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	16.6
2	33.1	51/50
3	49.7	35/34
4	66.2	27/26
5	82.8	43/41
6	99.3
7	115.9	31/29
8	132.4
9	149
10	165.5	11/10
11	182.1	10/9
12	198.6	37/33
13	215.2	17/15
14	231.7
15	248.3	15/13
16	264.8
17	281.4
18	297.9
19	314.5
20	331	23/19
21	347.6	11/9
22	364.1	37/30
23	380.7
24	397.2	39/31
25	413.8	33/26, 47/37
26	430.3	50/39
27	446.9
28	463.4	17/13
29	480
30	496.6
31	513.1	35/26, 39/29
32	529.7
33	546.2	37/27
34	562.8
35	579.3
36	595.9	55/39
37	612.4	37/26, 47/33
38	629
39	645.5	45/31
40	662.1
41	678.6
42	695.2
43	711.7
44	728.3	35/23
45	744.8
46	761.4	45/29
47	777.9	47/30
48	794.5
49	811
50	827.6	50/31
51	844.1
52	860.7	51/31
53	877.2
54	893.8
55	910.3
56	926.9
57	943.4	50/29
58	960	47/27
59	976.6	51/29
60	993.1	55/31
61	1009.7
62	1026.2	38/21, 47/26
63	1042.8
64	1059.3
65	1075.9
66	1092.4
67	1109	55/29
68	1125.5
69	1142.1	29/15
70	1158.6
71	1175.2
72	1191.7
73	1208.3
74	1224.8
75	1241.4
76	1257.9	31/15
77	1274.5
78	1291
79	1307.6
80	1324.1
81	1340.7
82	1357.2	46/21
83	1373.8
84	1390.3	29/13
85	1406.9
86	1423.4
87	1440
88	1456.6
89	1473.1
90	1489.7	26/11
91	1506.2
92	1522.8	41/17
93	1539.3
94	1555.9	27/11
95	1572.4
96	1589
97	1605.5	43/17
98	1622.1
99	1638.6
100	1655.2	13/5
101	1671.7
102	1688.3
103	1704.8
104	1721.4
105	1737.9	30/11
106	1754.5
107	1771
108	1787.6
109	1804.1
110	1820.7
111	1837.2	26/9
112	1853.8
113	1870.3
114	1886.9
115	1903.4	3/1
116	1920
117	1936.6
118	1953.1	34/11
119	1969.7
120	1986.2
121	2002.8	35/11
122	2019.3
123	2035.9
124	2052.4
125	2069
126	2085.5	10/3
127	2102.1
128	2118.6	17/5
129	2135.2
130	2151.7
131	2168.3	7/2
132	2184.8
133	2201.4
134	2217.9
135	2234.5
136	2251
137	2267.6
138	2284.1
139	2300.7	34/9
140	2317.2
141	2333.8
142	2350.3	35/9
143	2366.9	51/13
144	2383.4
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)