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	24.2
2	48.5	35/34, 36/35, 37/36, 38/37
3	72.7
4	97	18/17, 37/35
5	121.2
6	145.5	25/23, 37/34
7	169.7
8	193.9	19/17
9	218.2	17/15, 42/37
10	242.4
11	266.7	7/6
12	290.9	13/11
13	315.2	6/5
14	339.4
15	363.6	21/17, 37/30
16	387.9
17	412.1
18	436.4
19	460.6	30/23
20	484.8	41/31
21	509.1
22	533.3	34/25
23	557.6	29/21
24	581.8	7/5
25	606.1
26	630.3	36/25
27	654.5	19/13
28	678.8	34/23, 37/25
29	703
30	727.3	35/23, 38/25
31	751.5	17/11
32	775.8	36/23
33	800
34	824.2	29/18, 37/23
35	848.5	31/19
36	872.7	43/26
37	897	42/25
38	921.2
39	945.5	19/11
40	969.7
41	993.9
42	1018.2
43	1042.4	31/17, 42/23
44	1066.7
45	1090.9
46	1115.2
47	1139.4	29/15
48	1163.6
49	1187.9
50	1212.1
51	1236.4
52	1260.6
53	1284.8
54	1309.1
55	1333.3	41/19
56	1357.6
57	1381.8
58	1406.1
59	1430.3
60	1454.5
61	1478.8
62	1503	31/13
63	1527.3
64	1551.5
65	1575.8
66	1600
67	1624.2
68	1648.5
69	1672.7
70	1697
71	1721.2
72	1745.5
73	1769.7
74	1793.9	31/11
75	1818.2
76	1842.4
77	1866.7
78	1890.9
79	1915.2
80	1939.4
81	1963.6
82	1987.9	41/13
83	2012.1
84	2036.4
85	2060.6	23/7
86	2084.8
87	2109.1
88	2133.3
89	2157.6
90	2181.8
91	2206.1	25/7
92	2230.3
93	2254.5
94	2278.8	41/11
95	2303
96	2327.3	23/6
97	2351.5
98	2375.8
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)