191edt

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191edt

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Prime factorization	191 (prime)
Step size	9.95788 ¢
Octave	121\191edt (1204.9 ¢)
Consistency limit	3
Distinct consistency limit	3

191 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 191edt or 191ed3), is a nonoctave tuning system that divides the interval of 3/1 into 191 equal parts of about 9.96 ¢ each. Each step represents a frequency ratio of 3^1/191, or the 191st root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.96	6.81
2	19.92	13.61
3	29.87	20.42	58/57
4	39.83	27.23	43/42
5	49.79	34.03
6	59.75	40.84
7	69.71	47.64
8	79.66	54.45	45/43
9	89.62	61.26
10	99.58	68.06	18/17
11	109.54	74.87
12	119.49	81.68	15/14
13	129.45	88.48	14/13
14	139.41	95.29
15	149.37	102.09
16	159.33	108.9
17	169.28	115.71	43/39
18	179.24	122.51	51/46
19	189.2	129.32
20	199.16	136.13	37/33, 46/41
21	209.12	142.93	35/31
22	219.07	149.74	42/37
23	229.03	156.54
24	238.99	163.35	31/27
25	248.95	170.16
26	258.9	176.96
27	268.86	183.77
28	278.82	190.58
29	288.78	197.38	13/11
30	298.74	204.19
31	308.69	210.99	55/46
32	318.65	217.8
33	328.61	224.61
34	338.57	231.41	45/37, 62/51
35	348.53	238.22	11/9
36	358.48	245.03
37	368.44	251.83
38	378.4	258.64	51/41
39	388.36	265.45
40	398.32	272.25	39/31
41	408.27	279.06	19/15
42	418.23	285.86	14/11
43	428.19	292.67
44	438.15	299.48
45	448.1	306.28
46	458.06	313.09	43/33
47	468.02	319.9
48	477.98	326.7
49	487.94	333.51	57/43
50	497.89	340.31
51	507.85	347.12	55/41, 63/47
52	517.81	353.93	31/23, 58/43
53	527.77	360.73	19/14
54	537.73	367.54	15/11
55	547.68	374.35
56	557.64	381.15	29/21
57	567.6	387.96	25/18, 43/31
58	577.56	394.76
59	587.51	401.57
60	597.47	408.38	65/46
61	607.43	415.18	27/19
62	617.39	421.99
63	627.35	428.8
64	637.3	435.6	13/9
65	647.26	442.41
66	657.22	449.21	19/13
67	667.18	456.02	25/17
68	677.14	462.83
69	687.09	469.63	55/37, 58/39
70	697.05	476.44
71	707.01	483.25
72	716.97	490.05	62/41
73	726.93	496.86	35/23
74	736.88	503.66
75	746.84	510.47
76	756.8	517.28	65/42
77	766.76	524.08
78	776.71	530.89
79	786.67	537.7
80	796.63	544.5	65/41
81	806.59	551.31	43/27
82	816.55	558.12
83	826.5	564.92
84	836.46	571.73	47/29
85	846.42	578.53	31/19
86	856.38	585.34	41/25
87	866.34	592.15
88	876.29	598.95
89	886.25	605.76
90	896.21	612.57
91	906.17	619.37
92	916.12	626.18
93	926.08	632.98
94	936.04	639.79
95	946	646.6	19/11
96	955.96	653.4	33/19
97	965.91	660.21
98	975.87	667.02	58/33, 65/37
99	985.83	673.82
100	995.79	680.63
101	1005.75	687.43
102	1015.7	694.24
103	1025.66	701.05
104	1035.62	707.85
105	1045.58	714.66
106	1055.54	721.47	46/25, 57/31
107	1065.49	728.27
108	1075.45	735.08
109	1085.41	741.88	58/31
110	1095.37	748.69
111	1105.32	755.5
112	1115.28	762.3
113	1125.24	769.11
114	1135.2	775.92
115	1145.16	782.72
116	1155.11	789.53
117	1165.07	796.34
118	1175.03	803.14
119	1184.99	809.95
120	1194.95	816.75
121	1204.9	823.56
122	1214.86	830.37
123	1224.82	837.17
124	1234.78	843.98	51/25
125	1244.73	850.79	39/19
126	1254.69	857.59
127	1264.65	864.4	27/13
128	1274.61	871.2
129	1284.57	878.01
130	1294.52	884.82	19/9
131	1304.48	891.62
132	1314.44	898.43
133	1324.4	905.24	58/27
134	1334.36	912.04	54/25
135	1344.31	918.85	63/29
136	1354.27	925.65
137	1364.23	932.46	11/5
138	1374.19	939.27	42/19
139	1384.15	946.07
140	1394.1	952.88	47/21
141	1404.06	959.69
142	1414.02	966.49	43/19
143	1423.98	973.3
144	1433.93	980.1
145	1443.89	986.91
146	1453.85	993.72
147	1463.81	1000.52
148	1473.77	1007.33
149	1483.72	1014.14	33/14
150	1493.68	1020.94	45/19
151	1503.64	1027.75	31/13
152	1513.6	1034.55
153	1523.56	1041.36	41/17
154	1533.51	1048.17
155	1543.47	1054.97
156	1553.43	1061.78	27/11
157	1563.39	1068.59	37/15
158	1573.34	1075.39	62/25
159	1583.3	1082.2
160	1593.26	1089.01
161	1603.22	1095.81
162	1613.18	1102.62	33/13
163	1623.13	1109.42
164	1633.09	1116.23
165	1643.05	1123.04
166	1653.01	1129.84
167	1662.97	1136.65
168	1672.92	1143.46
169	1682.88	1150.26	37/14
170	1692.84	1157.07
171	1702.8	1163.87
172	1712.76	1170.68
173	1722.71	1177.49	46/17
174	1732.67	1184.29
175	1742.63	1191.1
176	1752.59	1197.91
177	1762.54	1204.71
178	1772.5	1211.52	39/14
179	1782.46	1218.32	14/5
180	1792.42	1225.13
181	1802.38	1231.94	17/6
182	1812.33	1238.74
183	1822.29	1245.55	43/15
184	1832.25	1252.36
185	1842.21	1259.16
186	1852.17	1265.97
187	1862.12	1272.77
188	1872.08	1279.58
189	1882.04	1286.39
190	1892	1293.19
191	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 191edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.90	+0.00	-0.15	+1.89	+4.90	-3.06	+4.75	+0.00	-3.16	+1.12	-0.15
	Relative (%)	+49.2	+0.0	-1.5	+19.0	+49.2	-30.8	+47.7	+0.0	-31.8	+11.2	-1.5
Steps (reduced)		121 (121)	191 (0)	241 (50)	280 (89)	312 (121)	338 (147)	362 (171)	382 (0)	400 (18)	417 (35)	432 (50)

Approximation of harmonics in 191edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+0.69	+1.84	+1.89	-0.30	+4.28	+4.90	+0.92	+1.74	-3.06	-3.94	-1.23
	Relative (%)	+6.9	+18.5	+19.0	-3.0	+43.0	+49.2	+9.3	+17.5	-30.8	-39.5	-12.4
Steps (reduced)		446 (64)	459 (77)	471 (89)	482 (100)	493 (111)	503 (121)	512 (130)	521 (139)	529 (147)	537 (155)	545 (163)