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	15.463
2	30.926
3	46.389
4	61.852
5	77.315	23/22, 45/43
6	92.778	19/18, 39/37
7	108.241	33/31, 49/46, 50/47
8	123.704	29/27, 44/41
9	139.167
10	154.63	47/43
11	170.094	43/39
12	185.557	39/35, 49/44
13	201.02	46/41
14	216.483	17/15
15	231.946
16	247.409	15/13
17	262.872	50/43
18	278.335	27/23
19	293.798
20	309.261	49/41
21	324.724	35/29, 41/34, 47/39
22	340.187	45/37
23	355.65	27/22, 43/35
24	371.113	26/21, 31/25
25	386.576
26	402.039	29/23
27	417.502
28	432.965
29	448.428	35/27
30	463.891	17/13
31	479.355	29/22, 33/25
32	494.818
33	510.281	47/35
34	525.744
35	541.207	26/19, 41/30
36	556.67
37	572.133
38	587.596
39	603.059
40	618.522	10/7
41	633.985	49/34
42	649.448
43	664.911	22/15
44	680.374	37/25, 43/29
45	695.837
46	711.3
47	726.763	35/23
48	742.226
49	757.689
50	773.152
51	788.615	41/26
52	804.079	35/22, 43/27
53	819.542
54	835.005	34/21, 47/29
55	850.468	49/30
56	865.931
57	881.394
58	896.857
59	912.32	22/13, 39/23
60	927.783
61	943.246	50/29
62	958.709	47/27
63	974.172
64	989.635	23/13, 39/22
65	1005.098
66	1020.561
67	1036.024
68	1051.487
69	1066.95	50/27
70	1082.413	43/23
71	1097.876	49/26
72	1113.34
73	1128.803
74	1144.266
75	1159.729	41/21, 43/22
76	1175.192
77	1190.655
78	1206.118
79	1221.581
80	1237.044	45/22, 47/23
81	1252.507
82	1267.97
83	1283.433	21/10
84	1298.896
85	1314.359	47/22
86	1329.822	41/19
87	1345.285	37/17, 50/23
88	1360.748
89	1376.211
90	1391.674
91	1407.137
92	1422.6	25/11
93	1438.064	39/17
94	1453.527	44/19
95	1468.99
96	1484.453
97	1499.916	50/21
98	1515.379
99	1530.842	46/19
100	1546.305	22/9
101	1561.768	37/15
102	1577.231
103	1592.694
104	1608.157	43/17
105	1623.62	23/9
106	1639.083	49/19
107	1654.546	13/5
108	1670.009
109	1685.472	45/17
110	1700.935
111	1716.398	35/13
112	1731.861	49/18
113	1747.325
114	1762.788
115	1778.251
116	1793.714	31/11
117	1809.177	37/13
118	1824.64	43/15
119	1840.103
120	1855.566
121	1871.029
122	1886.492
123	1901.955	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)