123edt

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123edt

124edt →

Prime factorization	3 × 41
Step size	15.463¢
Octave	78\123edt (1206.12¢) (→26\41edt)
Consistency limit	2
Distinct consistency limit	2

123 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 123edt or 123ed3), is a nonoctave tuning system that divides the interval of 3/1 into 123 equal parts of about 15.5 ¢ each. Each step represents a frequency ratio of 3^1/123, or the 123rd root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.5
2	30.9
3	46.4
4	61.9
5	77.3	23/22, 45/43
6	92.8	19/18, 39/37
7	108.2	33/31, 49/46, 50/47
8	123.7	29/27, 44/41
9	139.2
10	154.6	47/43
11	170.1	43/39
12	185.6	39/35, 49/44
13	201	46/41
14	216.5	17/15
15	231.9
16	247.4	15/13
17	262.9	50/43
18	278.3	27/23
19	293.8
20	309.3	49/41
21	324.7	35/29, 41/34, 47/39
22	340.2	45/37
23	355.7	27/22, 43/35
24	371.1	26/21, 31/25
25	386.6
26	402	29/23
27	417.5
28	433
29	448.4	35/27
30	463.9	17/13
31	479.4	29/22, 33/25
32	494.8
33	510.3	47/35
34	525.7
35	541.2	26/19, 41/30
36	556.7
37	572.1
38	587.6
39	603.1
40	618.5	10/7
41	634	49/34
42	649.4
43	664.9	22/15
44	680.4	37/25, 43/29
45	695.8
46	711.3
47	726.8	35/23
48	742.2
49	757.7
50	773.2
51	788.6	41/26
52	804.1	35/22, 43/27
53	819.5
54	835	34/21, 47/29
55	850.5	49/30
56	865.9
57	881.4
58	896.9
59	912.3	22/13, 39/23
60	927.8
61	943.2	50/29
62	958.7	47/27
63	974.2
64	989.6	23/13, 39/22
65	1005.1
66	1020.6
67	1036
68	1051.5
69	1067	50/27
70	1082.4	43/23
71	1097.9	49/26
72	1113.3
73	1128.8
74	1144.3
75	1159.7	41/21, 43/22
76	1175.2
77	1190.7
78	1206.1
79	1221.6
80	1237	45/22, 47/23
81	1252.5
82	1268
83	1283.4	21/10
84	1298.9
85	1314.4	47/22
86	1329.8	41/19
87	1345.3	37/17, 50/23
88	1360.7
89	1376.2
90	1391.7
91	1407.1
92	1422.6	25/11
93	1438.1	39/17
94	1453.5	44/19
95	1469
96	1484.5
97	1499.9	50/21
98	1515.4
99	1530.8	46/19
100	1546.3	22/9
101	1561.8	37/15
102	1577.2
103	1592.7
104	1608.2	43/17
105	1623.6	23/9
106	1639.1	49/19
107	1654.5	13/5
108	1670
109	1685.5	45/17
110	1700.9
111	1716.4	35/13
112	1731.9	49/18
113	1747.3
114	1762.8
115	1778.3
116	1793.7	31/11
117	1809.2	37/13
118	1824.6	43/15
119	1840.1
120	1855.6
121	1871
122	1886.5
123	1902	3/1

Harmonics

Approximation of harmonics in 123edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+6.12	+0.00	-3.23	-2.96	+6.12	+2.12	+2.89	+0.00	+3.15	-7.22	-3.23
	Relative (%)	+39.6	+0.0	-20.9	-19.2	+39.6	+13.7	+18.7	+0.0	+20.4	-46.7	-20.9
Steps (reduced)		78 (78)	123 (0)	155 (32)	180 (57)	201 (78)	218 (95)	233 (110)	246 (0)	258 (12)	268 (22)	278 (32)

Approximation of harmonics in 123edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	-7.23	-2.96	-6.45	-3.17	+6.12	+5.29	-6.19	+2.12	-1.10	-0.74
	Relative (%)	-17.0	-46.7	-19.2	-41.7	-20.5	+39.6	+34.2	-40.0	+13.7	-7.1	-4.8
Steps (reduced)		287 (41)	295 (49)	303 (57)	310 (64)	317 (71)	324 (78)	330 (84)	335 (89)	341 (95)	346 (100)	351 (105)