195edt

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195edt

196edt →

Prime factorization	3 × 5 × 13
Step size	9.75362 ¢
Octave	123\195edt (1199.69 ¢) (→ 41\65edt)
Consistency limit	6
Distinct consistency limit	6

195 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 195edt or 195ed3), is a nonoctave tuning system that divides the interval of 3/1 into 195 equal parts of about 9.75 ¢ each. Each step represents a frequency ratio of 3^1/195, or the 195th root of 3.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	9.75	6.67
2	19.51	13.33
3	29.26	20	58/57
4	39.01	26.67	44/43, 45/44, 46/45
5	48.77	33.33	36/35
6	58.52	40	30/29
7	68.28	46.67
8	78.03	53.33	23/22, 45/43, 68/65
9	87.78	60	20/19
10	97.54	66.67
11	107.29	73.33	33/31
12	117.04	80	46/43
13	126.8	86.67
14	136.55	93.33
15	146.3	100	37/34, 62/57
16	156.06	106.67	35/32
17	165.81	113.33	11/10
18	175.57	120	52/47
19	185.32	126.67
20	195.07	133.33	47/42
21	204.83	140	9/8
22	214.58	146.67	43/38
23	224.33	153.33	33/29, 41/36
24	234.09	160
25	243.84	166.67	38/33
26	253.59	173.33	22/19
27	263.35	180
28	273.1	186.67	41/35, 48/41
29	282.85	193.33
30	292.61	200	45/38
31	302.36	206.67	56/47
32	312.12	213.33
33	321.87	220	65/54
34	331.62	226.67	23/19, 63/52
35	341.38	233.33	39/32
36	351.13	240
37	360.88	246.67
38	370.64	253.33	26/21, 57/46
39	380.39	260
40	390.14	266.67
41	399.9	273.33	34/27
42	409.65	280	19/15
43	419.41	286.67	65/51
44	429.16	293.33	41/32
45	438.91	300	58/45
46	448.67	306.67	35/27, 57/44
47	458.42	313.33	43/33
48	468.17	320	38/29
49	477.93	326.67	29/22, 54/41
50	487.68	333.33	57/43
51	497.43	340	4/3
52	507.19	346.67	63/47
53	516.94	353.33	31/23, 58/43
54	526.7	360
55	536.45	366.67	15/11
56	546.2	373.33	37/27, 48/35
57	555.96	380	40/29, 51/37
58	565.71	386.67	43/31
59	575.46	393.33	46/33
60	585.22	400
61	594.97	406.67
62	604.72	413.33
63	614.48	420
64	624.23	426.67	33/23, 43/30
65	633.99	433.33	62/43
66	643.74	440	29/20
67	653.49	446.67	35/24, 54/37
68	663.25	453.33	22/15
69	673	460
70	682.75	466.67	43/29, 46/31
71	692.51	473.33
72	702.26	480	3/2
73	712.01	486.67
74	721.77	493.33	44/29
75	731.52	500	29/19
76	741.27	506.67	66/43
77	751.03	513.33	54/35
78	760.78	520	45/29
79	770.54	526.67	64/41
80	780.29	533.33
81	790.04	540	30/19
82	799.8	546.67	27/17, 46/29
83	809.55	553.33
84	819.3	560
85	829.06	566.67
86	838.81	573.33
87	848.56	580	31/19
88	858.32	586.67	64/39
89	868.07	593.33	33/20
90	877.83	600
91	887.58	606.67
92	897.33	613.33	47/28
93	907.09	620
94	916.84	626.67
95	926.59	633.33	41/24
96	936.35	640
97	946.1	646.67	19/11
98	955.85	653.33	33/19
99	965.61	660
100	975.36	666.67	58/33, 65/37
101	985.12	673.33
102	994.87	680
103	1004.62	686.67
104	1014.38	693.33
