196edt

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196 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 196edt or 196ed3), is a nonoctave tuning system that divides the interval of 3/1 into 196 equal parts of about 9.7 ¢ each. Each step represents a frequency ratio of 3^1/196, or the 196th root of 3.

← 195edt

196edt

197edt →

Prime factorization	22 × 72
Step size	9.70385 ¢
Octave	124\196edt (1203.28 ¢) (→ 31\49edt)
Consistency limit	3
Distinct consistency limit	3

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.7	6.63
2	19.41	13.27
3	29.11	19.9
4	38.82	26.53	46/45
5	48.52	33.16
6	58.22	39.8	30/29
7	67.93	46.43
8	77.63	53.06	45/43, 68/65
9	87.33	59.69	41/39
10	97.04	66.33	37/35
11	106.74	72.96	50/47
12	116.45	79.59	31/29, 46/43
13	126.15	86.22
14	135.85	92.86
15	145.56	99.49	37/34
16	155.26	106.12
17	164.97	112.76	11/10
18	174.67	119.39
19	184.37	126.02
20	194.08	132.65	47/42
21	203.78	139.29
22	213.48	145.92	43/38
23	223.19	152.55	33/29
24	232.89	159.18
25	242.6	165.82
26	252.3	172.45
27	262	179.08	50/43, 57/49
28	271.71	185.71	55/47
29	281.41	192.35
30	291.12	198.98
31	300.82	205.61	25/21
32	310.52	212.24
33	320.23	218.88	65/54
34	329.93	225.51	23/19
35	339.63	232.14	45/37
36	349.34	238.78
37	359.04	245.41
38	368.75	252.04	47/38
39	378.45	258.67
40	388.15	265.31
41	397.86	271.94	39/31
42	407.56	278.57	43/34
43	417.27	285.2	14/11
44	426.97	291.84	55/43
45	436.67	298.47
46	446.38	305.1
47	456.08	311.73
48	465.78	318.37	55/42
49	475.49	325	25/19
50	485.19	331.63	45/34, 49/37
51	494.9	338.27
52	504.6	344.9
53	514.3	351.53
54	524.01	358.16	23/17
55	533.71	364.8
56	543.42	371.43	63/46
57	553.12	378.06
58	562.82	384.69	18/13
59	572.53	391.33	39/28
60	582.23	397.96	7/5
61	591.93	404.59	38/27, 69/49
62	601.64	411.22	58/41
63	611.34	417.86	47/33
64	621.05	424.49
65	630.75	431.12
66	640.45	437.76	42/29, 55/38, 68/47
67	650.16	444.39
68	659.86	451.02	41/28, 60/41
69	669.57	457.65
70	679.27	464.29	37/25
71	688.97	470.92
72	698.68	477.55
73	708.38	484.18
74	718.09	490.82
75	727.79	497.45	35/23
76	737.49	504.08
77	747.2	510.71	57/37
78	756.9	517.35	65/42
79	766.6	523.98
80	776.31	530.61	47/30
81	786.01	537.24
82	795.72	543.88
83	805.42	550.51	43/27
84	815.12	557.14
85	824.83	563.78	29/18, 66/41
86	834.53	570.41	34/21
87	844.24	577.04	57/35
88	853.94	583.67
89	863.64	590.31
90	873.35	596.94
91	883.05	603.57
92	892.75	610.2
93	902.46	616.84
94	912.16	623.47
95	921.87	630.1	46/27, 63/37
96	931.57	636.73
97	941.27	643.37	31/18
98	950.98	650
99	960.68	656.63	47/27, 54/31
100	970.39	663.27
101	980.09	669.9	37/21
102	989.79	676.53
103	999.5	683.16
104	1009.2	689.8
105	1018.9	696.43
106	1028.61	703.06
107	1038.31	709.69
108	1048.02	716.33
109	1057.72	722.96	35/19
110	1067.42	729.59	50/27, 63/34
111	1077.13	736.22	41/22, 54/29
112	1086.83	742.86
113	1096.54	749.49
114	1106.24	756.12
115	1115.94	762.76
116	1125.65	769.39
117	1135.35	776.02
118	1145.05	782.65
119	1154.76	789.29	37/19
120	1164.46	795.92	49/25
121	1174.17	802.55	65/33, 69/35
122	1183.87	809.18
123	1193.57	815.82
124	1203.28	822.45
125	1212.98	829.08
126	1222.69	835.71
127	1232.39	842.35	55/27
128	1242.09	848.98	41/20
129	1251.8	855.61	68/33
130	1261.5	862.24	29/14
131	1271.2	868.88
132	1280.91	875.51	65/31
133	1290.61	882.14
134	1300.32	888.78
135	1310.02	895.41	49/23
136	1319.72	902.04	15/7
137	1329.43	908.67	28/13
138	1339.13	915.31	13/6
139	1348.84	921.94
140	1358.54	928.57	46/21
141	1368.24	935.2
142	1377.95	941.84	51/23
143	1387.65	948.47
144	1397.35	955.1	65/29
145	1407.06	961.73
146	1416.76	968.37	34/15
147	1426.47	975	57/25
148	1436.17	981.63
149	1445.87	988.27
150	1455.58	994.9
151	1465.28	1001.53
152	1474.99	1008.16	68/29
153	1484.69	1014.8	33/14
154	1494.39	1021.43
155	1504.1	1028.06	31/13
156	1513.8	1034.69
157	1523.5	1041.33
158	1533.21	1047.96
159	1542.91	1054.59
160	1552.62	1061.22
161	1562.32	1067.86	37/15
162	1572.02	1074.49	57/23
163	1581.73	1081.12
164	1591.43	1087.76
165	1601.14	1094.39	63/25
166	1610.84	1101.02
167	1620.54	1107.65
168	1630.25	1114.29
169	1639.95	1120.92	49/19
170	1649.65	1127.55
171	1659.36	1134.18
172	1669.06	1140.82
173	1678.77	1147.45	29/11
174	1688.47	1154.08
175	1698.17	1160.71
176	1707.88	1167.35
177	1717.58	1173.98
178	1727.29	1180.61
179	1736.99	1187.24	30/11
180	1746.69	1193.88
181	1756.4	1200.51
182	1766.1	1207.14
183	1775.8	1213.78
184	1785.51	1220.41
185	1795.21	1227.04
186	1804.92	1233.67
187	1814.62	1240.31
188	1824.32	1246.94	43/15
189	1834.03	1253.57
190	1843.73	1260.2	29/10
191	1853.44	1266.84
192	1863.14	1273.47
193	1872.84	1280.1
194	1882.55	1286.73
195	1892.25	1293.37
196	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 196edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.28	+0.00	-3.15	-1.31	+3.28	-1.59	+0.13	+0.00	+1.97	+1.93	-3.15
	Relative (%)	+33.8	+0.0	-32.4	-13.5	+33.8	-16.4	+1.3	+0.0	+20.3	+19.9	-32.4
Steps (reduced)		124 (124)	196 (0)	247 (51)	287 (91)	320 (124)	347 (151)	371 (175)	392 (0)	411 (19)	428 (36)	443 (51)

Approximation of harmonics in 196edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.84	+1.69	-1.31	+3.41	-4.51	+3.28	-2.99	-4.46	-1.59	-4.50	-3.82
	Relative (%)	+39.5	+17.4	-13.5	+35.1	-46.5	+33.8	-30.8	-45.9	-16.4	-46.3	-39.4
Steps (reduced)		458 (66)	471 (79)	483 (91)	495 (103)	505 (113)	516 (124)	525 (133)	534 (142)	543 (151)	551 (159)	559 (167)