203edt

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203edt

204edt →

Prime factorization	7 × 29
Step size	9.36924¢
Octave	128\203edt (1199.26¢)
Consistency limit	5
Distinct consistency limit	5

203 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 203edt or 203ed3), is a nonoctave tuning system that divides the interval of 3/1 into 203 equal parts of about 9.37⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/203, or the 203rd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.37	6.4
2	18.74	12.81
3	28.11	19.21	63/62
4	37.48	25.62	46/45, 47/46, 48/47
5	46.85	32.02	37/36, 38/37
6	56.22	38.42
7	65.58	44.83	27/26
8	74.95	51.23	47/45
9	84.32	57.64
10	93.69	64.04	19/18
11	103.06	70.44	69/65
12	112.43	76.85	16/15
13	121.8	83.25	44/41
14	131.17	89.66	41/38, 68/63, 69/64
15	140.54	96.06
16	149.91	102.46	12/11
17	159.28	108.87	34/31, 57/52
18	168.65	115.27	43/39
19	178.02	121.67	41/37
20	187.38	128.08	39/35
21	196.75	134.48	65/58
22	206.12	140.89
23	215.49	147.29
24	224.86	153.69	41/36
25	234.23	160.1
26	243.6	166.5	38/33
27	252.97	172.91	22/19
28	262.34	179.31	64/55
29	271.71	185.71	55/47
30	281.08	192.12
31	290.45	198.52
32	299.82	204.93	44/37, 69/58
33	309.18	211.33	55/46
34	318.55	217.73
35	327.92	224.14	29/24
36	337.29	230.54	62/51
37	346.66	236.95	11/9
38	356.03	243.35	43/35, 70/57
39	365.4	249.75	21/17
40	374.77	256.16	36/29, 41/33
41	384.14	262.56
42	393.51	268.97	54/43, 69/55
43	402.88	275.37
44	412.25	281.77	33/26, 52/41
45	421.62	288.18	37/29
46	430.98	294.58
47	440.35	300.99	58/45
48	449.72	307.39	35/27, 48/37
49	459.09	313.79	30/23, 43/33
50	468.46	320.2	38/29
51	477.83	326.6	29/22, 54/41
52	487.2	333	57/43
53	496.57	339.41
54	505.94	345.81
55	515.31	352.22	35/26
56	524.68	358.62	42/31, 65/48
57	534.05	365.02	64/47
58	543.42	371.43	26/19
59	552.78	377.83
60	562.15	384.24	65/47
61	571.52	390.64	32/23
62	580.89	397.04
63	590.26	403.45	45/32, 52/37
64	599.63	409.85	41/29, 58/41, 65/46
65	609	416.26	27/19, 64/45
66	618.37	422.66
67	627.74	429.06	23/16
68	637.11	435.47	13/9
69	646.48	441.87
70	655.85	448.28
71	665.22	454.68	47/32, 69/47
72	674.59	461.08	31/21, 65/44
73	683.95	467.49
74	693.32	473.89
75	702.69	480.3	3/2
76	712.06	486.7
77	721.43	493.1	44/29
78	730.8	499.51
79	740.17	505.91	23/15
80	749.54	512.32	37/24
81	758.91	518.72
82	768.28	525.12
83	777.65	531.53	47/30, 58/37
84	787.02	537.93	52/33
85	796.39	544.33	19/12
86	805.75	550.74	43/27
87	815.12	557.14
88	824.49	563.55	66/41
89	833.86	569.95	34/21
90	843.23	576.35	70/43
91	852.6	582.76	18/11
92	861.97	589.16	51/31
93	871.34	595.57	43/26, 48/29
94	880.71	601.97
95	890.08	608.37
96	899.45	614.78	37/22
97	908.82	621.18
98	918.19	627.59
99	927.55	633.99	41/24
100	936.92	640.39	55/32
101	946.29	646.8	19/11
102	955.66	653.2	33/19
103	965.03	659.61
104	974.4	666.01
105	983.77	672.41
106	993.14	678.82
107	1002.51	685.22	66/37