105	1024.13	700	47/26
106	1033.88	706.67	20/11
107	1043.64	713.33
108	1053.39	720	57/31, 68/37
109	1063.14	726.67
110	1072.9	733.33
111	1082.65	740	43/23
112	1092.4	746.67	62/33
113	1102.16	753.33	17/9
114	1111.91	760	19/10
115	1121.67	766.67	65/34
116	1131.42	773.33
117	1141.17	780	29/15
118	1150.93	786.67	35/18, 68/35
119	1160.68	793.33	43/22
120	1170.43	800	57/29
121	1180.19	806.67
122	1189.94	813.33
123	1199.69	820	2/1
124	1209.45	826.67
125	1219.2	833.33
126	1228.96	840
127	1238.71	846.67	45/22
128	1248.46	853.33	37/18
129	1258.22	860	60/29
130	1267.97	866.67
131	1277.72	873.33	23/11
132	1287.48	880
133	1297.23	886.67
134	1306.98	893.33
135	1316.74	900
136	1326.49	906.67
137	1336.25	913.33
138	1346	920	37/17
139	1355.75	926.67	35/16
140	1365.51	933.33	11/5
141	1375.26	940
142	1385.01	946.67
143	1394.77	953.33	47/21
144	1404.52	960	9/4
145	1414.27	966.67	43/19
146	1424.03	973.33	41/18, 66/29
147	1433.78	980
148	1443.54	986.67
149	1453.29	993.33	44/19
150	1463.04	1000
151	1472.8	1006.67
152	1482.55	1013.33
153	1492.3	1020	45/19
154	1502.06	1026.67
155	1511.81	1033.33
156	1521.56	1040	65/27
157	1531.32	1046.67	46/19, 63/26
158	1541.07	1053.33
159	1550.82	1060
160	1560.58	1066.67	32/13
161	1570.33	1073.33	52/21, 57/23
162	1580.09	1080
163	1589.84	1086.67
164	1599.59	1093.33	68/27
165	1609.35	1100	38/15
166	1619.1	1106.67
167	1628.85	1113.33	41/16
168	1638.61	1120
169	1648.36	1126.67	57/22
170	1658.11	1133.33
171	1667.87	1140
172	1677.62	1146.67	29/11
173	1687.38	1153.33
174	1697.13	1160	8/3
175	1706.88	1166.67
176	1716.64	1173.33	62/23
177	1726.39	1180
178	1736.14	1186.67	30/11
179	1745.9	1193.33
180	1755.65	1200
181	1765.4	1206.67
182	1775.16	1213.33
183	1784.91	1220
184	1794.67	1226.67	31/11
185	1804.42	1233.33
186	1814.17	1240	57/20
187	1823.93	1246.67	43/15, 66/23
188	1833.68	1253.33
189	1843.43	1260	29/10
190	1853.19	1266.67	35/12
191	1862.94	1273.33	44/15
192	1872.69	1280
193	1882.45	1286.67
194	1892.2	1293.33
195	1901.96	1300	3/1

Harmonics

Approximation of harmonics in 195edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.31	+0.00	-0.61	+3.22	-0.31	-3.83	-0.92	+0.00	+2.91	+3.72	-0.61
	Relative (%)	-3.1	+0.0	-6.3	+33.0	-3.1	-39.3	-9.4	+0.0	+29.9	+38.2	-6.3
Steps (reduced)		123 (123)	195 (0)	246 (51)	286 (91)	318 (123)	345 (150)	369 (174)	390 (0)	409 (19)	426 (36)	441 (51)

Approximation of harmonics in 195edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-4.13	+3.22	-1.22	+1.11	-0.31	+3.63	+2.61	-3.83	+3.42	+4.49
	Relative (%)	-27.0	-42.4	+33.0	-12.5	+11.4	-3.1	+37.2	+26.8	-39.3	+35.0	+46.0
Steps (reduced)		455 (65)	468 (78)	481 (91)	492 (102)	503 (113)	513 (123)	523 (133)	532 (142)	540 (150)	549 (159)	557 (167)