125edt

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125edt

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Prime factorization	53
Step size	15.2156¢
Octave	79\125edt (1202.04¢)
Consistency limit	5
Distinct consistency limit	5

125 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 125edt or 125ed3), is a nonoctave tuning system that divides the interval of 3/1 into 125 equal parts of about 15.2 ¢ each. Each step represents a frequency ratio of 3^1/125, or the 125th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.216
2	30.431
3	45.647	37/36, 38/37, 39/38, 40/39
4	60.863	29/28
5	76.078	23/22, 47/45
6	91.294	39/37
7	106.509	33/31, 50/47
8	121.725	44/41
9	136.941	13/12
10	152.156	12/11, 47/43
11	167.372	43/39
12	182.588	10/9
13	197.803	28/25, 37/33, 46/41
14	213.019	26/23, 43/38
15	228.235
16	243.45	23/20, 38/33
17	258.666	29/25, 36/31, 43/37
18	273.882	34/29, 48/41
19	289.097	13/11
20	304.313	31/26
21	319.528
22	334.744	17/14, 40/33
23	349.96
24	365.175	21/17
25	380.391
26	395.607	39/31
27	410.822	19/15
28	426.038	23/18
29	441.254	31/24, 40/31
30	456.469	43/33
31	471.685
32	486.9	45/34
33	502.116
34	517.332	31/23
35	532.547	34/25
36	547.763
37	562.979	18/13
38	578.194
39	593.41	31/22, 38/27
40	608.626	27/19
41	623.841	33/23, 43/30
42	639.057
43	654.273
44	669.488	25/17, 28/19
45	684.704	46/31
46	699.919
47	715.135
48	730.351	29/19
49	745.566	20/13
50	760.782	45/29
51	775.998	36/23, 47/30
52	791.213	30/19
53	806.429	43/27
54	821.645	37/23, 45/28
55	836.86	47/29
56	852.076	18/11
57	867.291	33/20
58	882.507	5/3
59	897.723	42/25, 47/28
60	912.938	39/23
61	928.154	41/24
62	943.37	50/29
63	958.585	40/23, 47/27
64	973.801
65	989.017	23/13
66	1004.232	25/14
67	1019.448	9/5
68	1034.664	20/11
69	1049.879	11/6
70	1065.095	37/20, 50/27
71	1080.31	28/15
72	1095.526
73	1110.742	19/10
74	1125.957	23/12
75	1141.173	29/15
76	1156.389	39/20
77	1171.604
78	1186.82
79	1202.036
80	1217.251
81	1232.467	51/25
82	1247.682	37/18
83	1262.898
84	1278.114	23/11
85	1293.329	19/9
86	1308.545
87	1323.761	43/20
88	1338.976	13/6
89	1354.192
90	1369.408
91	1384.623
92	1399.839
93	1415.055	34/15, 43/19
94	1430.27
95	1445.486
96	1460.701
97	1475.917
98	1491.133	45/19
99	1506.348	31/13, 43/18
100	1521.564
101	1536.78	17/7
102	1551.995
103	1567.211	42/17, 47/19
104	1582.427
105	1597.642
106	1612.858	33/13
107	1628.073	41/16
108	1643.289	31/12
109	1658.505
110	1673.72	50/19
111	1688.936
112	1704.152
113	1719.367	27/10
114	1734.583
115	1749.799	11/4
116	1765.014	36/13
117	1780.23
118	1795.446	31/11
119	1810.661	37/13
120	1825.877
121	1841.092
122	1856.308	38/13
123	1871.524
124	1886.739
125	1901.955	3/1

Harmonics

Approximation of harmonics in 125edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+2.04	+0.00	+4.07	-1.85	+2.04	-6.17	+6.11	+0.00	+0.18	+2.55	+4.07
	Relative (%)	+13.4	+0.0	+26.8	-12.2	+13.4	-40.5	+40.1	+0.0	+1.2	+16.8	+26.8
Steps (reduced)		79 (79)	125 (0)	158 (33)	183 (58)	204 (79)	221 (96)	237 (112)	250 (0)	262 (12)	273 (23)	283 (33)

Approximation of harmonics in 125edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.44	-4.13	-1.85	-7.07	-5.52	+2.04	-0.27	+2.22	-6.17	+4.59	+3.71
	Relative (%)	+16.0	-27.2	-12.2	-46.5	-36.3	+13.4	-1.8	+14.6	-40.5	+30.1	+24.4
Steps (reduced)		292 (42)	300 (50)	308 (58)	315 (65)	322 (72)	329 (79)	335 (85)	341 (91)	346 (96)	352 (102)	357 (107)