121ed4

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121ed4

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Prime factorization	112
Step size	19.8347¢
Octave	61\121ed4 (1209.92¢)
Twelfth	96\121ed4 (1904.13¢)
Consistency limit	1
Distinct consistency limit	1

121 equal divisions of the 4th harmonic (abbreviated 121ed4) is a nonoctave tuning system that divides the interval of 4/1 into 121 equal parts of about 19.8 ¢ each. Each step represents a frequency ratio of 4^1/121, or the 121st root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	19.835
2	39.669
3	59.504	30/29
4	79.339	22/21, 45/43
5	99.174
6	119.008
7	138.843
8	158.678	23/21, 34/31
9	178.512	41/37
10	198.347	37/33
11	218.182	17/15
12	238.017	31/27, 39/34, 47/41
13	257.851
14	277.686	27/23
15	297.521
16	317.355
17	337.19	45/37
18	357.025	43/35
19	376.86	41/33
20	396.694	39/31, 49/39
21	416.529
22	436.364	9/7
23	456.198	13/10
24	476.033
25	495.868
26	515.702	31/23
27	535.537	15/11
28	555.372
29	575.207
30	595.041	31/22
31	614.876
32	634.711	13/9
33	654.545
34	674.38	31/21
35	694.215
36	714.05
37	733.884	29/19
38	753.719	17/11
39	773.554
40	793.388	49/31
41	813.223
42	833.058	34/21
43	852.893
44	872.727
45	892.562
46	912.397	22/13, 39/23
47	932.231
48	952.066
49	971.901
50	991.736	39/22
51	1011.57
52	1031.405	49/27
53	1051.24
54	1071.074	13/7
55	1090.909
56	1110.744	19/10
57	1130.579
58	1150.413
59	1170.248
60	1190.083
61	1209.917
62	1229.752
63	1249.587	35/17
64	1269.421
65	1289.256
66	1309.091	49/23
67	1328.926
68	1348.76
69	1368.595
70	1388.43	29/13
71	1408.264
72	1428.099
73	1447.934	30/13
74	1467.769	7/3
75	1487.603
76	1507.438
77	1527.273
78	1547.107	22/9
79	1566.942	47/19
80	1586.777
81	1606.612	43/17
82	1626.446
83	1646.281
84	1666.116	34/13
85	1685.95	45/17
86	1705.785
87	1725.62
88	1745.455
89	1765.289
90	1785.124
91	1804.959
92	1824.793	43/15
93	1844.628	29/10
94	1864.463
95	1884.298
96	1904.132
97	1923.967
98	1943.802
99	1963.636
100	1983.471	22/7
101	2003.306	35/11
102	2023.14
103	2042.975
104	2062.81
105	2082.645	10/3
106	2102.479
107	2122.314
108	2142.149	31/9
109	2161.983
110	2181.818
111	2201.653
112	2221.488
113	2241.322
114	2261.157
115	2280.992
116	2300.826	34/9
117	2320.661
118	2340.496
119	2360.331	43/11
120	2380.165
121	2400

Harmonics

Approximation of harmonics in 121ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.92	+2.18	+0.00	-9.45	-7.74	+3.07	+9.92	+4.35	+0.46	-5.86	+2.18
	Relative (%)	+50.0	+11.0	+0.0	-47.7	-39.0	+15.5	+50.0	+22.0	+2.3	-29.6	+11.0
Steps (reduced)		61 (61)	96 (96)	121 (0)	140 (19)	156 (35)	170 (49)	182 (61)	192 (71)	201 (80)	209 (88)	217 (96)

Approximation of harmonics in 121ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.45	-6.84	-7.28	+0.00	-5.78	-5.56	+0.01	-9.45	+5.25	+4.05	+6.44
	Relative (%)	+12.3	-34.5	-36.7	+0.0	-29.2	-28.0	+0.0	-47.7	+26.5	+20.4	+32.5
Steps (reduced)		224 (103)	230 (109)	236 (115)	242 (0)	247 (5)	252 (10)	257 (15)	261 (19)	266 (24)	270 (28)	274 (32)