197edt

197 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 197edt or 197ed3), is a nonoctave tuning system that divides the interval of 3/1 into 197 equal parts of about 9.65 ¢ each. Each step represents a frequency ratio of 3^1/197, or the 197th root of 3.

← 196edt

197edt

198edt →

Prime factorization	197 (prime)
Step size	9.65459 ¢
Octave	124\197edt (1197.17 ¢)
Consistency limit	3
Distinct consistency limit	3

197edt can be described as approximately 124.293edo. This implies that each step of 197edt can be approximated by 7 steps of 870edo.

It is a very strong no-twos, no-fives 19-limit system.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.65	6.6
2	19.31	13.2
3	28.96	19.8
4	38.62	26.4
5	48.27	32.99	37/36
6	57.93	39.59	30/29
7	67.58	46.19
8	77.24	52.79	23/22
9	86.89	59.39	41/39
10	96.55	65.99
11	106.2	72.59
12	115.86	79.19	31/29, 46/43
13	125.51	85.79	43/40
14	135.16	92.39	40/37
15	144.82	98.98	62/57
16	154.47	105.58	47/43
17	164.13	112.18	11/10
18	173.78	118.78	21/19
19	183.44	125.38	10/9
20	193.09	131.98	19/17
21	202.75	138.58
22	212.4	145.18	26/23
23	222.06	151.78	58/51
24	231.71	158.38
25	241.36	164.97	23/20, 54/47
26	251.02	171.57
27	260.67	178.17	43/37
28	270.33	184.77
29	279.98	191.37	47/40
30	289.64	197.97	13/11
31	299.29	204.57	44/37
32	308.95	211.17	49/41
33	318.6	217.77
34	328.26	224.37	52/43
35	337.91	230.96	62/51
36	347.57	237.56	11/9
37	357.22	244.16
38	366.87	250.76	21/17, 47/38
39	376.53	257.36	41/33, 46/37
40	386.18	263.96
41	395.84	270.56	49/39
42	405.49	277.16	43/34
43	415.15	283.76	47/37
44	424.8	290.36	23/18
45	434.46	296.95	9/7
46	444.11	303.55
47	453.77	310.15	13/10
48	463.42	316.75	17/13
49	473.08	323.35
50	482.73	329.95	37/28
51	492.38	336.55
52	502.04	343.15
53	511.69	349.75
54	521.35	356.35
55	531	362.94
56	540.66	369.54	41/30
57	550.31	376.14
58	559.97	382.74	47/34
59	569.62	389.34	57/41
60	579.28	395.94
61	588.93	402.54	52/37
62	598.58	409.14	41/29
63	608.24	415.74	27/19
64	617.89	422.34	10/7
65	627.55	428.93
66	637.2	435.53	13/9
67	646.86	442.13
68	656.51	448.73	19/13
69	666.17	455.33
70	675.82	461.93	34/23
71	685.48	468.53	49/33
72	695.13	475.13
73	704.79	481.73
74	714.44	488.32
75	724.09	494.92	41/27
76	733.75	501.52
77	743.4	508.12	43/28, 63/41
78	753.06	514.72	17/11
79	762.71	521.32
80	772.37	527.92
81	782.02	534.52	11/7
82	791.68	541.12	30/19, 49/31
83	801.33	547.72	27/17
84	810.99	554.31
85	820.64	560.91
86	830.3	567.51	21/13
87	839.95	574.11
88	849.6	580.71	49/30
89	859.26	587.31	23/14
90	868.91	593.91	38/23
91	878.57	600.51
92	888.22	607.11
93	897.88	613.71
94	907.53	620.3	49/29
95	917.19	626.9
96	926.84	633.5
97	936.5	640.1
98	946.15	646.7	19/11
99	955.8	653.3	33/19
100	965.46	659.9
101	975.11	666.5
102	984.77	673.1
103	994.42	679.7
104	1004.08	686.29
