200edt

← 199edt 200edt 201edt →
Prime factorization	23 × 52
Step size	9.50978 ¢
Octave	126\200edt (1198.23 ¢) (→ 63\100edt)
Consistency limit	7
Distinct consistency limit	7

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

200 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 200edt or 200ed3), is a nonoctave tuning system that divides the interval of 3/1 into 200 equal parts of about 9.51 ¢ each. Each step represents a frequency ratio of 3^1/200, or the 200th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.51	6.5
2	19.02	13
3	28.53	19.5	63/62
4	38.04	26	45/44, 46/45, 47/46
5	47.55	32.5	37/36
6	57.06	39	31/30
7	66.57	45.5
8	76.08	52	23/22, 47/45
9	85.59	58.5	41/39
10	95.1	65
11	104.61	71.5
12	114.12	78	47/44
13	123.63	84.5	29/27
14	133.14	91	27/25, 68/63
15	142.65	97.5	38/35, 63/58
16	152.16	104
17	161.67	110.5	45/41
18	171.18	117
19	180.69	123.5
20	190.2	130
21	199.71	136.5	46/41
22	209.22	143	35/31, 44/39
23	218.72	149.5	42/37
24	228.23	156	65/57
25	237.74	162.5	39/34
26	247.25	169	15/13
27	256.76	175.5	29/25
28	266.27	182	7/6
29	275.78	188.5	34/29
30	285.29	195	46/39
31	294.8	201.5	51/43
32	304.31	208	31/26
33	313.82	214.5
34	323.33	221	41/34, 47/39
35	332.84	227.5	63/52
36	342.35	234
37	351.86	240.5	38/31, 49/40
38	361.37	247
39	370.88	253.5	57/46
40	380.39	260
41	389.9	266.5
42	399.41	273	34/27, 63/50
43	408.92	279.5	19/15
44	418.43	286
45	427.94	292.5
46	437.45	299
47	446.96	305.5	22/17
48	456.47	312
49	465.98	318.5
50	475.49	325	25/19
51	485	331.5	41/31, 45/34
52	494.51	338
53	504.02	344.5
54	513.53	351	35/26, 39/29
55	523.04	357.5	23/17
56	532.55	364	34/25
57	542.06	370.5	26/19
58	551.57	377
59	561.08	383.5	47/34, 65/47
60	570.59	390	57/41
61	580.1	396.5
62	589.61	403	52/37
63	599.12	409.5	41/29, 65/46
64	608.63	416	27/19
65	618.14	422.5	10/7
66	627.65	429
67	637.15	435.5	13/9
68	646.66	442
69	656.17	448.5	19/13
70	665.68	455	69/47
71	675.19	461.5	31/21, 65/44
72	684.7	468	52/35
73	694.21	474.5
74	703.72	481
75	713.23	487.5
76	722.74	494	41/27, 44/29
77	732.25	500.5	29/19
78	741.76	507	66/43
79	751.27	513.5	54/35
80	760.78	520	45/29
81	770.29	526.5	39/25
82	779.8	533	69/44
83	789.31	539.5	41/26
84	798.82	546	46/29, 65/41
85	808.33	552.5
86	817.84	559	69/43
87	827.35	565.5	50/31
88	836.86	572	47/29, 60/37
89	846.37	578.5	44/27
90	855.88	585	41/25
91	865.39	591.5
92	874.9	598	58/35, 63/38, 68/41
93	884.41	604.5	5/3
94	893.92	611	57/34, 62/37
95	903.43	617.5
96	912.94	624
97	922.45	630.5	46/27, 63/37
98	931.96	637
99	941.47	643.5	31/18
100	950.98	650
101	960.49	656.5	47/27, 54/31
102	970	663
103	979.51	669.5	37/21, 44/25
104	989.02	676	62/35
105	998.53	682.5
106	1008.04	689	34/19
