193edt

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193edt

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Prime factorization	193 (prime)
Step size	9.85469 ¢
Octave	122\193edt (1202.27 ¢)
Consistency limit	7
Distinct consistency limit	7

193 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 193edt or 193ed3), is a nonoctave tuning system that divides the interval of 3/1 into 193 equal parts of about 9.85 ¢ each. Each step represents a frequency ratio of 3^1/193, or the 193rd root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.85	6.74
2	19.71	13.47
3	29.56	20.21
4	39.42	26.94	44/43, 45/44
5	49.27	33.68	35/34, 36/35
6	59.13	40.41	30/29
7	68.98	47.15	26/25, 51/49
8	78.84	53.89	45/43, 68/65
9	88.69	60.62
10	98.55	67.36	18/17
11	108.4	74.09	33/31, 49/46
12	118.26	80.83
13	128.11	87.56	14/13
14	137.97	94.3	13/12
15	147.82	101.04	49/45
16	157.68	107.77	23/21
17	167.53	114.51	54/49
18	177.38	121.24	41/37
19	187.24	127.98	39/35, 49/44
20	197.09	134.72	28/25, 37/33, 65/58
21	206.95	141.45	62/55
22	216.8	148.19	17/15
23	226.66	154.92	49/43
24	236.51	161.66	39/34, 47/41
25	246.37	168.39
26	256.22	175.13	29/25, 51/44
27	266.08	181.87	7/6
28	275.93	188.6	34/29
29	285.79	195.34	46/39
30	295.64	202.07	51/43
31	305.5	208.81	37/31
32	315.35	215.54	6/5
33	325.2	222.28	35/29
34	335.06	229.02	17/14, 57/47
35	344.91	235.75
36	354.77	242.49	27/22
37	364.62	249.22
38	374.48	255.96	36/29
39	384.33	262.69
40	394.19	269.43	49/39, 54/43
41	404.04	276.17
42	413.9	282.9	47/37
43	423.75	289.64	23/18
44	433.61	296.37
45	443.46	303.11
46	453.32	309.84	13/10
47	463.17	316.58
48	473.03	323.32	46/35
49	482.88	330.05	41/31
50	492.73	336.79
51	502.59	343.52
52	512.44	350.26	39/29
53	522.3	356.99	23/17
54	532.15	363.73	34/25
55	542.01	370.47
56	551.86	377.2
57	561.72	383.94
58	571.57	390.67
59	581.43	397.41	7/5
60	591.28	404.15	38/27
61	601.14	410.88
62	610.99	417.62
63	620.85	424.35	63/44
64	630.7	431.09	36/25
65	640.55	437.82	42/29, 55/38
66	650.41	444.56
67	660.26	451.3	63/43
68	670.12	458.03
69	679.97	464.77
70	689.83	471.5
71	699.68	478.24
72	709.54	484.97
73	719.39	491.71	47/31
74	729.25	498.45
75	739.1	505.18	23/15
76	748.96	511.92	57/37
77	758.81	518.65
78	768.67	525.39
79	778.52	532.12
80	788.38	538.86
81	798.23	545.6	46/29
82	808.08	552.33
83	817.94	559.07
84	827.79	565.8
85	837.65	572.54
86	847.5	579.27	31/19
87	857.36	586.01
88	867.21	592.75
89	877.07	599.48
90	886.92	606.22
91	896.78	612.95
92	906.63	619.69
93	916.49	626.42
94	926.34	633.16
95	936.2	639.9
96	946.05	646.63	19/11
97	955.9	653.37	33/19
98	965.76	660.1
99	975.61	666.84
100	985.47	673.58
101	995.32	680.31
102	1005.18	687.05
103	1015.03	693.78
104	1024.89	700.52
105	1034.74	707.25
106	1044.6	713.99
107	1054.45	720.73	57/31
108	1064.31	727.46
109	1074.16	734.2
110	1084.02	740.93	43/23
111	1093.87	747.67
112	1103.73	754.4
113	1113.58	761.14
114	1123.43	767.88	44/23
115	1133.29	774.61
116	1143.14	781.35
117	1153	788.08	37/19
118	1162.85	794.82	45/23
119	1172.71	801.55
120	1182.56	808.29
121	1192.42	815.03
122	1202.27	821.76
123	1212.13	828.5
124	1221.98	835.23
125	1231.84	841.97	55/27
126	1241.69	848.7	43/21
127	1251.55	855.44
128	1261.4	862.18	29/14
129	1271.25	868.91	25/12
130	1281.11	875.65	44/21
131	1290.96	882.38
132	1300.82	889.12
133	1310.67	895.85
134	1320.53	902.59	15/7
135	1330.38	909.33
136	1340.24	916.06
137	1350.09	922.8
138	1359.95	929.53
139	1369.8	936.27
140	1379.66	943.01	51/23
141	1389.51	949.74	29/13
142	1399.37	956.48
143	1409.22	963.21
144	1419.08	969.95
145	1428.93	976.68
146	1438.78	983.42	62/27
147	1448.64	990.16	30/13
148	1458.49	996.89	65/28
149	1468.35	1003.63
150	1478.2	1010.36	54/23
151	1488.06	1017.1
152	1497.91	1023.83
153	1507.77	1030.57	43/18
154	1517.62	1037.31
155	1527.48	1044.04	29/12
156	1537.33	1050.78
157	1547.19	1057.51	22/9
158	1557.04	1064.25
159	1566.9	1070.98	42/17, 47/19
160	1576.75	1077.72
161	1586.6	1084.46	5/2
162	1596.46	1091.19
163	1606.31	1097.93	43/17
164	1616.17	1104.66
165	1626.02	1111.4
166	1635.88	1118.13	18/7
167	1645.73	1124.87	44/17
168	1655.59	1131.61
169	1665.44	1138.34	34/13
170	1675.3	1145.08
171	1685.15	1151.81	45/17
172	1695.01	1158.55
173	1704.86	1165.28
174	1714.72	1172.02	35/13
175	1724.57	1178.76	65/24
176	1734.43	1185.49	49/18
177	1744.28	1192.23	63/23
178	1754.13	1198.96
179	1763.99	1205.7	36/13
180	1773.84	1212.44	39/14
181	1783.7	1219.17
182	1793.55	1225.91	31/11
183	1803.41	1232.64	17/6
184	1813.26	1239.38
185	1823.12	1246.11	43/15
186	1832.97	1252.85	49/17
187	1842.83	1259.59	29/10
188	1852.68	1266.32	35/12
189	1862.54	1273.06	44/15
190	1872.39	1279.79
191	1882.25	1286.53
192	1892.1	1293.26
193	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 193edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.27	+0.00	+4.54	+2.56	+2.27	+1.48	-3.04	+0.00	+4.84	-2.49	+4.54
	Relative (%)	+23.1	+0.0	+46.1	+26.0	+23.1	+15.0	-30.8	+0.0	+49.1	-25.3	+46.1
Steps (reduced)		122 (122)	193 (0)	244 (51)	283 (90)	315 (122)	342 (149)	365 (172)	386 (0)	405 (19)	421 (35)	437 (51)

Approximation of harmonics in 193edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.94	+3.75	+2.56	-0.77	+2.68	+2.27	-2.64	-2.75	+1.48	-0.22	+1.66
	Relative (%)	+40.0	+38.1	+26.0	-7.8	+27.2	+23.1	-26.8	-27.9	+15.0	-2.3	+16.8
Steps (reduced)		451 (65)	464 (78)	476 (90)	487 (101)	498 (112)	508 (122)	517 (131)	526 (140)	535 (149)	543 (157)	551 (165)