	939.66	642.26	43/25
84	950.98	650	26/15, 45/26
85	962.3	657.74
86	973.62	665.48
87	984.94	673.21
88	996.26	680.95	16/9
89	1007.58	688.69	34/19
90	1018.9	696.43	9/5
91	1030.23	704.17	29/16
92	1041.55	711.9
93	1052.87	719.64
94	1064.19	727.38	37/20
95	1075.51	735.12	54/29
96	1086.83	742.86
97	1098.15	750.6
98	1109.47	758.33
99	1120.79	766.07	21/11
100	1132.12	773.81	25/13
101	1143.44	781.55	60/31
102	1154.76	789.29	37/19
103	1166.08	797.02	51/26
104	1177.4	804.76
105	1188.72	812.5
106	1200.04	820.24	2/1
107	1211.36	827.98
108	1222.69	835.71
109	1234.01	843.45	51/25
110	1245.33	851.19	39/19
111	1256.65	858.93	31/15
112	1267.97	866.67	52/25
113	1279.29	874.4	44/21
114	1290.61	882.14
115	1301.93	889.88
116	1313.25	897.62	47/22
117	1324.58	905.36	43/20, 58/27
118	1335.9	913.1
119	1347.22	920.83	37/17
120	1358.54	928.57	57/26
121	1369.86	936.31
122	1381.18	944.05	20/9
123	1392.5	951.79	38/17
124	1403.82	959.52	9/4
125	1415.15	967.26	43/19
126	1426.47	975	41/18, 57/25
127	1437.79	982.74	39/17
128	1449.11	990.48
129	1460.43	998.21
130	1471.75	1005.95
131	1483.07	1013.69
132	1494.39	1021.43
133	1505.71	1029.17	31/13
134	1517.04	1036.9
135	1528.36	1044.64	29/12
136	1539.68	1052.38
137	1551	1060.12
138	1562.32	1067.86	37/15
139	1573.64	1075.6	62/25
140	1584.96	1083.33	5/2
141	1596.28	1091.07
142	1607.6	1098.81	43/17
143	1618.93	1106.55
144	1630.25	1114.29	41/16
145	1641.57	1122.02
146	1652.89	1129.76	13/5
147	1664.21	1137.5	34/13
148	1675.53	1145.24	50/19
149	1686.85	1152.98
150	1698.17	1160.71	8/3
151	1709.5	1168.45	51/19
152	1720.82	1176.19	27/10
153	1732.14	1183.93
154	1743.46	1191.67	52/19
155	1754.78	1199.4
156	1766.1	1207.14
157	1777.42	1214.88
158	1788.74	1222.62
159	1800.06	1230.36
160	1811.39	1238.1	37/13
161	1822.71	1245.83	43/15
162	1834.03	1253.57
163	1845.35	1261.31
164	1856.67	1269.05	38/13
165	1867.99	1276.79	50/17
166	1879.31	1284.52
167	1890.63	1292.26
168	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 168edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.04	+0.00	+0.09	-1.31	+0.04	+4.88	+0.13	+0.00	-1.27	+3.55	+0.09
Error	Relative (%)	+0.4	+0.0	+0.8	-11.6	+0.4	+43.1	+1.1	+0.0	-11.2	+31.3	+0.8
Steps (reduced)		106 (106)	168 (0)	212 (44)	246 (78)	274 (106)	298 (130)	318 (150)	336 (0)	352 (16)	367 (31)	380 (44)

Approximation of harmonics in 168edt
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+4.92	-1.31	+0.17	-2.89	+0.04	-2.99	-1.22	+4.88	+3.59	-5.44
Error	Relative (%)	-23.3	+43.5	-11.6	+1.5	-25.6	+0.4	-26.4	-10.8	+43.1	+31.7	-48.0
Steps (reduced)		392 (56)	404 (68)	414 (78)	424 (88)	433 (97)	442 (106)	450 (114)	458 (122)	466 (130)	473 (137)	479 (143)