121edt

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121edt

122edt →

Prime factorization	112
Step size	15.7186¢
Octave	76\121edt (1194.62¢)
Consistency limit	2
Distinct consistency limit	2

121 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 121edt or 121ed3), is a nonoctave tuning system that divides the interval of 3/1 into 121 equal parts of about 15.7 ¢ each. Each step represents a frequency ratio of 3^1/121, or the 121st root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.719
2	31.437
3	47.156	36/35
4	62.875
5	78.593	22/21, 23/22, 45/43
6	94.312	19/18
7	110.03	33/31, 49/46
8	125.749
9	141.468	38/35
10	157.186	23/21
11	172.905	21/19
12	188.624	29/26
13	204.342
14	220.061	25/22
15	235.78	47/41
16	251.498
17	267.217	7/6
18	282.935
19	298.654
20	314.373	6/5
21	330.091	23/19
22	345.81	11/9
23	361.529
24	377.247	41/33
25	392.966
26	408.685	19/15
27	424.403	23/18
28	440.122	49/38
29	455.84
30	471.559	46/35
31	487.278
32	502.996
33	518.715	31/23
34	534.434	49/36
35	550.152
36	565.871	43/31
37	581.59	7/5
38	597.308
39	613.027	47/33
40	628.745
41	644.464	45/31
42	660.183
43	675.901	31/21, 34/23
44	691.62
45	707.339
46	723.057	38/25, 41/27
47	738.776	23/15
48	754.495	17/11
49	770.213
50	785.932
51	801.65	27/17
52	817.369
53	833.088	34/21
54	848.806	31/19, 49/30
55	864.525
56	880.244
57	895.962
58	911.681
59	927.4
60	943.118
61	958.837	47/27
62	974.555
63	990.274
64	1005.993	34/19
65	1021.711
66	1037.43
67	1053.149
68	1068.867
69	1084.586	43/23
70	1100.305	17/9
71	1116.023
72	1131.742
73	1147.46	33/17
74	1163.179	45/23, 49/25
75	1178.898
76	1194.616
77	1210.335
78	1226.054
79	1241.772	43/21
80	1257.491	31/15
81	1273.21
82	1288.928
83	1304.647
84	1320.365	15/7
85	1336.084
86	1351.803
87	1367.521
88	1383.24
89	1398.959
90	1414.677	43/19
91	1430.396
92	1446.115
93	1461.833
94	1477.552
95	1493.27	45/19
96	1508.989	43/18
97	1524.708	41/17
98	1540.426
99	1556.145	27/11
100	1571.864
101	1587.582	5/2
102	1603.301
103	1619.02
104	1634.738	18/7
105	1650.457
106	1666.175
107	1681.894
108	1697.613
109	1713.331
110	1729.05	19/7
111	1744.769
112	1760.487	47/17
113	1776.206
114	1791.925	31/11
115	1807.643
116	1823.362	43/15
117	1839.08
118	1854.799	35/12
119	1870.518
120	1886.236
121	1901.955	3/1

Harmonics

Approximation of harmonics in 121edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-5.38	+0.00	+4.95	-4.12	-5.38	-5.04	-0.43	+0.00	+6.22	-1.60	+4.95
	Relative (%)	-34.3	+0.0	+31.5	-26.2	-34.3	-32.0	-2.8	+0.0	+39.6	-10.2	+31.5
Steps (reduced)		76 (76)	121 (0)	153 (32)	177 (56)	197 (76)	214 (93)	229 (108)	242 (0)	254 (12)	264 (22)	274 (32)

Approximation of harmonics in 121edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+7.85	+5.30	-4.12	-5.82	-0.74	-5.38	-4.67	+0.84	-5.04	-6.98	-5.34
	Relative (%)	+49.9	+33.7	-26.2	-37.0	-4.7	-34.3	-29.7	+5.3	-32.0	-44.4	-34.0
Steps (reduced)		283 (41)	291 (49)	298 (56)	305 (63)	312 (70)	318 (76)	324 (82)	330 (88)	335 (93)	340 (98)	345 (103)