293edt

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293edt

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Prime factorization	293 (prime)
Step size	6.49131 ¢
Octave	185\293edt (1200.89 ¢)
Consistency limit	4
Distinct consistency limit	4

293 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 293edt or 293ed3), is a nonoctave tuning system that divides the interval of 3/1 into 293 equal parts of about 6.49 ¢ each. Each step represents a frequency ratio of 3^1/293, or the 293rd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	6.49	4.44
2	12.98	8.87
3	19.47	13.31	87/86, 91/90, 92/91
4	25.97	17.75
5	32.46	22.18	55/54
6	38.95	26.62
7	45.44	31.06	39/38
8	51.93	35.49	34/33
9	58.42	39.93	30/29
10	64.91	44.37	27/26
11	71.4	48.81
12	77.9	53.24	91/87
13	84.39	57.68	21/20
14	90.88	62.12	39/37
15	97.37	66.55	55/52, 91/86, 92/87
16	103.86	70.99	69/65, 86/81
17	110.35	75.43	81/76
18	116.84	79.86	46/43, 77/72
19	123.33	84.3	29/27
20	129.83	88.74
21	136.32	93.17	92/85
22	142.81	97.61	38/35, 63/58
23	149.3	102.05	85/78
24	155.79	106.48	81/74, 93/85
25	162.28	110.92	56/51
26	168.77	115.36	43/39, 54/49
27	175.27	119.8	52/47
28	181.76	124.23	10/9
29	188.25	128.67
30	194.74	133.11	47/42
31	201.23	137.54	91/81
32	207.72	141.98	62/55
33	214.21	146.42	43/38
34	220.7	150.85	92/81
35	227.2	155.29	57/50, 65/57
36	233.69	159.73	87/76
37	240.18	164.16	54/47, 85/74
38	246.67	168.6
39	253.16	173.04	81/70
40	259.65	177.47	43/37
41	266.14	181.91
42	272.64	186.35	55/47
43	279.13	190.78	47/40, 74/63
44	285.62	195.22	46/39
45	292.11	199.66	45/38, 58/49
46	298.6	204.1	82/69
47	305.09	208.53	31/26
48	311.58	212.97	91/76
49	318.07	217.41
50	324.57	221.84	76/63
51	331.06	226.28	23/19
52	337.55	230.72	62/51
53	344.04	235.15	50/41
54	350.53	239.59	60/49
55	357.02	244.03	43/35
56	363.51	248.46	37/30, 58/47
57	370	252.9	26/21
58	376.5	257.34	46/37, 87/70
59	382.99	261.77
60	389.48	266.21
61	395.97	270.65	93/74
62	402.46	275.09	82/65
63	408.95	279.52	19/15
64	415.44	283.96
65	421.94	288.4	37/29
66	428.43	292.83
67	434.92	297.27	9/7
68	441.41	301.71	40/31
69	447.9	306.14
70	454.39	310.58	13/10
71	460.88	315.02
72	467.37	319.45	38/29, 55/42
73	473.87	323.89
74	480.36	328.33
75	486.85	332.76	49/37
76	493.34	337.2
77	499.83	341.64
78	506.32	346.08
79	512.81	350.51	39/29
80	519.31	354.95	27/20
81	525.8	359.39	42/31
82	532.29	363.82
83	538.78	368.26	86/63
84	545.27	372.7	37/27
85	551.76	377.13	11/8
86	558.25	381.57	29/21, 69/50
87	564.74	386.01
88	571.24	390.44
89	577.73	394.88	81/58
90	584.22	399.32
91	590.71	403.75
92	597.2	408.19	24/17
93	603.69	412.63	17/12
94	610.18	417.06	37/26
95	616.67	421.5
96	623.17	425.94	43/30
97	629.66	430.38	82/57
98	636.15	434.81	13/9
99	642.64	439.25	29/20
100	649.13	443.69	16/11
101	655.62	448.12	92/63
102	662.11	452.56	85/58
103	668.61	457
104	675.1	461.43
105	681.59	465.87	43/29
106	688.08	470.31
107	694.57	474.74
108	701.06	479.18
109	707.55	483.62
110	714.04	488.05	74/49
111	720.54	492.49	47/31, 91/60
112	727.03	496.93	35/23
113	733.52	501.37	55/36, 84/55
114	740.01	505.8	23/15
115	746.5	510.24
116	752.99	514.68	17/11
117	759.48	519.11	76/49
118	765.98	523.55
119	772.47	527.99
120	778.96	532.42	80/51
121	785.45	536.86	74/47, 85/54
122	791.94	541.3	49/31
123	798.43	545.73	46/29, 65/41
124	804.92	550.17	78/49
125	811.41	554.61
126	817.91	559.04	77/48, 93/58
127	824.4	563.48
128	830.89	567.92	21/13
129	837.38	572.35	60/37
130	843.87	576.79	57/35, 70/43
131	850.36	581.23	85/52
132	856.85	585.67	41/25
133	863.34	590.1	28/17
134	869.84	594.54	38/23, 81/49
135	876.33	598.98	78/47
136	882.82	603.41
137	889.31	607.85
138	895.8	612.29	52/31
139	902.29	616.72
140	908.78	621.16	93/55
141	915.28	625.6	56/33
142	921.77	630.03	46/27, 63/37
143	928.26	634.47
144	934.75	638.91
145	941.24	643.34	31/18
146	947.73	647.78
147	954.22	652.22	85/49
148	960.71	656.66	54/31
149	967.21	661.09
150	973.7	665.53	86/49
151	980.19	669.97	37/21, 81/46
152	986.68	674.4	76/43
