235edt

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235 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 235edt or 235ed3), is a nonoctave tuning system that divides the interval of 3/1 into 235 equal parts of about 8.09 ¢ each. Each step represents a frequency ratio of 3^1/235, or the 235th root of 3.

← 234edt

235edt

236edt →

Prime factorization	5 × 47
Step size	8.09343 ¢
Octave	148\235edt (1197.83 ¢)
Consistency limit	3
Distinct consistency limit	3

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	8.09	5.53
2	16.19	11.06
3	24.28	16.6
4	32.37	22.13	55/54
5	40.47	27.66
6	48.56	33.19	36/35
7	56.65	38.72
8	64.75	44.26	27/26
9	72.84	49.79
10	80.93	55.32	22/21, 65/62
11	89.03	60.85
12	97.12	66.38	55/52
13	105.21	71.91
14	113.31	77.45
15	121.4	82.98	44/41
16	129.49	88.51
17	137.59	94.04
18	145.68	99.57	37/34, 62/57
19	153.78	105.11	47/43
20	161.87	110.64	45/41
21	169.96	116.17	75/68
22	178.06	121.7	41/37, 51/46
23	186.15	127.23	49/44
24	194.24	132.77
25	202.34	138.3
26	210.43	143.83
27	218.52	149.36	42/37
28	226.62	154.89	65/57
29	234.71	160.43	63/55
30	242.8	165.96
31	250.9	171.49	52/45
32	258.99	177.02
33	267.08	182.55	7/6
34	275.18	188.09	34/29
35	283.27	193.62
36	291.36	199.15	58/49
37	299.46	204.68	44/37
38	307.55	210.21
39	315.64	215.74	6/5
40	323.74	221.28	41/34, 47/39
41	331.83	226.81	63/52
42	339.92	232.34
43	348.02	237.87	11/9
44	356.11	243.4
45	364.2	248.94
46	372.3	254.47
47	380.39	260
48	388.48	265.53
49	396.58	271.06	39/31, 44/35
50	404.67	276.6
51	412.76	282.13	33/26
52	420.86	287.66	37/29
53	428.95	293.19
54	437.04	298.72
55	445.14	304.26	75/58
56	453.23	309.79
57	461.33	315.32
58	469.42	320.85
59	477.51	326.38	29/22, 54/41
60	485.61	331.91	45/34, 49/37
61	493.7	337.45
62	501.79	342.98
63	509.89	348.51	51/38
64	517.98	354.04
65	526.07	359.57
66	534.17	365.11	49/36
67	542.26	370.64	26/19
68	550.35	376.17
69	558.45	381.7	29/21
70	566.54	387.23	43/31, 68/49
71	574.63	392.77	46/33
72	582.73	398.3	7/5
73	590.82	403.83	38/27
74	598.91	409.36	41/29, 65/46
75	607.01	414.89
76	615.1	420.43	77/54
77	623.19	425.96
78	631.29	431.49	36/25
79	639.38	437.02	55/38
80	647.47	442.55
81	655.57	448.09
82	663.66	453.62	22/15
83	671.75	459.15
84	679.85	464.68	77/52
85	687.94	470.21
86	696.03	475.74
87	704.13	481.28
88	712.22	486.81
89	720.31	492.34	47/31
90	728.41	497.87
91	736.5	503.4	75/49
92	744.6	508.94
93	752.69	514.47
94	760.78	520	45/29
95	768.88	525.53
96	776.97	531.06
97	785.06	536.6
98	793.16	542.13
99	801.25	547.66	27/17
100	809.34	553.19
101	817.44	558.72
102	825.53	564.26	29/18
103	833.62	569.79	34/21
104	841.72	575.32
105	849.81	580.85	49/30
106	857.9	586.38
107	866	591.91
108	874.09	597.45	58/35
109	882.18	602.98
110	890.28	608.51
111	898.37	614.04	42/25
112	906.46	619.57	76/45
113	914.56	625.11	39/23
114	922.65	630.64	46/27, 75/44
115	930.74	636.17	77/45
116	938.84	641.7
117	946.93	647.23	19/11
118	955.02	652.77	33/19
119	963.12	658.3
120	971.21	663.83
121	979.3	669.36	44/25
122	987.4	674.89	23/13
123	995.49	680.43
124	1003.58	685.96	25/14
125	1011.68	691.49	52/29
126	1019.77	697.02
127	1027.87	702.55
128	1035.96	708.09
129	1044.05	713.62
130	1052.15	719.15
131	1060.24	724.68
132	1068.33	730.21	63/34, 76/41
133	1076.43	735.74	54/29
134	1084.52	741.28
135	1092.61	746.81	62/33
136	1100.71	752.34	17/9
137	1108.8	757.87	55/29
138	1116.89	763.4
139	1124.99	768.94
140	1133.08	774.47
141	1141.17	780	29/15
142	1149.27	785.53	68/35
143	1157.36	791.06
144	1165.45	796.6	49/25
145	1173.55	802.13	65/33
146	1181.64	807.66
147	1189.73	813.19
148	1197.83	818.72
149	1205.92	824.26
150	1214.01	829.79
151	1222.11	835.32	77/38
152	1230.2	840.85
153	1238.29	846.38	45/22
154	1246.39	851.91	76/37
155	1254.48	857.45
156	1262.57	862.98
157	1270.67	868.51	25/12
158	1278.76	874.04
159	1286.85	879.57
160	1294.95	885.11
161	1303.04	890.64
162	1311.13	896.17
163	1319.23	901.7	15/7
164	1327.32	907.23
165	1335.42	912.77
166	1343.51	918.3	63/29
167	1351.6	923.83
168	1359.7	929.36	57/26
169	1367.79	934.89
170	1375.88	940.43
171	1383.98	945.96
172	1392.07	951.49	38/17
173	1400.16	957.02
174	1408.26	962.55
175	1416.35	968.09	34/15
176	1424.44	973.62	41/18, 66/29
177	1432.54	979.15
178	1440.63	984.68
179	1448.72	990.21
180	1456.82	995.74	58/25
181	1464.91	1001.28
182	1473	1006.81
183	1481.1	1012.34
184	1489.19	1017.87	26/11
185	1497.28	1023.4
186	1505.38	1028.94	31/13
187	1513.47	1034.47
188	1521.56	1040	65/27
189	1529.66	1045.53
190	1537.75	1051.06
191	1545.84	1056.6
192	1553.94	1062.13	27/11
193	1562.03	1067.66
194	1570.12	1073.19	52/21
195	1578.22	1078.72
196	1586.31	1084.26	5/2
197	1594.4	1089.79
198	1602.5	1095.32
199	1610.59	1100.85
200	1618.69	1106.38
201	1626.78	1111.91
202	1634.87	1117.45	18/7
203	1642.97	1122.98
204	1651.06	1128.51
205	1659.15	1134.04
206	1667.25	1139.57	55/21, 76/29
207	1675.34	1145.11
208	1683.43	1150.64	37/14
209	1691.53	1156.17
210	1699.62	1161.7
211	1707.71	1167.23
212	1715.81	1172.77
213	1723.9	1178.3	46/17
214	1731.99	1183.83	68/25
215	1740.09	1189.36	41/15
216	1748.18	1194.89
217	1756.27	1200.43
218	1764.37	1205.96
219	1772.46	1211.49
220	1780.55	1217.02
221	1788.65	1222.55
222	1796.74	1228.09
223	1804.83	1233.62
224	1812.93	1239.15
225	1821.02	1244.68	63/22
226	1829.11	1250.21
227	1837.21	1255.74	26/9
228	1845.3	1261.28
229	1853.39	1266.81	35/12
230	1861.49	1272.34
231	1869.58	1277.87
232	1877.67	1283.4
233	1885.77	1288.94
234	1893.86	1294.47
235	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 235edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.17	+0.00	+3.75	-2.18	-2.17	-1.96	+1.57	+0.00	+3.75	+0.61	+3.75
	Relative (%)	-26.8	+0.0	+46.3	-26.9	-26.8	-24.2	+19.5	+0.0	+46.3	+7.5	+46.3
Steps (reduced)		148 (148)	235 (0)	297 (62)	344 (109)	383 (148)	416 (181)	445 (210)	470 (0)	493 (23)	513 (43)	532 (62)