108	1011.88	691.63	52/29, 70/39
109	1021.25	698.03
110	1030.62	704.43	29/16
111	1039.99	710.84	31/17
112	1049.35	717.24	11/6
113	1058.72	723.65
114	1068.09	730.05	63/34
115	1077.46	736.45	41/22
116	1086.83	742.86
117	1096.2	749.26
118	1105.57	755.67	36/19
119	1114.94	762.07
120	1124.31	768.47
121	1133.68	774.88	52/27
122	1143.05	781.28
123	1152.42	787.68
124	1161.79	794.09	45/23
125	1171.15	800.49
126	1180.52	806.9
127	1189.89	813.3
128	1199.26	819.7	2/1
129	1208.63	826.11
130	1218	832.51
131	1227.37	838.92	63/31, 65/32
132	1236.74	845.32	47/23
133	1246.11	851.72
134	1255.48	858.13
135	1264.85	864.53	27/13
136	1274.22	870.94	48/23
137	1283.59	877.34
138	1292.95	883.74	19/9
139	1302.32	890.15	70/33
140	1311.69	896.55	32/15
141	1321.06	902.96
142	1330.43	909.36	69/32
143	1339.8	915.76
144	1349.17	922.17
145	1358.54	928.57	57/26
146	1367.91	934.98
147	1377.28	941.38	31/14
148	1386.65	947.78
149	1396.02	954.19
150	1405.39	960.59
151	1414.75	967	43/19
152	1424.12	973.4	41/18, 66/29
153	1433.49	979.8
154	1442.86	986.21	23/10
155	1452.23	992.61	37/16
156	1461.6	999.01
157	1470.97	1005.42
158	1480.34	1011.82
159	1489.71	1018.23	26/11
160	1499.08	1024.63
161	1508.45	1031.03	43/18, 55/23
162	1517.82	1037.44
163	1527.19	1043.84	29/12
164	1536.55	1050.25	17/7
165	1545.92	1056.65
166	1555.29	1063.05	27/11
167	1564.66	1069.46
168	1574.03	1075.86
169	1583.4	1082.27
170	1592.77	1088.67
171	1602.14	1095.07	58/23
172	1611.51	1101.48
173	1620.88	1107.88
174	1630.25	1114.29
175	1639.62	1120.69
176	1648.99	1127.09	57/22, 70/27
177	1658.35	1133.5
178	1667.72	1139.9
179	1677.09	1146.31
180	1686.46	1152.71
181	1695.83	1159.11
182	1705.2	1165.52
183	1714.57	1171.92	35/13
184	1723.94	1178.33	65/24
185	1733.31	1184.73
186	1742.68	1191.13	52/19
187	1752.05	1197.54	11/4
188	1761.42	1203.94
189	1770.79	1210.34	64/23
190	1780.15	1216.75
191	1789.52	1223.15	45/16
192	1798.89	1229.56	65/23
193	1808.26	1235.96	54/19
194	1817.63	1242.36
195	1827	1248.77
196	1836.37	1255.17	26/9
197	1845.74	1261.58
198	1855.11	1267.98
199	1864.48	1274.38	47/16
200	1873.85	1280.79	62/21
201	1883.22	1287.19
202	1892.59	1293.6
203	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 203edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.74	+0.00	-1.48	-3.65	-0.74	+4.10	-2.21	+0.00	-4.39	-0.75	-1.48
	Relative (%)	-7.9	+0.0	-15.7	-39.0	-7.9	+43.8	-23.6	+0.0	-46.8	-8.0	-15.7
Steps (reduced)		128 (128)	203 (0)	256 (53)	297 (94)	331 (128)	360 (157)	384 (181)	406 (0)	425 (19)	443 (37)	459 (53)

Approximation of harmonics in 203edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.49	+3.36	-3.65	-2.95	+4.52	-0.74	-0.65	+4.24	+4.10	-1.48	-3.49
	Relative (%)	+5.2	+35.9	-39.0	-31.5	+48.3	-7.9	-6.9	+45.3	+43.8	-15.8	-37.2
Steps (reduced)		474 (68)	488 (82)	500 (94)	512 (106)	524 (118)	534 (128)	544 (138)	554 (148)	563 (157)	571 (165)	579 (173)