153	993.17	678.84	55/31
154	999.66	683.28
155	1006.15	687.71	93/52
156	1012.64	692.15	70/39
157	1019.14	696.59
158	1025.63	701.02	47/26, 85/47
159	1032.12	705.46	49/27, 69/38
160	1038.61	709.9	51/28, 82/45
161	1045.1	714.33	75/41
162	1051.59	718.77
163	1058.08	723.21	35/19
164	1064.58	727.65	37/20
165	1071.07	732.08	13/7
166	1077.56	736.52
167	1084.05	740.96	58/31
168	1090.54	745.39	92/49
169	1097.03	749.83	49/26
170	1103.52	754.27	70/37, 87/46
171	1110.01	758.7	93/49
172	1116.51	763.14
173	1123	767.58
174	1129.49	772.01
175	1135.98	776.45
176	1142.47	780.89
177	1148.96	785.32	33/17
178	1155.45	789.76	76/39
179	1161.95	794.2	45/23
180	1168.44	798.63	55/28
181	1174.93	803.07	69/35
182	1181.42	807.51	91/46, 93/47
183	1187.91	811.95
184	1194.4	816.38
185	1200.89	820.82
186	1207.38	825.26
187	1213.88	829.69
188	1220.37	834.13	85/42, 87/43
189	1226.86	838.57
190	1233.35	843
191	1239.84	847.44
192	1246.33	851.88	76/37
193	1252.82	856.31	33/16
194	1259.31	860.75	60/29
195	1265.81	865.19	27/13
196	1272.3	869.62
197	1278.79	874.06	90/43
198	1285.28	878.5
199	1291.77	882.94	78/37
200	1298.26	887.37	36/17, 91/43
201	1304.75	891.81	17/8
202	1311.25	896.25
203	1317.74	900.68
204	1324.23	905.12	58/27
205	1330.72	909.56
206	1337.21	913.99
207	1343.7	918.43	50/23, 63/29
208	1350.19	922.87	24/11
209	1356.68	927.3	81/37
210	1363.18	931.74
211	1369.67	936.18	86/39
212	1376.16	940.61	31/14
213	1382.65	945.05	20/9
214	1389.14	949.49	29/13
215	1395.63	953.92
216	1402.12	958.36
217	1408.62	962.8
218	1415.11	967.24	77/34
219	1421.6	971.67
220	1428.09	976.11
221	1434.58	980.55	87/38
222	1441.07	984.98
223	1447.56	989.42	30/13
224	1454.05	993.86
225	1460.55	998.29	86/37, 93/40
226	1467.04	1002.73	7/3
227	1473.53	1007.17	82/35
228	1480.02	1011.6	87/37
229	1486.51	1016.04
230	1493	1020.48	45/19
231	1499.49	1024.91
232	1505.98	1029.35	74/31
233	1512.48	1033.79	91/38
234	1518.97	1038.23
235	1525.46	1042.66	70/29
236	1531.95	1047.1	63/26
237	1538.44	1051.54	90/37
238	1544.93	1055.97
239	1551.42	1060.41	49/20
240	1557.92	1064.85	91/37
241	1564.41	1069.28
242	1570.9	1073.72	57/23
243	1577.39	1078.16	92/37
244	1583.88	1082.59
245	1590.37	1087.03
246	1596.86	1091.47	78/31
247	1603.35	1095.9
248	1609.85	1100.34	38/15
249	1616.34	1104.78
250	1622.83	1109.22
251	1629.32	1113.65
252	1635.81	1118.09
253	1642.3	1122.53
254	1648.79	1126.96	70/27
255	1655.29	1131.4
256	1661.78	1135.84	47/18
257	1668.27	1140.27	76/29
258	1674.76	1144.71	50/19
259	1681.25	1149.15
260	1687.74	1153.58
261	1694.23	1158.02
262	1700.72	1162.46
263	1707.22	1166.89
264	1713.71	1171.33
265	1720.2	1175.77	27/10
266	1726.69	1180.2
267	1733.18	1184.64	49/18
268	1739.67	1189.08
269	1746.16	1193.52	74/27, 85/31
270	1752.65	1197.95
271	1759.15	1202.39	58/21
272	1765.64	1206.83
273	1772.13	1211.26
274	1778.62	1215.7	81/29
275	1785.11	1220.14
276	1791.6	1224.57	76/27
277	1798.09	1229.01	65/23
278	1804.59	1233.45
279	1811.08	1237.88	37/13
280	1817.57	1242.32	20/7
281	1824.06	1246.76
282	1830.55	1251.19
283	1837.04	1255.63	26/9
284	1843.53	1260.07	29/10
285	1850.02	1264.51
286	1856.52	1268.94	38/13
287	1863.01	1273.38
288	1869.5	1277.82
289	1875.99	1282.25
290	1882.48	1286.69	86/29
291	1888.97	1291.13
292	1895.46	1295.56
293	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 293edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.89	+0.00	+1.79	-1.54	+0.89	+0.17	+2.68	+0.00	-0.65	+3.12	+1.79
	Relative (%)	+13.8	+0.0	+27.5	-23.7	+13.8	+2.6	+41.3	+0.0	-10.0	+48.1	+27.5
Steps (reduced)		185 (185)	293 (0)	370 (77)	429 (136)	478 (185)	519 (226)	555 (262)	586 (0)	614 (28)	640 (54)	663 (77)

Approximation of harmonics in 293edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-0.47	+1.06	-1.54	-2.92	+2.48	+0.89	-1.83	+0.25	+0.17	-2.48	-1.54
	Relative (%)	-7.2	+16.3	-23.7	-45.0	+38.2	+13.8	-28.2	+3.8	+2.6	-38.1	-23.7
Steps (reduced)		684 (98)	704 (118)	722 (136)	739 (153)	756 (170)	771 (185)	785 (199)	799 (213)	812 (226)	824 (238)	836 (250)