199edt

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199edt

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Prime factorization	199 (prime)
Step size	9.55756 ¢
Octave	126\199edt (1204.25 ¢)
Consistency limit	3
Distinct consistency limit	3

199 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 199edt or 199ed3), is a nonoctave tuning system that divides the interval of 3/1 into 199 equal parts of about 9.56 ¢ each. Each step represents a frequency ratio of 3^1/199, or the 199th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.56	6.53
2	19.12	13.07
3	28.67	19.6
4	38.23	26.13	45/44, 46/45
5	47.79	32.66
6	57.35	39.2
7	66.9	45.73	26/25
8	76.46	52.26	23/22
9	86.02	58.79	41/39
10	95.58	65.33	37/35
11	105.13	71.86
12	114.69	78.39	31/29
13	124.25	84.92	29/27
14	133.81	91.46
15	143.36	97.99	38/35
16	152.92	104.52	47/43
17	162.48	111.06
18	172.04	117.59
19	181.59	124.12
20	191.15	130.65
21	200.71	137.19
22	210.27	143.72	35/31
23	219.82	150.25	42/37
24	229.38	156.78
25	238.94	163.32	31/27
26	248.5	169.85	15/13
27	258.05	176.38	65/56
28	267.61	182.91
29	277.17	189.45	27/23
30	286.73	195.98	46/39
31	296.28	202.51	51/43
32	305.84	209.05	37/31
33	315.4	215.58	6/5
34	324.96	222.11	35/29, 41/34
35	334.51	228.64	57/47
36	344.07	235.18
37	353.63	241.71	27/22
38	363.19	248.24
39	372.74	254.77
40	382.3	261.31
41	391.86	267.84	69/55
42	401.42	274.37	29/23
43	410.98	280.9
44	420.53	287.44
45	430.09	293.97
46	439.65	300.5	58/45
47	449.21	307.04	35/27
48	458.76	313.57	43/33
49	468.32	320.1	38/29
50	477.88	326.63	29/22, 54/41
51	487.44	333.17	57/43
52	496.99	339.7
53	506.55	346.23	63/47
54	516.11	352.76	31/23
55	525.67	359.3	42/31
56	535.22	365.83
57	544.78	372.36	37/27
58	554.34	378.89	62/45
59	563.9	385.43	18/13
60	573.45	391.96	39/28
61	583.01	398.49
62	592.57	405.03	38/27
63	602.13	411.56
64	611.68	418.09	47/33
65	621.24	424.62
66	630.8	431.16	36/25
67	640.36	437.69	42/29, 55/38
68	649.91	444.22
69	659.47	450.75	41/28
70	669.03	457.29
71	678.59	463.82
72	688.14	470.35	58/39
73	697.7	476.88
74	707.26	483.42
75	716.82	489.95	62/41
76	726.37	496.48	35/23
77	735.93	503.02
78	745.49	509.55
79	755.05	516.08
80	764.61	522.61	14/9
81	774.16	529.15
82	783.72	535.68
83	793.28	542.21
84	802.84	548.74	35/22, 62/39
85	812.39	555.28
86	821.95	561.81	45/28
87	831.51	568.34
88	841.07	574.87
89	850.62	581.41
90	860.18	587.94	23/14
91	869.74	594.47	38/23
92	879.3	601.01
93	888.85	607.54
94	898.41	614.07
95	907.97	620.6
96	917.53	627.14
97	927.08	633.67
98	936.64	640.2
99	946.2	646.73	19/11
100	955.76	653.27	33/19
101	965.31	659.8
102	974.87	666.33
103	984.43	672.86
104	993.99	679.4
105	1003.54	685.93
106	1013.1	692.46
107	1022.66	698.99	65/36
108	1032.22	705.53	69/38
109	1041.77	712.06	42/23
110	1051.33	718.59
111	1060.89	725.13
112	1070.45	731.66
113	1080	738.19	28/15
114	1089.56	744.72
115	1099.12	751.26	66/35
116	1108.68	757.79	55/29
117	1118.23	764.32
118	1127.79	770.85
119	1137.35	777.39	27/14
120	1146.91	783.92
121	1156.47	790.45
122	1166.02	796.98
123	1175.58	803.52	69/35
124	1185.14	810.05
125	1194.7	816.58
126	1204.25	823.12
127	1213.81	829.65
128	1223.37	836.18
129	1232.93	842.71
130	1242.48	849.25
131	1252.04	855.78
132	1261.6	862.31	29/14
133	1271.16	868.84	25/12
134	1280.71	875.38
135	1290.27	881.91
136	1299.83	888.44
137	1309.39	894.97
138	1318.94	901.51
139	1328.5	908.04	28/13
140	1338.06	914.57	13/6
141	1347.62	921.11
142	1357.17	927.64
143	1366.73	934.17
144	1376.29	940.7	31/14
145	1385.85	947.24	69/31
146	1395.4	953.77	47/21, 56/25
147	1404.96	960.3
148	1414.52	966.83	43/19
149	1424.08	973.37	41/18, 66/29
150	1433.63	979.9
151	1443.19	986.43
152	1452.75	992.96
153	1462.31	999.5
154	1471.86	1006.03
155	1481.42	1012.56
156	1490.98	1019.1
157	1500.54	1025.63	69/29
158	1510.09	1032.16	55/23
159	1519.65	1038.69
160	1529.21	1045.23
161	1538.77	1051.76
162	1548.33	1058.29	22/9
163	1557.88	1064.82
164	1567.44	1071.36	47/19
165	1577	1077.89
166	1586.56	1084.42	5/2
167	1596.11	1090.95
168	1605.67	1097.49	43/17
169	1615.23	1104.02
170	1624.79	1110.55	23/9
171	1634.34	1117.09
172	1643.9	1123.62
173	1653.46	1130.15	13/5
174	1663.02	1136.68
175	1672.57	1143.22
176	1682.13	1149.75	37/14
177	1691.69	1156.28
178	1701.25	1162.81
179	1710.8	1169.35
180	1720.36	1175.88
181	1729.92	1182.41
182	1739.48	1188.94
183	1749.03	1195.48
184	1758.59	1202.01
185	1768.15	1208.54
186	1777.71	1215.08
187	1787.26	1221.61
188	1796.82	1228.14
189	1806.38	1234.67
190	1815.94	1241.21
191	1825.49	1247.74	66/23
192	1835.05	1254.27
193	1844.61	1260.8
194	1854.17	1267.34
195	1863.72	1273.87	44/15
196	1873.28	1280.4
197	1882.84	1286.93
198	1892.4	1293.47
199	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 199edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.25	+0.00	-1.05	+4.49	+4.25	-4.56	+3.20	+0.00	-0.81	-3.34	-1.05
	Relative (%)	+44.5	+0.0	-11.0	+47.0	+44.5	-47.8	+33.5	+0.0	-8.5	-34.9	-11.0
Steps (reduced)		126 (126)	199 (0)	251 (52)	292 (93)	325 (126)	352 (153)	377 (178)	398 (0)	417 (19)	434 (36)	450 (52)

Approximation of harmonics in 199edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.74	-0.31	+4.49	-2.10	-1.93	+4.25	-3.33	+3.44	-4.56	+0.92	+0.42
	Relative (%)	+39.1	-3.3	+47.0	-22.0	-20.1	+44.5	-34.9	+36.0	-47.8	+9.6	+4.4
Steps (reduced)		465 (67)	478 (80)	491 (93)	502 (104)	513 (115)	524 (126)	533 (135)	543 (145)	551 (153)	560 (162)	568 (170)