205edt

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205edt

206edt →

Prime factorization	5 × 41
Step size	9.27783 ¢
Octave	129\205edt (1196.84 ¢)
Consistency limit	3
Distinct consistency limit	3

205 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 205edt or 205ed3), is a nonoctave tuning system that divides the interval of 3/1 into 205 equal parts of about 9.28 ¢ each. Each step represents a frequency ratio of 3^1/205, or the 205th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.28	6.34
2	18.56	12.68
3	27.83	19.02	63/62
4	37.11	25.37	46/45, 47/46
5	46.39	31.71
6	55.67	38.05
7	64.94	44.39	27/26
8	74.22	50.73	47/45
9	83.5	57.07	43/41
10	92.78	63.41	19/18, 58/55
11	102.06	69.76	35/33, 52/49
12	111.33	76.1
13	120.61	82.44
14	129.89	88.78
15	139.17	95.12
16	148.45	101.46	49/45
17	157.72	107.8	23/21
18	167	114.15
19	176.28	120.49
20	185.56	126.83	69/62
21	194.83	133.17	47/42
22	204.11	139.51
23	213.39	145.85
24	222.67	152.2	33/29
25	231.95	158.54
26	241.22	164.88	54/47
27	250.5	171.22	52/45
28	259.78	177.56	43/37
29	269.06	183.9
30	278.33	190.24	27/23
31	287.61	196.59
32	296.89	202.93
33	306.17	209.27	37/31, 68/57
34	315.45	215.61	6/5
35	324.72	221.95	35/29, 41/34
36	334	228.29	57/47
37	343.28	234.63
38	352.56	240.98
39	361.84	247.32
40	371.11	253.66	57/46
41	380.39	260
42	389.67	266.34
43	398.95	272.68	34/27
44	408.22	279.02	19/15, 62/49
45	417.5	285.37	14/11
46	426.78	291.71
47	436.06	298.05	9/7
48	445.34	304.39
49	454.61	310.73
50	463.89	317.07	17/13
51	473.17	323.41	46/35
52	482.45	329.76
53	491.72	336.1
54	501	342.44
55	510.28	348.78	47/35
56	519.56	355.12
57	528.84	361.46	19/14
58	538.11	367.8
59	547.39	374.15
60	556.67	380.49
61	565.95	386.83	43/31
62	575.23	393.17	46/33
63	584.5	399.51
64	593.78	405.85
65	603.06	412.2
66	612.34	418.54	47/33
67	621.61	424.88
68	630.89	431.22	36/25
69	640.17	437.56	42/29, 55/38, 68/47
70	649.45	443.9
71	658.73	450.24
72	668	456.59
73	677.28	462.93	34/23
74	686.56	469.27
75	695.84	475.61
76	705.12	481.95
77	714.39	488.29	65/43, 68/45
78	723.67	494.63	41/27
79	732.95	500.98	29/19, 55/36
80	742.23	507.32
81	751.5	513.66	54/35
82	760.78	520	45/29
83	770.06	526.34
84	779.34	532.68
85	788.62	539.02	41/26
86	797.89	545.37	46/29, 65/41
87	807.17	551.71
88	816.45	558.05
89	825.73	564.39	29/18
90	835	570.73	34/21, 47/29
91	844.28	577.07	57/35
92	853.56	583.41	18/11
93	862.84	589.76	51/31
94	872.12	596.1
95	881.39	602.44
96	890.67	608.78
97	899.95	615.12
98	909.23	621.46
99	918.51	627.8
100	927.78	634.15
101	937.06	640.49
102	946.34	646.83	19/11
103	955.62	653.17	33/19
104	964.89	659.51
105	974.17	665.85
106	983.45	672.2
107	992.73	678.54
108	1002.01	684.88
109	1011.28	691.22	52/29
110	1020.56	697.56
111	1029.84	703.9
