125edt

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125edt

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Prime factorization	53
Step size	15.2156 ¢
Octave	79\125edt (1202.04 ¢)
Consistency limit	6
Distinct consistency limit	6

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	Hekts	Approximate ratios
0	0	0	1/1
1	15.2	10.4
2	30.4	20.8
3	45.6	31.2	37/36, 38/37, 39/38, 40/39
4	60.9	41.6	29/28
5	76.1	52	23/22, 47/45
6	91.3	62.4	39/37
7	106.5	72.8	33/31, 50/47
8	121.7	83.2	44/41
9	136.9	93.6	13/12
10	152.2	104	12/11, 47/43
11	167.4	114.4	43/39
12	182.6	124.8	10/9
13	197.8	135.2	28/25, 37/33, 46/41
14	213	145.6	26/23, 43/38
15	228.2	156
16	243.5	166.4	23/20, 38/33
17	258.7	176.8	29/25, 36/31, 43/37
18	273.9	187.2	34/29, 48/41
19	289.1	197.6	13/11
20	304.3	208	31/26
21	319.5	218.4
22	334.7	228.8	17/14, 40/33
23	350	239.2
24	365.2	249.6	21/17
25	380.4	260
26	395.6	270.4	39/31
27	410.8	280.8	19/15
28	426	291.2	23/18
29	441.3	301.6	31/24, 40/31
30	456.5	312	43/33
31	471.7	322.4
32	486.9	332.8	45/34
33	502.1	343.2
34	517.3	353.6	31/23
35	532.5	364	34/25
36	547.8	374.4
37	563	384.8	18/13
38	578.2	395.2
39	593.4	405.6	31/22, 38/27
40	608.6	416	27/19
41	623.8	426.4	33/23, 43/30
42	639.1	436.8
43	654.3	447.2
44	669.5	457.6	25/17, 28/19
45	684.7	468	46/31
46	699.9	478.4
47	715.1	488.8
48	730.4	499.2	29/19
49	745.6	509.6	20/13
50	760.8	520	45/29
51	776	530.4	36/23, 47/30
52	791.2	540.8	30/19
53	806.4	551.2	43/27
54	821.6	561.6	37/23, 45/28
55	836.9	572	47/29
56	852.1	582.4	18/11
57	867.3	592.8	33/20
58	882.5	603.2	5/3
59	897.7	613.6	42/25, 47/28
60	912.9	624	39/23
61	928.2	634.4	41/24
62	943.4	644.8	50/29
63	958.6	655.2	40/23, 47/27
64	973.8	665.6
65	989	676	23/13
66	1004.2	686.4	25/14
67	1019.4	696.8	9/5
68	1034.7	707.2	20/11
69	1049.9	717.6	11/6
70	1065.1	728	37/20, 50/27
71	1080.3	738.4	28/15
72	1095.5	748.8
73	1110.7	759.2	19/10
74	1126	769.6	23/12
75	1141.2	780	29/15
76	1156.4	790.4	39/20
77	1171.6	800.8
78	1186.8	811.2
79	1202	821.6
80	1217.3	832
81	1232.5	842.4	51/25
82	1247.7	852.8	37/18
83	1262.9	863.2
84	1278.1	873.6	23/11
85	1293.3	884	19/9
86	1308.5	894.4
87	1323.8	904.8	43/20
88	1339	915.2	13/6
89	1354.2	925.6
90	1369.4	936
91	1384.6	946.4
92	1399.8	956.8
93	1415.1	967.2	34/15, 43/19
94	1430.3	977.6
95	1445.5	988
96	1460.7	998.4
97	1475.9	1008.8
98	1491.1	1019.2	45/19
99	1506.3	1029.6	31/13, 43/18
100	1521.6	1040
101	1536.8	1050.4	17/7
102	1552	1060.8
103	1567.2	1071.2	42/17, 47/19
104	1582.4	1081.6
105	1597.6	1092
106	1612.9	1102.4	33/13
107	1628.1	1112.8	41/16
108	1643.3	1123.2	31/12
109	1658.5	1133.6
110	1673.7	1144	50/19
111	1688.9	1154.4
112	1704.2	1164.8
113	1719.4	1175.2	27/10
114	1734.6	1185.6
115	1749.8	1196	11/4
116	1765	1206.4	36/13
117	1780.2	1216.8
118	1795.4	1227.2	31/11
119	1810.7	1237.6	37/13
120	1825.9	1248
121	1841.1	1258.4
122	1856.3	1268.8	38/13
123	1871.5	1279.2
124	1886.7	1289.6
125	1902	1300	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)