202edt

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202edt

203edt →

Prime factorization	2 × 101
Step size	9.41562 ¢
Octave	127\202edt (1195.78 ¢)
Consistency limit	3
Distinct consistency limit	3

202 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 202edt or 202ed3), is a nonoctave tuning system that divides the interval of 3/1 into 202 equal parts of about 9.42 ¢ each. Each step represents a frequency ratio of 3^1/202, or the 202nd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.42	6.44
2	18.83	12.87
3	28.25	19.31
4	37.66	25.74	46/45, 47/46
5	47.08	32.18
6	56.49	38.61	31/30
7	65.91	45.05	27/26
8	75.32	51.49	47/45
9	84.74	57.92
10	94.16	64.36	19/18
11	103.57	70.79	69/65
12	112.99	77.23
13	122.4	83.66
14	131.82	90.1
15	141.23	96.53	51/47
16	150.65	102.97
17	160.07	109.41	34/31
18	169.48	115.84	43/39
19	178.9	122.28	51/46
20	188.31	128.71	29/26, 39/35
21	197.73	135.15	37/33
22	207.14	141.58
23	216.56	148.02	17/15
24	225.97	154.46	49/43, 57/50
25	235.39	160.89	47/41, 63/55
26	244.81	167.33
27	254.22	173.76	22/19
28	263.64	180.2
29	273.05	186.63	41/35, 55/47
30	282.47	193.07
31	291.88	199.5
32	301.3	205.94	25/21
33	310.72	212.38
34	320.13	218.81
35	329.55	225.25
36	338.96	231.68	45/37
37	348.38	238.12	11/9
38	357.79	244.55
39	367.21	250.99
40	376.62	257.43	41/33, 46/37
41	386.04	263.86
42	395.46	270.3	49/39
43	404.87	276.73
44	414.29	283.17	47/37
45	423.7	289.6
46	433.12	296.04
47	442.53	302.48
48	451.95	308.91
49	461.37	315.35
50	470.78	321.78
51	480.2	328.22	33/25
52	489.61	334.65	65/49
53	499.03	341.09
54	508.44	347.52	55/41
55	517.86	353.96
56	527.27	360.4
57	536.69	366.83	15/11
58	546.11	373.27	37/27
59	555.52	379.7	51/37
60	564.94	386.14
61	574.35	392.57	46/33
62	583.77	399.01
63	593.18	405.45	31/22, 69/49
64	602.6	411.88
65	612.02	418.32	47/33
66	621.43	424.75
67	630.85	431.19
68	640.26	437.62	42/29
69	649.68	444.06
70	659.09	450.5
71	668.51	456.93	25/17
72	677.92	463.37	37/25
73	687.34	469.8	55/37
74	696.76	476.24
75	706.17	482.67
76	715.59	489.11	65/43
77	725	495.54
78	734.42	501.98
79	743.83	508.42	63/41
80	753.25	514.85	17/11
81	762.67	521.29
82	772.08	527.72
83	781.5	534.16	11/7
84	790.91	540.59	30/19
85	800.33	547.03	27/17
86	809.74	553.47
87	819.16	559.9	69/43
88	828.57	566.34	50/31
89	837.99	572.77
90	847.41	579.21	31/19
91	856.82	585.64	41/25
92	866.24	592.08
93	875.65	598.51
94	885.07	604.95	5/3
95	894.48	611.39	52/31, 57/34
96	903.9	617.82
97	913.32	624.26	39/23
98	922.73	630.69	46/27
99	932.15	637.13
100	941.56	643.56	31/18
101	950.98	650
102	960.39	656.44	47/27, 54/31
103	969.81	662.87
104	979.22	669.31
105	988.64	675.74	23/13
106	998.06	682.18
107	1007.47	688.61	34/19
108	1016.89	695.05	9/5
109	1026.3	701.49