112	1039.12	710.24	31/17
113	1048.39	716.59	11/6
114	1057.67	722.93	35/19
115	1066.95	729.27	63/34
116	1076.23	735.61	54/29
117	1085.51	741.95
118	1094.78	748.29
119	1104.06	754.63
120	1113.34	760.98
121	1122.62	767.32	65/34
122	1131.9	773.66
123	1141.17	780	29/15
124	1150.45	786.34	35/18, 68/35
125	1159.73	792.68
126	1169.01	799.02	55/28, 57/29
127	1178.28	805.37
128	1187.56	811.71
129	1196.84	818.05
130	1206.12	824.39
131	1215.4	830.73
132	1224.67	837.07	69/34
133	1233.95	843.41
134	1243.23	849.76
135	1252.51	856.1	68/33
136	1261.78	862.44	29/14
137	1271.06	868.78	25/12
138	1280.34	875.12
139	1289.62	881.46
140	1298.9	887.8
141	1308.17	894.15
142	1317.45	900.49
143	1326.73	906.83
144	1336.01	913.17
145	1345.29	919.51
146	1354.56	925.85
147	1363.84	932.2
148	1373.12	938.54	42/19
149	1382.4	944.88
150	1391.67	951.22
151	1400.95	957.56
152	1410.23	963.9
153	1419.51	970.24
154	1428.79	976.59
155	1438.06	982.93	39/17
156	1447.34	989.27
157	1456.62	995.61	58/25
158	1465.9	1001.95	7/3
159	1475.17	1008.29	68/29
160	1484.45	1014.63	33/14
161	1493.73	1020.98	45/19
162	1503.01	1027.32
163	1512.29	1033.66
164	1521.56	1040	65/27
165	1530.84	1046.34	46/19
166	1540.12	1052.68
167	1549.4	1059.02
168	1558.68	1065.37
169	1567.95	1071.71	47/19
170	1577.23	1078.05
171	1586.51	1084.39	5/2
172	1595.79	1090.73
173	1605.06	1097.07
174	1614.34	1103.41
175	1623.62	1109.76	23/9
176	1632.9	1116.1
177	1642.18	1122.44
178	1651.45	1128.78
179	1660.73	1135.12	47/18
180	1670.01	1141.46
181	1679.29	1147.8	29/11
182	1688.56	1154.15
183	1697.84	1160.49
184	1707.12	1166.83
185	1716.4	1173.17	62/23
186	1725.68	1179.51
187	1734.95	1185.85
188	1744.23	1192.2	63/23
189	1753.51	1198.54
190	1762.79	1204.88
191	1772.07	1211.22
192	1781.34	1217.56
193	1790.62	1223.9
194	1799.9	1230.24
195	1809.18	1236.59	54/19
196	1818.45	1242.93
197	1827.73	1249.27
198	1837.01	1255.61	26/9
199	1846.29	1261.95
200	1855.57	1268.29
201	1864.84	1274.63
202	1874.12	1280.98	62/21
203	1883.4	1287.32
204	1892.68	1293.66
205	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 205edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-3.16	+0.00	+2.96	-2.96	-3.16	-0.97	-0.20	+0.00	+3.15	-4.13	+2.96
	Relative (%)	-34.1	+0.0	+31.9	-32.0	-34.1	-10.5	-2.2	+0.0	+34.0	-44.5	+31.9
Steps (reduced)		129 (129)	205 (0)	259 (54)	300 (95)	334 (129)	363 (158)	388 (183)	410 (0)	430 (20)	447 (37)	464 (54)

Approximation of harmonics in 205edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.55	-4.13	-2.96	-3.36	+3.02	-3.16	-3.98	-0.01	-0.97	+1.99	-0.74
	Relative (%)	+38.3	-44.6	-32.0	-36.2	+32.5	-34.1	-42.9	-0.1	-10.5	+21.4	-8.0
Steps (reduced)		479 (69)	492 (82)	505 (95)	517 (107)	529 (119)	539 (129)	549 (139)	559 (149)	568 (158)	577 (167)	585 (175)