107	1017.55	695.5	9/5
108	1027.06	702	38/21
109	1036.57	708.5
110	1046.08	715
111	1055.59	721.5	46/25
112	1065.09	728	37/20
113	1074.6	734.5
114	1084.11	741	43/23, 58/31
115	1093.62	747.5	47/25
116	1103.13	754	70/37
117	1112.64	760.5
118	1122.15	767	44/23, 65/34
119	1131.66	773.5	25/13
120	1141.17	780	29/15
121	1150.68	786.5	35/18, 68/35
122	1160.19	793	43/22
123	1169.7	799.5	57/29
124	1179.21	806
125	1188.72	812.5
126	1198.23	819
127	1207.74	825.5
128	1217.25	832
129	1226.76	838.5	63/31
130	1236.27	845	47/23, 49/24
131	1245.78	851.5	39/19
132	1255.29	858
133	1264.8	864.5	27/13
134	1274.31	871
135	1283.82	877.5	21/10
136	1293.33	884	19/9
137	1302.84	890.5
138	1312.35	897
139	1321.86	903.5
140	1331.37	910	41/19
141	1340.88	916.5
142	1350.39	923
143	1359.9	929.5	57/26, 68/31
144	1369.41	936
145	1378.92	942.5	51/23
146	1388.43	949	29/13
147	1397.94	955.5	65/29
148	1407.45	962
149	1416.96	968.5	34/15
150	1426.47	975	57/25
151	1435.98	981.5
152	1445.49	988
153	1455	994.5	51/22
154	1464.51	1001
155	1474.02	1007.5
156	1483.52	1014
157	1493.03	1020.5	45/19
158	1502.54	1027	50/21
159	1512.05	1033.5
160	1521.56	1040	65/27
161	1531.07	1046.5	46/19
162	1540.58	1053
163	1550.09	1059.5
164	1559.6	1066
165	1569.11	1072.5	52/21
166	1578.62	1079
167	1588.13	1085.5
168	1597.64	1092
169	1607.15	1098.5	43/17
170	1616.66	1105
171	1626.17	1111.5
172	1635.68	1118	18/7
173	1645.19	1124.5
174	1654.7	1131	13/5
175	1664.21	1137.5	34/13
176	1673.72	1144
177	1683.23	1150.5	37/14
178	1692.74	1157
179	1702.25	1163.5
180	1711.76	1170
181	1721.27	1176.5
182	1730.78	1183
183	1740.29	1189.5	41/15
184	1749.8	1196
185	1759.31	1202.5	58/21
186	1768.82	1209	25/9
187	1778.33	1215.5
188	1787.84	1222
189	1797.35	1228.5
190	1806.86	1235
191	1816.37	1241.5
192	1825.88	1248	66/23
193	1835.39	1254.5
194	1844.9	1261
195	1854.41	1267.5
196	1863.92	1274	44/15
197	1873.43	1280.5	62/21
198	1882.94	1287
199	1892.45	1293.5
200	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 200edt
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-1.77	+0.00	-3.54	+0.05	-1.77	-2.37	+4.20	+0.00	-1.72	+4.45	-3.54
Error	Relative (%)	-18.6	+0.0	-37.2	+0.5	-18.6	-24.9	+44.2	+0.0	-18.1	+46.8	-37.2
Steps (reduced)		126 (126)	200 (0)	252 (52)	293 (93)	326 (126)	354 (154)	379 (179)	400 (0)	419 (19)	437 (37)	452 (52)

Approximation of harmonics in 200edt
Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.54	-4.13	+0.05	+2.44	+2.09	-1.77	-0.27	-3.49	-2.37	+2.69	+1.81
Error	Relative (%)	+5.6	-43.5	+0.5	+25.6	+22.0	-18.6	-2.9	-36.7	-24.9	+28.2	+19.0
Steps (reduced)		467 (67)	480 (80)	493 (93)	505 (105)	516 (116)	526 (126)	536 (136)	545 (145)	554 (154)	563 (163)	571 (171)