99ed4

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99ed4

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Prime factorization	32 × 11
Step size	24.2424¢
Octave	50\99ed4 (1212.12¢)
Twelfth	78\99ed4 (1890.91¢) (→26\33ed4)
Consistency limit	1
Distinct consistency limit	1

99 equal divisions of the 4th harmonic (abbreviated 99ed4) is a nonoctave tuning system that divides the interval of 4/1 into 99 equal parts of about 24.2 ¢ each. Each step represents a frequency ratio of 4^1/99, or the 99th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	24.242
2	48.485	35/34, 36/35, 37/36, 38/37
3	72.727
4	96.97	18/17, 37/35
5	121.212
6	145.455	25/23, 37/34
7	169.697
8	193.939	19/17
9	218.182	17/15, 42/37
10	242.424
11	266.667	7/6
12	290.909	13/11
13	315.152	6/5
14	339.394
15	363.636	21/17, 37/30
16	387.879
17	412.121
18	436.364
19	460.606	30/23
20	484.848	41/31
21	509.091
22	533.333	34/25
23	557.576	29/21
24	581.818	7/5
25	606.061
26	630.303	36/25
27	654.545	19/13
28	678.788	34/23, 37/25
29	703.03
30	727.273	35/23, 38/25
31	751.515	17/11
32	775.758	36/23
33	800
34	824.242	29/18, 37/23
35	848.485	31/19
36	872.727	43/26
37	896.97	42/25
38	921.212
39	945.455	19/11
40	969.697
41	993.939
42	1018.182
43	1042.424	31/17, 42/23
44	1066.667
45	1090.909
46	1115.152
47	1139.394	29/15
48	1163.636
49	1187.879
50	1212.121
51	1236.364
52	1260.606
53	1284.848
54	1309.091
55	1333.333	41/19
56	1357.576
57	1381.818
58	1406.061
59	1430.303
60	1454.545
61	1478.788
62	1503.03	31/13
63	1527.273
64	1551.515
65	1575.758
66	1600
67	1624.242
68	1648.485
69	1672.727
70	1696.97
71	1721.212
72	1745.455
73	1769.697
74	1793.939	31/11
75	1818.182
76	1842.424
77	1866.667
78	1890.909
79	1915.152
80	1939.394
81	1963.636
82	1987.879	41/13
83	2012.121
84	2036.364
85	2060.606	23/7
86	2084.848
87	2109.091
88	2133.333
89	2157.576
90	2181.818
91	2206.061	25/7
92	2230.303
93	2254.545
94	2278.788	41/11
95	2303.03
96	2327.273	23/6
97	2351.515
98	2375.758
99	2400

Harmonics

Approximation of harmonics in 99ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+12.1	-11.0	+0.0	+1.6	+1.1	+0.9	+12.1	+2.2	-10.6	-5.9	-11.0
	Relative (%)	+50.0	-45.6	+0.0	+6.5	+4.4	+3.6	+50.0	+8.9	-43.5	-24.2	-45.6
Steps (reduced)		50 (50)	78 (78)	99 (0)	115 (16)	128 (29)	139 (40)	149 (50)	157 (58)	164 (65)	171 (72)	177 (78)

Approximation of harmonics in 99ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.2	-11.3	-9.5	+0.0	-8.0	-10.0	-6.6	+1.6	-10.2	+6.3	+2.0
	Relative (%)	-17.2	-46.4	-39.1	+0.0	-32.9	-41.1	-27.2	+6.5	-42.0	+25.8	+8.4
Steps (reduced)		183 (84)	188 (89)	193 (94)	198 (0)	202 (4)	206 (8)	210 (12)	214 (16)	217 (19)	221 (23)	224 (26)