105	1013.73	692.89
106	1023.39	699.49
107	1033.04	706.09	69/38
108	1042.7	712.69	42/23
109	1052.35	719.29
110	1062.01	725.89
111	1071.66	732.49	13/7
112	1081.31	739.09
113	1090.97	745.69	62/33
114	1100.62	752.28	17/9
115	1110.28	758.88	19/10
116	1119.93	765.48	21/11
117	1129.59	772.08
118	1139.24	778.68
119	1148.9	785.28	33/17
120	1158.55	791.88	41/21
121	1168.21	798.48
122	1177.86	805.08
123	1187.52	811.68
124	1197.17	818.27
125	1206.82	824.87
126	1216.48	831.47
127	1226.13	838.07	69/34
128	1235.79	844.67
129	1245.44	851.27	39/19
130	1255.1	857.87
131	1264.75	864.47	27/13
132	1274.41	871.07
133	1284.06	877.66	21/10
134	1293.72	884.26	19/9
135	1303.37	890.86
136	1313.02	897.46
137	1322.68	904.06	58/27
138	1332.33	910.66	41/19
139	1341.99	917.26
140	1351.64	923.86
141	1361.3	930.46
142	1370.95	937.06
143	1380.61	943.65
144	1390.26	950.25
145	1399.92	956.85
146	1409.57	963.45
147	1419.23	970.05
148	1428.88	976.65
149	1438.53	983.25	39/17, 62/27
150	1448.19	989.85	30/13
151	1457.84	996.45
152	1467.5	1003.05	7/3
153	1477.15	1009.64	54/23
154	1486.81	1016.24
155	1496.46	1022.84
156	1506.12	1029.44
157	1515.77	1036.04
158	1525.43	1042.64
159	1535.08	1049.24	17/7
160	1544.74	1055.84
161	1554.39	1062.44	27/11
162	1564.04	1069.04
163	1573.7	1075.63
164	1583.35	1082.23
165	1593.01	1088.83
166	1602.66	1095.43
167	1612.32	1102.03	33/13
168	1621.97	1108.63
169	1631.63	1115.23
170	1641.28	1121.83
171	1650.94	1128.43
172	1660.59	1135.03	47/18, 60/23
173	1670.24	1141.62
174	1679.9	1148.22
175	1689.55	1154.82	69/26
176	1699.21	1161.42
177	1708.86	1168.02	51/19
178	1718.52	1174.62	27/10
179	1728.17	1181.22	19/7
180	1737.83	1187.82	30/11
181	1747.48	1194.42
182	1757.14	1201.02
183	1766.79	1207.61
184	1776.45	1214.21
185	1786.1	1220.81
186	1795.75	1227.41
187	1805.41	1234.01
188	1815.06	1240.61
189	1824.72	1247.21	66/23
190	1834.37	1253.81
191	1844.03	1260.41	29/10
192	1853.68	1267.01
193	1863.34	1273.6
194	1872.99	1280.2
195	1882.65	1286.8
196	1892.3	1293.4
197	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 197edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.83	+0.00	+3.99	+3.86	-2.83	+0.63	+1.16	+0.00	+1.03	+0.16	+3.99
	Relative (%)	-29.3	+0.0	+41.4	+40.0	-29.3	+6.5	+12.1	+0.0	+10.7	+1.6	+41.4
Steps (reduced)		124 (124)	197 (0)	249 (52)	289 (92)	321 (124)	349 (152)	373 (176)	394 (0)	413 (19)	430 (36)	446 (52)

Approximation of harmonics in 197edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.59	-2.20	+3.86	-1.67	-0.42	-2.83	+0.11	-1.80	+0.63	-2.67	-2.39
	Relative (%)	+6.1	-22.8	+40.0	-17.3	-4.4	-29.3	+1.2	-18.6	+6.5	-27.7	-24.8
Steps (reduced)		460 (66)	473 (79)	486 (92)	497 (103)	508 (114)	518 (124)	528 (134)	537 (143)	546 (152)	554 (160)	562 (168)

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