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	Hekts	Approximate ratios
0	0	0	1/1
1	15.6	10.7
2	31.2	21.3
3	46.8	32	37/36, 38/37, 39/38
4	62.4	42.6	28/27, 29/28
5	77.9	53.3	23/22, 45/43
6	93.5	63.9	19/18
7	109.1	74.6	33/31, 49/46
8	124.7	85.2	29/27, 43/40
9	140.3	95.9	13/12
10	155.9	106.6	23/21, 35/32, 47/43
11	171.5	117.2	21/19, 32/29
12	187.1	127.9	39/35, 49/44
13	202.7	138.5	9/8
14	218.3	149.2	17/15, 42/37
15	233.8	159.8
16	249.4	170.5	15/13, 37/32
17	265	181.1	7/6
18	280.6	191.8	20/17, 47/40
19	296.2	202.5	19/16
20	311.8	213.1
21	327.4	223.8	29/24, 35/29
22	343	234.4	39/32
23	358.6	245.1	16/13
24	374.2	255.7	36/29, 41/33
25	389.7	266.4
26	405.3	277	24/19, 43/34
27	420.9	287.7	37/29
28	436.5	298.4	9/7
29	452.1	309	48/37
30	467.7	319.7	38/29
31	483.3	330.3	37/28, 41/31
32	498.9	341	4/3
33	514.5	351.6	35/26, 39/29
34	530.1	362.3	19/14
35	545.6	373	37/27, 48/35
36	561.2	383.6	47/34
37	576.8	394.3	46/33
38	592.4	404.9	31/22, 38/27
39	608	415.6	27/19, 44/31
40	623.6	426.2	33/23, 43/30
41	639.2	436.9
42	654.8	447.5	35/24
43	670.4	458.2	28/19
44	686	468.9	49/33
45	701.5	479.5	3/2
46	717.1	490.2
47	732.7	500.8	29/19
48	748.3	511.5	37/24
49	763.9	522.1	14/9
50	779.5	532.8
51	795.1	543.4	19/12
52	810.7	554.1
53	826.3	564.8	29/18
54	841.8	575.4	13/8
55	857.4	586.1
56	873	596.7	48/29
57	888.6	607.4
58	904.2	618	27/16, 32/19
59	919.8	628.7	17/10
60	935.4	639.3
61	951	650	26/15, 45/26
62	966.6	660.7
63	982.2	671.3	30/17, 37/21
64	997.7	682	16/9
65	1013.3	692.6
66	1028.9	703.3	29/16
67	1044.5	713.9
68	1060.1	724.6	24/13
69	1075.7	735.2
70	1091.3	745.9	47/25
71	1106.9	756.6	36/19
72	1122.5	767.2	44/23
73	1138.1	777.9	27/14
74	1153.6	788.5	37/19
75	1169.2	799.2
76	1184.8	809.8
77	1200.4	820.5	2/1
78	1216	831.1
79	1231.6	841.8
80	1247.2	852.5	37/18
81	1262.8	863.1
82	1278.4	873.8	23/11
83	1294	884.4	19/9
84	1309.5	895.1	49/23
85	1325.1	905.7	43/20
86	1340.7	916.4
87	1356.3	927	35/16, 46/21
88	1371.9	937.7	42/19
89	1387.5	948.4	29/13, 49/22
90	1403.1	959	9/4
91	1418.7	969.7
92	1434.3	980.3
93	1449.9	991	37/16
94	1465.4	1001.6	7/3
95	1481	1012.3	40/17, 47/20
96	1496.6	1023	19/8
97	1512.2	1033.6
98	1527.8	1044.3	29/12
99	1543.4	1054.9	39/16
100	1559	1065.6	32/13
101	1574.6	1076.2
102	1590.2	1086.9
103	1605.7	1097.5	43/17, 48/19
104	1621.3	1108.2
105	1636.9	1118.9	18/7
106	1652.5	1129.5	13/5
107	1668.1	1140.2
108	1683.7	1150.8	37/14, 45/17
109	1699.3	1161.5	8/3
110	1714.9	1172.1	35/13
111	1730.5	1182.8	19/7
112	1746.1	1193.4
113	1761.6	1204.1	36/13, 47/17
114	1777.2	1214.8
115	1792.8	1225.4	31/11
116	1808.4	1236.1
117	1824	1246.7	43/15
118	1839.6	1257.4
119	1855.2	1268	38/13
120	1870.8	1278.7
121	1886.4	1289.3
122	1902	1300	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)