145ed4

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145ed4

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Prime factorization	5 × 29
Step size	16.5517¢
Octave	73\145ed4 (1208.28¢)
Twelfth	115\145ed4 (1903.45¢) (→23\29ed4)
Consistency limit	1
Distinct consistency limit	1

145 equal divisions of the 4th harmonic (abbreviated 145ed4) is a nonoctave tuning system that divides the interval of 4/1 into 145 equal parts of about 16.6 ¢ each. Each step represents a frequency ratio of 4^1/145, or the 145th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	16.552
2	33.103	51/50
3	49.655	35/34
4	66.207	27/26
5	82.759	43/41
6	99.31
7	115.862	31/29
8	132.414
9	148.966
10	165.517	11/10
11	182.069	10/9
12	198.621	37/33
13	215.172	17/15
14	231.724
15	248.276	15/13
16	264.828
17	281.379
18	297.931
19	314.483
20	331.034	23/19
21	347.586	11/9
22	364.138	37/30
23	380.69
24	397.241	39/31
25	413.793	33/26, 47/37
26	430.345	50/39
27	446.897
28	463.448	17/13
29	480
30	496.552
31	513.103	35/26, 39/29
32	529.655
33	546.207	37/27
34	562.759
35	579.31
36	595.862	55/39
37	612.414	37/26, 47/33
38	628.966
39	645.517	45/31
40	662.069
41	678.621
42	695.172
43	711.724
44	728.276	35/23
45	744.828
46	761.379	45/29
47	777.931	47/30
48	794.483
49	811.034
50	827.586	50/31
51	844.138
52	860.69	51/31
53	877.241
54	893.793
55	910.345
56	926.897
57	943.448	50/29
58	960	47/27
59	976.552	51/29
60	993.103	55/31
61	1009.655
62	1026.207	38/21, 47/26
63	1042.759
64	1059.31
65	1075.862
66	1092.414
67	1108.966	55/29
68	1125.517
69	1142.069	29/15
70	1158.621
71	1175.172
72	1191.724
73	1208.276
74	1224.828
75	1241.379
76	1257.931	31/15
77	1274.483
78	1291.034
79	1307.586
80	1324.138
81	1340.69
82	1357.241	46/21
83	1373.793
84	1390.345	29/13
85	1406.897
86	1423.448
87	1440
88	1456.552
89	1473.103
90	1489.655	26/11
91	1506.207
92	1522.759	41/17
93	1539.31
94	1555.862	27/11
95	1572.414
96	1588.966
97	1605.517	43/17
98	1622.069
99	1638.621
100	1655.172	13/5
101	1671.724
102	1688.276
103	1704.828
104	1721.379
105	1737.931	30/11
106	1754.483
107	1771.034
108	1787.586
109	1804.138
110	1820.69
111	1837.241	26/9
112	1853.793
113	1870.345
114	1886.897
115	1903.448	3/1
116	1920
117	1936.552
118	1953.103	34/11
119	1969.655
120	1986.207
121	2002.759	35/11
122	2019.31
123	2035.862
124	2052.414
125	2068.966
126	2085.517	10/3
127	2102.069
128	2118.621	17/5
129	2135.172
130	2151.724
131	2168.276	7/2
132	2184.828
133	2201.379
134	2217.931
135	2234.483
136	2251.034
137	2267.586
138	2284.138
139	2300.69	34/9
140	2317.241
141	2333.793
142	2350.345	35/9
143	2366.897	51/13
144	2383.448
145	2400

Harmonics

Approximation of harmonics in 145ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+8.28	+1.49	+0.00	-5.62	-6.78	+7.73	+8.28	+2.99	+2.65	+3.16	+1.49
	Relative (%)	+50.0	+9.0	+0.0	-34.0	-41.0	+46.7	+50.0	+18.0	+16.0	+19.1	+9.0
Steps (reduced)		73 (73)	115 (115)	145 (0)	168 (23)	187 (42)	204 (59)	218 (73)	230 (85)	241 (96)	251 (106)	260 (115)

Approximation of harmonics in 145ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.67	-0.55	-4.13	+0.00	-5.65	-5.29	+0.42	-5.62	-7.33	-5.11	+0.69
	Relative (%)	-28.2	-3.3	-25.0	+0.0	-34.1	-32.0	+2.5	-34.0	-44.3	-30.9	+4.2
Steps (reduced)		268 (123)	276 (131)	283 (138)	290 (0)	296 (6)	302 (12)	308 (18)	313 (23)	318 (28)	323 (33)	328 (38)