198edt

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198 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 198edt or 198ed3), is a nonoctave tuning system that divides the interval of 3/1 into 198 equal parts of about 9.61 ¢ each. Each step represents a frequency ratio of 3^1/198, or the 198th root of 3.

← 197edt

198edt

199edt →

Prime factorization	2 × 32 × 11
Step size	9.60583 ¢
Octave	125\198edt (1200.73 ¢)
Consistency limit	12
Distinct consistency limit	12

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.61	6.57
2	19.21	13.13
3	28.82	19.7	63/62
4	38.42	26.26	45/44, 46/45
5	48.03	32.83	36/35, 37/36
6	57.64	39.39	30/29, 31/30
7	67.24	45.96	26/25
8	76.85	52.53	23/22
9	86.45	59.09	41/39
10	96.06	65.66	37/35, 55/52
11	105.66	72.22	17/16
12	115.27	78.79	31/29, 47/44
13	124.88	85.35	43/40
14	134.48	91.92	40/37
15	144.09	98.48	25/23, 63/58
16	153.69	105.05	47/43
17	163.3	111.62
18	172.91	118.18	21/19
19	182.51	124.75	10/9
20	192.12	131.31	19/17
21	201.72	137.88
22	211.33	144.44	26/23
23	220.93	151.01	25/22
24	230.54	157.58	8/7
25	240.15	164.14	31/27, 54/47
26	249.75	170.71	52/45
27	259.36	177.27	36/31, 43/37
28	268.96	183.84
29	278.57	190.4	27/23, 47/40
30	288.18	196.97	13/11
31	297.78	203.54	19/16
32	307.39	210.1	37/31, 43/36
33	316.99	216.67
34	326.6	223.23	29/24, 35/29
35	336.2	229.8	17/14
36	345.81	236.36
37	355.42	242.93	27/22, 43/35
38	365.02	249.49	21/17, 58/47
39	374.63	256.06	36/29
40	384.23	262.63
41	393.84	269.19	54/43, 64/51
42	403.45	275.76	24/19
43	413.05	282.32	33/26, 47/37
44	422.66	288.89	37/29, 60/47
45	432.26	295.45
46	441.87	302.02	40/31
47	451.47	308.59	48/37
48	461.08	315.15	30/23, 47/36
49	470.69	321.72	21/16
50	480.29	328.28	33/25, 62/47
51	489.9	334.85	69/52
52	499.5	341.41
53	509.11	347.98	51/38, 55/41
54	518.72	354.55	27/20, 58/43
55	528.32	361.11	19/14
56	537.93	367.68	15/11
57	547.53	374.24	48/35
58	557.14	380.81	40/29, 69/50
59	566.74	387.37	43/31, 68/49
60	576.35	393.94	60/43
61	585.96	400.51
62	595.56	407.07	55/39
63	605.17	413.64	44/31
64	614.77	420.2
65	624.38	426.77	33/23
66	633.99	433.33	62/43
67	643.59	439.9	29/20
68	653.2	446.46	35/24
69	662.8	453.03	22/15
70	672.41	459.6	28/19
71	682.01	466.16	43/29
72	691.62	472.73
73	701.23	479.29	3/2
74	710.83	485.86
75	720.44	492.42	47/31, 50/33
76	730.04	498.99	32/21
77	739.65	505.56	23/15
78	749.26	512.12	37/24
79	758.86	518.69	31/20
80	768.47	525.25
81	778.07	531.82	47/30, 58/37, 69/44
82	787.68	538.38	41/26, 52/33
83	797.28	544.95	65/41
84	806.89	551.52	51/32
85	816.5	558.08
86	826.1	564.65	29/18
87	835.71	571.21	47/29
88	845.31	577.78	44/27, 57/35
89	854.92	584.34
90	864.53	590.91	28/17
91	874.13	597.47	58/35, 63/38
92	883.74	604.04	5/3
93	893.34	610.61	62/37
94	902.95	617.17	32/19
95	912.55	623.74
96	922.16	630.3	46/27, 63/37
97	931.77	636.87
98	941.37	643.43	31/18
99	950.98	650
100	960.58	656.57	47/27, 54/31
101	970.19	663.13
102	979.8	669.7	37/21, 44/25
