208edt

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208edt

209edt →

Prime factorization	24 × 13
Step size	9.14401 ¢
Octave	131\208edt (1197.87 ¢)
Consistency limit	4
Distinct consistency limit	4

208 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 208edt or 208ed3), is a nonoctave tuning system that divides the interval of 3/1 into 208 equal parts of about 9.14 ¢ each. Each step represents a frequency ratio of 3^1/208, or the 208th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.14	6.25
2	18.29	12.5
3	27.43	18.75	63/62
4	36.58	25	47/46, 49/48
5	45.72	31.25
6	54.86	37.5
7	64.01	43.75
8	73.15	50
9	82.3	56.25	43/41
10	91.44	62.5	39/37, 58/55
11	100.58	68.75
12	109.73	75
13	118.87	81.25
14	128.02	87.5
15	137.16	93.75
16	146.3	100	62/57
17	155.45	106.25
18	164.59	112.5	11/10
19	173.74	118.75	21/19
20	182.88	125	10/9
21	192.02	131.25	19/17
22	201.17	137.5
23	210.31	143.75	35/31
24	219.46	150
25	228.6	156.25
26	237.74	162.5
27	246.89	168.75	15/13
28	256.03	175	29/25, 51/44
29	265.18	181.25
30	274.32	187.5	41/35
31	283.46	193.75
32	292.61	200
33	301.75	206.25
34	310.9	212.5
35	320.04	218.75
36	329.18	225	52/43
37	338.33	231.25	45/37, 62/51
38	347.47	237.5	11/9
39	356.62	243.75	43/35, 70/57
40	365.76	250	21/17
41	374.9	256.25	41/33
42	384.05	262.5
43	393.19	268.75	69/55
44	402.34	275	29/23
45	411.48	281.25	52/41
46	420.62	287.5	51/40
47	429.77	293.75	50/39
48	438.91	300	58/45
49	448.06	306.25	57/44
50	457.2	312.5	43/33
51	466.34	318.75
52	475.49	325
53	484.63	331.25	41/31
54	493.78	337.5
55	502.92	343.75
56	512.06	350	39/29
57	521.21	356.25	50/37
58	530.35	362.5
59	539.5	368.75
60	548.64	375	70/51
61	557.78	381.25	69/50
62	566.93	387.5	43/31, 68/49
63	576.07	393.75	60/43
64	585.22	400
65	594.36	406.25	31/22, 55/39
66	603.5	412.5	17/12
67	612.65	418.75	47/33, 57/40
68	621.79	425	63/44
69	630.94	431.25
70	640.08	437.5
71	649.23	443.75
72	658.37	450	60/41
73	667.51	456.25
74	676.66	462.5
75	685.8	468.75	52/35, 55/37
76	694.95	475
77	704.09	481.25
78	713.23	487.5
79	722.38	493.75	41/27
80	731.52	500
81	740.67	506.25	23/15
82	749.81	512.5	54/35
83	758.95	518.75	31/20
84	768.1	525
85	777.24	531.25	47/30, 58/37
86	786.39	537.5	52/33, 63/40
87	795.53	543.75	19/12
88	804.67	550	35/22, 43/27
89	813.82	556.25
90	822.96	562.5	37/23
91	832.11	568.75
92	841.25	575
93	850.39	581.25
94	859.54	587.5
95	868.68	593.75
96	877.83	600
97	886.97	606.25
98	896.11	612.5	52/31
99	905.26	618.75
100	914.4	625	39/23
101	923.55	631.25
102	932.69	637.5	12/7
103	941.83	643.75	31/18
104	950.98	650
105	960.12	656.25	47/27, 54/31
106	969.27	662.5	7/4
107	978.41	668.75
108	987.55	675	23/13
109	996.7	681.25
110	1005.84	687.5
111	1014.99	693.75
