124edt

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124edt

125edt →

Prime factorization	22 × 31
Step size	15.3383¢
Octave	78\124edt (1196.39¢) (→39\62edt)
Consistency limit	4
Distinct consistency limit	4

124 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 124edt or 124ed3), is a nonoctave tuning system that divides the interval of 3/1 into 124 equal parts of about 15.3 ¢ each. Each step represents a frequency ratio of 3^1/124, or the 124th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	15.338
2	30.677
3	46.015
4	61.353	28/27, 29/28
5	76.692	23/22, 47/45
6	92.03	19/18, 39/37
7	107.368	33/31, 50/47
8	122.707	29/27, 44/41
9	138.045
10	153.383	47/43
11	168.722	43/39
12	184.06	10/9
13	199.399	37/33, 46/41
14	214.737
15	230.075
16	245.414
17	260.752	43/37, 50/43
18	276.09	27/23, 34/29
19	291.429
20	306.767	37/31
21	322.105	47/39
22	337.444	17/14, 45/37
23	352.782	27/22
24	368.12	26/21
25	383.459
26	398.797	34/27, 39/31
27	414.135	33/26, 47/37
28	429.474	50/39
29	444.812	22/17
30	460.15	30/23, 43/33
31	475.489
32	490.827
33	506.165
34	521.504	23/17, 50/37
35	536.842	15/11
36	552.18
37	567.519	43/31
38	582.857	7/5
39	598.196	41/29
40	613.534	47/33
41	628.872
42	644.211	29/20, 45/31
43	659.549	41/28
44	674.887	31/21, 34/23
45	690.226
46	705.564
47	720.902	44/29, 47/31, 50/33
48	736.241	26/17
49	751.579
50	766.917
51	782.256	11/7
52	797.594	46/29
53	812.932
54	828.271	50/31
55	843.609	44/27
56	858.947	23/14
57	874.286
58	889.624
59	904.962
60	920.301	17/10
61	935.639
62	950.978	26/15, 45/26
63	966.316
64	981.654	30/17, 37/21
65	996.993
66	1012.331
67	1027.669
68	1043.008	42/23
69	1058.346
70	1073.684
71	1089.023
72	1104.361
73	1119.699	21/11
74	1135.038
75	1150.376
76	1165.714	49/25, 51/26
77	1181.053
78	1196.391
79	1211.729
80	1227.068
81	1242.406	41/20, 43/21
82	1257.744	31/15
83	1273.083
84	1288.421	40/19
85	1303.759
86	1319.098	15/7
87	1334.436
88	1349.775
89	1365.113	11/5
90	1380.451	51/23
91	1395.79	47/21
92	1411.128
93	1426.466	41/18
94	1441.805	23/10
95	1457.143	51/22
96	1472.481
97	1487.82	26/11
98	1503.158	31/13, 50/21
99	1518.496
100	1533.835
101	1549.173	22/9
102	1564.511	37/15, 42/17
103	1579.85
104	1595.188
105	1610.526
106	1625.865	23/9
107	1641.203
108	1656.541
109	1671.88
110	1687.218
111	1702.556
112	1717.895	27/10
113	1733.233
114	1748.572
115	1763.91
116	1779.248
117	1794.587	31/11
118	1809.925	37/13
119	1825.263
120	1840.602
121	1855.94
122	1871.278
123	1886.617
124	1901.955	3/1

Harmonics

Approximation of harmonics in 124edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-3.61	+0.00	-7.22	+5.27	-3.61	+5.61	+4.51	+0.00	+1.66	+5.37	-7.22
	Relative (%)	-23.5	+0.0	-47.1	+34.3	-23.5	+36.6	+29.4	+0.0	+10.8	+35.0	-47.1
Steps (reduced)		78 (78)	124 (0)	156 (32)	182 (58)	202 (78)	220 (96)	235 (111)	248 (0)	260 (12)	271 (23)	280 (32)

Approximation of harmonics in 124edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+7.59	+2.00	+5.27	+0.90	+3.32	-3.61	-5.18	-1.95	+5.61	+1.77	+1.50
	Relative (%)	+49.5	+13.0	+34.3	+5.9	+21.6	-23.5	-33.8	-12.7	+36.6	+11.5	+9.8
Steps (reduced)		290 (42)	298 (50)	306 (58)	313 (65)	320 (72)	326 (78)	332 (84)	338 (90)	344 (96)	349 (101)	354 (106)