122edt

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122edt

123edt →

Prime factorization	2 × 61
Step size	15.5898¢
Octave	77\122edt (1200.41¢)
Consistency limit	10
Distinct consistency limit	10

122 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 122edt or 122ed3), is a nonoctave tuning system that divides the interval of 3/1 into 122 equal parts of about 15.6 ¢ each. Each step represents a frequency ratio of 3^1/122, or the 122nd root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.59
2	31.18
3	46.769	37/36, 38/37, 39/38
4	62.359	28/27, 29/28
5	77.949	23/22, 45/43
6	93.539	19/18
7	109.129	33/31, 49/46
8	124.718	29/27, 43/40
9	140.308	13/12
10	155.898	23/21, 35/32, 47/43
11	171.488	21/19, 32/29
12	187.078	39/35, 49/44
13	202.667	9/8
14	218.257	17/15, 42/37
15	233.847
16	249.437	15/13, 37/32
17	265.027	7/6
18	280.616	20/17, 47/40
19	296.206	19/16
20	311.796
21	327.386	29/24, 35/29
22	342.975	39/32
23	358.565	16/13
24	374.155	36/29, 41/33
25	389.745
26	405.335	24/19, 43/34
27	420.924	37/29
28	436.514	9/7
29	452.104	48/37
30	467.694	38/29
31	483.284	37/28, 41/31
32	498.873	4/3
33	514.463	35/26, 39/29
34	530.053	19/14
35	545.643	37/27, 48/35
36	561.233	47/34
37	576.822	46/33
38	592.412	31/22, 38/27
39	608.002	27/19, 44/31
40	623.592	33/23, 43/30
41	639.182
42	654.771	35/24
43	670.361	28/19
44	685.951	49/33
45	701.541	3/2
46	717.131
47	732.72	29/19
48	748.31	37/24
49	763.9	14/9
50	779.49
51	795.08	19/12
52	810.669
53	826.259	29/18
54	841.849	13/8
55	857.439
56	873.029	48/29
57	888.618
58	904.208	27/16, 32/19
59	919.798	17/10
60	935.388
61	950.978	26/15, 45/26
62	966.567
63	982.157	30/17, 37/21
64	997.747	16/9
65	1013.337
66	1028.926	29/16
67	1044.516
68	1060.106	24/13
69	1075.696
70	1091.286	47/25
71	1106.875	36/19
72	1122.465	44/23
73	1138.055	27/14
74	1153.645	37/19
75	1169.235
76	1184.824
77	1200.414	2/1
78	1216.004
79	1231.594
80	1247.184	37/18
81	1262.773
82	1278.363	23/11
83	1293.953	19/9
84	1309.543	49/23
85	1325.133	43/20
86	1340.722
87	1356.312	35/16, 46/21
88	1371.902	42/19
89	1387.492	29/13, 49/22
90	1403.082	9/4
91	1418.671
92	1434.261
93	1449.851	37/16
94	1465.441	7/3
95	1481.031	40/17, 47/20
96	1496.62	19/8
97	1512.21
98	1527.8	29/12
99	1543.39	39/16
100	1558.98	32/13
101	1574.569
102	1590.159
103	1605.749	43/17, 48/19
104	1621.339
105	1636.928	18/7
106	1652.518	13/5
107	1668.108
108	1683.698	37/14, 45/17
109	1699.288	8/3
110	1714.877	35/13
111	1730.467	19/7
112	1746.057
113	1761.647	36/13, 47/17
114	1777.237
115	1792.826	31/11
116	1808.416
117	1824.006	43/15
118	1839.596
119	1855.186	38/13
120	1870.775
121	1886.365
122	1901.955	3/1

Harmonics

Approximation of harmonics in 122edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.41	+0.00	+0.83	+4.26	+0.41	-1.43	+1.24	+0.00	+4.67	-4.43	+0.83
	Relative (%)	+2.7	+0.0	+5.3	+27.3	+2.7	-9.2	+8.0	+0.0	+30.0	-28.4	+5.3
Steps (reduced)		77 (77)	122 (0)	154 (32)	179 (57)	199 (77)	216 (94)	231 (109)	244 (0)	256 (12)	266 (22)	276 (32)

Approximation of harmonics in 122edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.56	-1.02	+4.26	+1.66	+5.83	+0.41	+0.35	+5.09	-1.43	-4.02	-3.03
	Relative (%)	+16.4	-6.5	+27.3	+10.6	+37.4	+2.7	+2.2	+32.6	-9.2	-25.8	-19.4
Steps (reduced)		285 (41)	293 (49)	301 (57)	308 (64)	315 (71)	321 (77)	327 (83)	333 (89)	338 (94)	343 (99)	348 (104)