110	1035.72	707.92
111	1045.13	714.36
112	1054.55	720.79	57/31
113	1063.96	727.23
114	1073.38	733.66
115	1082.8	740.1	43/23
116	1092.21	746.53	47/25
117	1101.63	752.97	17/9
118	1111.04	759.41	19/10
119	1120.46	765.84	21/11
120	1129.87	772.28
121	1139.29	778.71
122	1148.71	785.15	33/17
123	1158.12	791.58	41/21
124	1167.54	798.02
125	1176.95	804.46
126	1186.37	810.89
127	1195.78	817.33
128	1205.2	823.76
129	1214.61	830.2
130	1224.03	836.63
131	1233.45	843.07	51/25
132	1242.86	849.5
133	1252.28	855.94
134	1261.69	862.38	29/14
135	1271.11	868.81
136	1280.52	875.25
137	1289.94	881.68
138	1299.36	888.12
139	1308.77	894.55	49/23, 66/31
140	1318.19	900.99
141	1327.6	907.43
142	1337.02	913.86
143	1346.43	920.3	37/17
144	1355.85	926.73
145	1365.26	933.17	11/5
146	1374.68	939.6
147	1384.1	946.04
148	1393.51	952.48
149	1402.93	958.91
150	1412.34	965.35
151	1421.76	971.78	25/11
152	1431.17	978.22
153	1440.59	984.65
154	1450.01	991.09
155	1459.42	997.52
156	1468.84	1003.96
157	1478.25	1010.4
158	1487.67	1016.83
159	1497.08	1023.27
160	1506.5	1029.7
161	1515.91	1036.14
162	1525.33	1042.57	70/29
163	1534.75	1049.01
164	1544.16	1055.45
165	1553.58	1061.88	27/11
166	1562.99	1068.32	37/15
167	1572.41	1074.75
168	1581.82	1081.19
169	1591.24	1087.62
170	1600.66	1094.06	63/25
171	1610.07	1100.5
172	1619.49	1106.93
173	1628.9	1113.37
174	1638.32	1119.8
175	1647.73	1126.24	57/22
176	1657.15	1132.67
177	1666.56	1139.11	55/21
178	1675.98	1145.54	50/19
179	1685.4	1151.98	45/17
180	1694.81	1158.42
181	1704.23	1164.85
182	1713.64	1171.29	35/13
183	1723.06	1177.72	46/17
184	1732.47	1184.16
185	1741.89	1190.59
186	1751.31	1197.03
187	1760.72	1203.47	47/17
188	1770.14	1209.9
189	1779.55	1216.34
190	1788.97	1222.77
191	1798.38	1229.21	65/23
192	1807.8	1235.64	54/19
193	1817.21	1242.08
194	1826.63	1248.51
195	1836.05	1254.95	26/9
196	1845.46	1261.39
197	1854.88	1267.82
198	1864.29	1274.26
199	1873.71	1280.69
200	1883.12	1287.13
201	1892.54	1293.56
202	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 202edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.22	+0.00	+0.98	+0.71	-4.22	+1.97	-3.23	+0.00	-3.51	+0.97	+0.98
	Relative (%)	-44.8	+0.0	+10.4	+7.5	-44.8	+20.9	-34.3	+0.0	-37.2	+10.3	+10.4
Steps (reduced)		127 (127)	202 (0)	255 (53)	296 (94)	329 (127)	358 (156)	382 (180)	404 (0)	423 (19)	441 (37)	457 (53)

Approximation of harmonics in 202edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.64	-2.25	+0.71	+1.97	+0.58	-4.22	-3.66	+1.69	+1.97	-3.25	+4.54
	Relative (%)	+38.7	-23.9	+7.5	+20.9	+6.2	-44.8	-38.9	+18.0	+20.9	-34.5	+48.2
Steps (reduced)		472 (68)	485 (81)	498 (94)	510 (106)	521 (117)	531 (127)	541 (137)	551 (147)	560 (156)	568 (164)	577 (173)