Approximation of harmonics in 235edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.76	+3.96	-2.18	-0.60	-0.34	-2.17	+1.35	+1.57	-1.96	-1.56	+2.41
	Relative (%)	+34.1	+48.9	-26.9	-7.4	-4.2	-26.8	+16.6	+19.4	-24.2	-19.3	+29.8
Steps (reduced)		549 (79)	565 (95)	579 (109)	593 (123)	606 (136)	618 (148)	630 (160)	641 (171)	651 (181)	661 (191)	671 (201)

Harmonics

Approximation of harmonics in 235edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.17	+0.00	+3.75	-2.18	-2.17	-1.96	+1.57	+0.00	+3.75	+0.61	+3.75
	Relative (%)	-26.8	+0.0	+46.3	-26.9	-26.8	-24.2	+19.5	+0.0	+46.3	+7.5	+46.3
Steps (reduced)		148 (148)	235 (0)	297 (62)	344 (109)	383 (148)	416 (181)	445 (210)	470 (0)	493 (23)	513 (43)	532 (62)

Approximation of harmonics in 235edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.76	+3.96	-2.18	-0.60	-0.34	-2.17	+1.35	+1.57	-1.96	-1.56	+2.41
	Relative (%)	+34.1	+48.9	-26.9	-7.4	-4.2	-26.8	+16.6	+19.4	-24.2	-19.3	+29.8
Steps (reduced)		549 (79)	565 (95)	579 (109)	593 (123)	606 (136)	618 (148)	630 (160)	641 (171)	651 (181)	661 (191)	671 (201)