103	989.4	676.26	62/35
104	999.01	682.83	57/32
105	1008.61	689.39	43/24
106	1018.22	695.96	9/5
107	1027.82	702.53	38/21
108	1037.43	709.09	51/28
109	1047.04	715.66
110	1056.64	722.22	35/19, 46/25
111	1066.25	728.79	50/27
112	1075.85	735.35	54/29
113	1085.46	741.92	58/31
114	1095.07	748.48	32/17
115	1104.67	755.05
116	1114.28	761.62
117	1123.88	768.18	44/23
118	1133.49	774.75
119	1143.09	781.31	60/31
120	1152.7	787.88
121	1162.31	794.44	45/23
122	1171.91	801.01	63/32
123	1181.52	807.58
124	1191.12	814.14
125	1200.73	820.71	2/1
126	1210.34	827.27
127	1219.94	833.84
128	1229.55	840.4	57/28
129	1239.15	846.97	45/22
130	1248.76	853.54
131	1258.36	860.1	60/29
132	1267.97	866.67	52/25
133	1277.58	873.23	23/11
134	1287.18	879.8
135	1296.79	886.36	55/26
136	1306.39	892.93
137	1316	899.49	62/29
138	1325.61	906.06	43/20
139	1335.21	912.63
140	1344.82	919.19	50/23
141	1354.42	925.76	35/16
142	1364.03	932.32	11/5
143	1373.63	938.89	42/19
144	1383.24	945.45	20/9
145	1392.85	952.02	38/17
146	1402.45	958.59
147	1412.06	965.15	52/23
148	1421.66	971.72	25/11
149	1431.27	978.28	16/7
150	1440.88	984.85	23/10
151	1450.48	991.41	37/16
152	1460.09	997.98
153	1469.69	1004.55
154	1479.3	1011.11	47/20
155	1488.9	1017.68	26/11
156	1498.51	1024.24	19/8
157	1508.12	1030.81	43/18
158	1517.72	1037.37
159	1527.33	1043.94	29/12
160	1536.93	1050.51	17/7
161	1546.54	1057.07	22/9
162	1556.15	1063.64
163	1565.75	1070.2	42/17
164	1575.36	1076.77
165	1584.96	1083.33
166	1594.57	1089.9
167	1604.17	1096.46	48/19
168	1613.78	1103.03	33/13
169	1623.39	1109.6	23/9
170	1632.99	1116.16
171	1642.6	1122.73	31/12
172	1652.2	1129.29
173	1661.81	1135.86	47/18
174	1671.42	1142.42	21/8
175	1681.02	1148.99	66/25
176	1690.63	1155.56	69/26
177	1700.23	1162.12
178	1709.84	1168.69	51/19
179	1719.44	1175.25	27/10
180	1729.05	1181.82	19/7
181	1738.66	1188.38
182	1748.26	1194.95
183	1757.87	1201.52	58/21, 69/25
184	1767.47	1208.08
185	1777.08	1214.65
186	1786.69	1221.21
187	1796.29	1227.78	48/17
188	1805.9	1234.34
189	1815.5	1240.91
190	1825.11	1247.47	66/23
191	1834.71	1254.04
192	1844.32	1260.61	29/10
193	1853.93	1267.17	35/12
194	1863.53	1273.74	44/15
195	1873.14	1280.3	62/21
196	1882.74	1286.87
197	1892.35	1293.43
198	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 198edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.73	+0.00	+1.46	-0.62	+0.73	+2.82	+2.19	+0.00	+0.11	-1.60	+1.46
	Relative (%)	+7.6	+0.0	+15.2	-6.5	+7.6	+29.4	+22.8	+0.0	+1.1	-16.6	+15.2
Steps (reduced)		125 (125)	198 (0)	250 (52)	290 (92)	323 (125)	351 (153)	375 (177)	396 (0)	415 (19)	432 (36)	448 (52)

Approximation of harmonics in 198edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+3.55	-0.62	+2.92	+3.63	+0.73	+3.18	+0.84	+2.82	-0.87	-0.98
	Relative (%)	-27.4	+37.0	-6.5	+30.4	+37.7	+7.6	+33.2	+8.7	+29.4	-9.0	-10.2
Steps (reduced)		462 (66)	476 (80)	488 (92)	500 (104)	511 (115)	521 (125)	531 (135)	540 (144)	549 (153)	557 (161)	565 (169)