112	1024.13	700	47/26
113	1033.27	706.25
114	1042.42	712.5
115	1051.56	718.75
116	1060.71	725
117	1069.85	731.25
118	1078.99	737.5	69/37
119	1088.14	743.75
120	1097.28	750	66/35
121	1106.43	756.25	36/19
122	1115.57	762.5	40/21
123	1124.71	768.75
124	1133.86	775	52/27
125	1143	781.25	60/31
126	1152.15	787.5	35/18
127	1161.29	793.75	45/23
128	1170.43	800
129	1179.58	806.25
130	1188.72	812.5
131	1197.87	818.75
132	1207.01	825
133	1216.15	831.25
134	1225.3	837.5
135	1234.44	843.75
136	1243.59	850	41/20
137	1252.73	856.25
138	1261.87	862.5
139	1271.02	868.75
140	1280.16	875	44/21
141	1289.31	881.25	40/19
142	1298.45	887.5	36/17
143	1307.59	893.75	66/31
144	1316.74	900
145	1325.88	906.25	43/20
146	1335.03	912.5
147	1344.17	918.75	50/23
148	1353.31	925
149	1362.46	931.25
150	1371.6	937.5
151	1380.75	943.75
152	1389.89	950	29/13
153	1399.03	956.25
154	1408.18	962.5
155	1417.32	968.75
156	1426.47	975
157	1435.61	981.25
158	1444.75	987.5
159	1453.9	993.75	44/19
160	1463.04	1000
161	1472.19	1006.25
162	1481.33	1012.5	40/17
163	1490.47	1018.75
164	1499.62	1025	69/29
165	1508.76	1031.25	55/23
166	1517.91	1037.5
167	1527.05	1043.75
168	1536.19	1050	17/7
169	1545.34	1056.25
170	1554.48	1062.5	27/11
171	1563.63	1068.75	37/15
172	1572.77	1075
173	1581.91	1081.25
174	1591.06	1087.5
175	1600.2	1093.75
176	1609.35	1100
177	1618.49	1106.25
178	1627.63	1112.5
179	1636.78	1118.75
180	1645.92	1125	44/17
181	1655.07	1131.25	13/5
182	1664.21	1137.5
183	1673.35	1143.75
184	1682.5	1150
185	1691.64	1156.25
186	1700.79	1162.5
187	1709.93	1168.75	51/19
188	1719.07	1175	27/10
189	1728.22	1181.25	19/7
190	1737.36	1187.5	30/11
191	1746.51	1193.75
192	1755.65	1200
193	1764.79	1206.25
194	1773.94	1212.5
195	1783.08	1218.75
196	1792.23	1225
197	1801.37	1231.25
198	1810.51	1237.5	37/13
199	1819.66	1243.75
200	1828.8	1250
201	1837.95	1256.25
202	1847.09	1262.5
203	1856.23	1268.75
204	1865.38	1275
205	1874.52	1281.25	62/21
206	1883.67	1287.5
207	1892.81	1293.75
208	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 208edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.13	+0.00	-4.27	+2.61	-2.13	-3.83	+2.74	+0.00	+0.48	+0.06	-4.27
	Relative (%)	-23.3	+0.0	-46.7	+28.6	-23.3	-41.9	+30.0	+0.0	+5.2	+0.7	-46.7
Steps (reduced)		131 (131)	208 (0)	262 (54)	305 (97)	339 (131)	368 (160)	394 (186)	416 (0)	436 (20)	454 (38)	470 (54)

Approximation of harmonics in 208edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.46	+3.18	+2.61	+0.61	-3.76	-2.13	-4.30	-1.66	-3.83	-2.07	+3.27
	Relative (%)	+37.9	+34.8	+28.6	+6.6	-41.2	-23.3	-47.0	-18.1	-41.9	-22.6	+35.8
Steps (reduced)		486 (70)	500 (84)	513 (97)	525 (109)	536 (120)	547 (131)	557 (141)	567 (151)	576 (160)	585 (169)	594 (178)