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	15.2
2	30.4
3	45.6	37/36, 38/37, 39/38, 40/39
4	60.9	29/28
5	76.1	23/22, 47/45
6	91.3	39/37
7	106.5	33/31, 50/47
8	121.7	44/41
9	136.9	13/12
10	152.2	12/11, 47/43
11	167.4	43/39
12	182.6	10/9
13	197.8	28/25, 37/33, 46/41
14	213	26/23, 43/38
15	228.2
16	243.5	23/20, 38/33
17	258.7	29/25, 36/31, 43/37
18	273.9	34/29, 48/41
19	289.1	13/11
20	304.3	31/26
21	319.5
22	334.7	17/14, 40/33
23	350
24	365.2	21/17
25	380.4
26	395.6	39/31
27	410.8	19/15
28	426	23/18
29	441.3	31/24, 40/31
30	456.5	43/33
31	471.7
32	486.9	45/34
33	502.1
34	517.3	31/23
35	532.5	34/25
36	547.8
37	563	18/13
38	578.2
39	593.4	31/22, 38/27
40	608.6	27/19
41	623.8	33/23, 43/30
42	639.1
43	654.3
44	669.5	25/17, 28/19
45	684.7	46/31
46	699.9
47	715.1
48	730.4	29/19
49	745.6	20/13
50	760.8	45/29
51	776	36/23, 47/30
52	791.2	30/19
53	806.4	43/27
54	821.6	37/23, 45/28
55	836.9	47/29
56	852.1	18/11
57	867.3	33/20
58	882.5	5/3
59	897.7	42/25, 47/28
60	912.9	39/23
61	928.2	41/24
62	943.4	50/29
63	958.6	40/23, 47/27
64	973.8
65	989	23/13
66	1004.2	25/14
67	1019.4	9/5
68	1034.7	20/11
69	1049.9	11/6
70	1065.1	37/20, 50/27
71	1080.3	28/15
72	1095.5
73	1110.7	19/10
74	1126	23/12
75	1141.2	29/15
76	1156.4	39/20
77	1171.6
78	1186.8
79	1202
80	1217.3
81	1232.5	51/25
82	1247.7	37/18
83	1262.9
84	1278.1	23/11
85	1293.3	19/9
86	1308.5
87	1323.8	43/20
88	1339	13/6
89	1354.2
90	1369.4
91	1384.6
92	1399.8
93	1415.1	34/15, 43/19
94	1430.3
95	1445.5
96	1460.7
97	1475.9
98	1491.1	45/19
99	1506.3	31/13, 43/18
100	1521.6
101	1536.8	17/7
102	1552
103	1567.2	42/17, 47/19
104	1582.4
105	1597.6
106	1612.9	33/13
107	1628.1	41/16
108	1643.3	31/12
109	1658.5
110	1673.7	50/19
111	1688.9
112	1704.2
113	1719.4	27/10
114	1734.6
115	1749.8	11/4
116	1765	36/13
117	1780.2
118	1795.4	31/11
119	1810.7	37/13
120	1825.9
121	1841.1
122	1856.3	38/13
123	1871.5
124	1886.7
125	1902	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)