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	19.8
2	39.7
3	59.5	30/29
4	79.3	22/21, 45/43
5	99.2
6	119
7	138.8
8	158.7	23/21, 34/31
9	178.5	41/37
10	198.3	37/33
11	218.2	17/15
12	238	31/27, 39/34, 47/41
13	257.9
14	277.7	27/23
15	297.5
16	317.4
17	337.2	45/37
18	357	43/35
19	376.9	41/33
20	396.7	39/31, 49/39
21	416.5
22	436.4	9/7
23	456.2	13/10
24	476
25	495.9
26	515.7	31/23
27	535.5	15/11
28	555.4
29	575.2
30	595	31/22
31	614.9
32	634.7	13/9
33	654.5
34	674.4	31/21
35	694.2
36	714
37	733.9	29/19
38	753.7	17/11
39	773.6
40	793.4	49/31
41	813.2
42	833.1	34/21
43	852.9
44	872.7
45	892.6
46	912.4	22/13, 39/23
47	932.2
48	952.1
49	971.9
50	991.7	39/22
51	1011.6
52	1031.4	49/27
53	1051.2
54	1071.1	13/7
55	1090.9
56	1110.7	19/10
57	1130.6
58	1150.4
59	1170.2
60	1190.1
61	1209.9
62	1229.8
63	1249.6	35/17
64	1269.4
65	1289.3
66	1309.1	49/23
67	1328.9
68	1348.8
69	1368.6
70	1388.4	29/13
71	1408.3
72	1428.1
73	1447.9	30/13
74	1467.8	7/3
75	1487.6
76	1507.4
77	1527.3
78	1547.1	22/9
79	1566.9	47/19
80	1586.8
81	1606.6	43/17
82	1626.4
83	1646.3
84	1666.1	34/13
85	1686	45/17
86	1705.8
87	1725.6
88	1745.5
89	1765.3
90	1785.1
91	1805
92	1824.8	43/15
93	1844.6	29/10
94	1864.5
95	1884.3
96	1904.1
97	1924
98	1943.8
99	1963.6
100	1983.5	22/7
101	2003.3	35/11
102	2023.1
103	2043
104	2062.8
105	2082.6	10/3
106	2102.5
107	2122.3
108	2142.1	31/9
109	2162
110	2181.8
111	2201.7
112	2221.5
113	2241.3
114	2261.2
115	2281
116	2300.8	34/9
117	2320.7
118	2340.5
119	2360.3	43/11
120	2380.2
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)