125ed4

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125ed4

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Prime factorization	53
Step size	19.2 ¢
Octave	63\125ed4 (1209.6 ¢)
Twelfth	99\125ed4 (1900.8 ¢)
Consistency limit	1
Distinct consistency limit	1

125 equal divisions of the 4th harmonic (abbreviated 125ed4) is a nonoctave tuning system that divides the interval of 4/1 into 125 equal parts of exactly 19.2 ¢ each. Each step represents a frequency ratio of 4^1/125, or the 125th root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	19.2
2	38.4
3	57.6	30/29, 31/30
4	76.8	23/22, 45/43, 47/45
5	96
6	115.2	31/29
7	134.4	27/25
8	153.6	47/43
9	172.8	21/19
10	192	19/17
11	211.2	26/23
12	230.4
13	249.6	15/13
14	268.8
15	288	13/11
16	307.2	37/31
17	326.4
18	345.6	11/9
19	364.8	21/17, 37/30
20	384
21	403.2	29/23
22	422.4	37/29
23	441.6
24	460.8	30/23
25	480	29/22, 33/25
26	499.2
27	518.4	31/23
28	537.6	15/11
29	556.8
30	576
31	595.2	31/22
32	614.4
33	633.6
34	652.8	51/35
35	672
36	691.2
37	710.4
38	729.6
39	748.8
40	768	39/25
41	787.2	41/26
42	806.4	43/27
43	825.6	29/18
44	844.8
45	864
46	883.2	5/3
47	902.4
48	921.6
49	940.8	31/18, 43/25
50	960	47/27
51	979.2
52	998.4
53	1017.6	9/5
54	1036.8
55	1056	35/19
56	1075.2
57	1094.4	47/25
58	1113.6
59	1132.8	25/13
60	1152
61	1171.2
62	1190.4
63	1209.6
64	1228.8
65	1248	37/18
66	1267.2	27/13
67	1286.4
68	1305.6
69	1324.8
70	1344	50/23
71	1363.2	11/5
72	1382.4
73	1401.6
74	1420.8	25/11
75	1440
76	1459.2
77	1478.4
78	1497.6
79	1516.8
80	1536	17/7
81	1555.2	27/11
82	1574.4
83	1593.6
84	1612.8	33/13
85	1632
86	1651.2
87	1670.4
88	1689.6
89	1708.8	51/19
90	1728	19/7
91	1747.2
92	1766.4
93	1785.6
94	1804.8
95	1824	43/15
96	1843.2	29/10
97	1862.4
98	1881.6
99	1900.8	3/1
100	1920
101	1939.2
102	1958.4	31/10
103	1977.6	47/15
104	1996.8
105	2016
106	2035.2
107	2054.4
108	2073.6
109	2092.8
110	2112
111	2131.2
112	2150.4	45/13
113	2169.6
114	2188.8
115	2208
116	2227.2
117	2246.4
118	2265.6	37/10
119	2284.8
120	2304
121	2323.2
122	2342.4
123	2361.6	43/11
124	2380.8
125	2400

Harmonics

Approximation of harmonics in 125ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.60	-1.16	+0.00	-2.31	+8.44	-8.83	+9.60	-2.31	+7.29	-4.12	-1.16
	Relative (%)	+50.0	-6.0	+0.0	-12.1	+44.0	-46.0	+50.0	-12.0	+37.9	-21.4	-6.0
Steps (reduced)		63 (63)	99 (99)	125 (0)	145 (20)	162 (37)	175 (50)	188 (63)	198 (73)	208 (83)	216 (91)	224 (99)

Approximation of harmonics in 125ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-5.33	+0.77	-3.47	+0.00	-8.96	+7.29	-9.51	-2.31	+9.22	+5.48	+5.33
	Relative (%)	-27.7	+4.0	-18.1	+0.0	-46.6	+38.0	-49.5	-12.1	+48.0	+28.6	+27.7
Steps (reduced)		231 (106)	238 (113)	244 (119)	250 (0)	255 (5)	261 (11)	265 (15)	270 (20)	275 (25)	279 (29)	283 (33)