124edt

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← 123edt

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.

Theory

This tuning tempers out 128/125 in the 5-limit; 126/125 and 64/63 in the 7-limit; 120/119 in the 17-limit; 96/95 in the 19-limit; 92/91 in the 23-limit; 116/115 in the 29-limit; 112/111 in the 37-limit; and 106/105 in the 53-limit.

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	15.3	10.5
2	30.7	21
3	46	31.5
4	61.4	41.9	28/27, 29/28
5	76.7	52.4	23/22, 47/45
6	92	62.9	19/18, 39/37
7	107.4	73.4	33/31, 50/47
8	122.7	83.9	29/27, 44/41
9	138	94.4
10	153.4	104.8	47/43
11	168.7	115.3	43/39
12	184.1	125.8	10/9
13	199.4	136.3	37/33, 46/41
14	214.7	146.8
15	230.1	157.3
16	245.4	167.7
17	260.8	178.2	43/37, 50/43
18	276.1	188.7	27/23, 34/29
19	291.4	199.2
20	306.8	209.7	37/31
21	322.1	220.2	47/39
22	337.4	230.6	17/14, 45/37
23	352.8	241.1	27/22
24	368.1	251.6	26/21
25	383.5	262.1
26	398.8	272.6	34/27, 39/31
27	414.1	283.1	33/26, 47/37
28	429.5	293.5	50/39
29	444.8	304	22/17
30	460.2	314.5	30/23, 43/33
31	475.5	325
32	490.8	335.5
33	506.2	346
34	521.5	356.5	23/17, 50/37
35	536.8	366.9	15/11
36	552.2	377.4
37	567.5	387.9	43/31
38	582.9	398.4	7/5
39	598.2	408.9	41/29
40	613.5	419.4	47/33
41	628.9	429.8
42	644.2	440.3	29/20, 45/31
43	659.5	450.8	41/28
44	674.9	461.3	31/21, 34/23
45	690.2	471.8
46	705.6	482.3
47	720.9	492.7	44/29, 47/31, 50/33
48	736.2	503.2	26/17
49	751.6	513.7
50	766.9	524.2
51	782.3	534.7	11/7
52	797.6	545.2	46/29
53	812.9	555.6
54	828.3	566.1	50/31
55	843.6	576.6	44/27
56	858.9	587.1	23/14
57	874.3	597.6
58	889.6	608.1
59	905	618.5
60	920.3	629	17/10
61	935.6	639.5
62	951	650	26/15, 45/26
63	966.3	660.5
64	981.7	671	30/17, 37/21
65	997	681.5
66	1012.3	691.9
67	1027.7	702.4
68	1043	712.9	42/23
69	1058.3	723.4
70	1073.7	733.9
71	1089	744.4
72	1104.4	754.8
73	1119.7	765.3	21/11
74	1135	775.8
75	1150.4	786.3
76	1165.7	796.8	49/25, 51/26
77	1181.1	807.3
78	1196.4	817.7
79	1211.7	828.2
80	1227.1	838.7
81	1242.4	849.2	41/20, 43/21
82	1257.7	859.7	31/15
83	1273.1	870.2
84	1288.4	880.6	40/19
85	1303.8	891.1
86	1319.1	901.6	15/7
87	1334.4	912.1
88	1349.8	922.6
89	1365.1	933.1	11/5
90	1380.5	943.5	51/23
91	1395.8	954	47/21
92	1411.1	964.5
93	1426.5	975	41/18
94	1441.8	985.5	23/10
95	1457.1	996	51/22
96	1472.5	1006.5
97	1487.8	1016.9	26/11
98	1503.2	1027.4	31/13, 50/21
99	1518.5	1037.9
100	1533.8	1048.4
101	1549.2	1058.9	22/9
102	1564.5	1069.4	37/15, 42/17
103	1579.8	1079.8
104	1595.2	1090.3
105	1610.5	1100.8
106	1625.9	1111.3	23/9
107	1641.2	1121.8
108	1656.5	1132.3
109	1671.9	1142.7
110	1687.2	1153.2
111	1702.6	1163.7
112	1717.9	1174.2	27/10
113	1733.2	1184.7
114	1748.6	1195.2
115	1763.9	1205.6
116	1779.2	1216.1
117	1794.6	1226.6	31/11
118	1809.9	1237.1	37/13
119	1825.3	1247.6
120	1840.6	1258.1
121	1855.9	1268.5
122	1871.3	1279
123	1886.6	1289.5
124	1902	1300	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)