99ed7/3

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99ed7/3

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Prime factorization	32 × 11
Step size	14.8169¢
Octave	81\99ed7/3 (1200.17¢) (→9\11ed7/3)
Twelfth	128\99ed7/3 (1896.56¢)
Consistency limit	8
Distinct consistency limit	8

99 equal divisions of 7/3 (abbreviated 99ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 99 equal parts of about 14.8 ¢ each. Each step represents a frequency ratio of (7/3)^1/99, or the 99th root of 7/3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	14.817
2	29.634
3	44.451	38/37, 39/38, 40/39, 41/40
4	59.268	29/28, 30/29, 31/30
5	74.084	24/23
6	88.901	20/19, 39/37, 41/39
7	103.718	17/16, 35/33
8	118.535	15/14
9	133.352	40/37, 41/38
10	148.169	12/11, 37/34
11	162.986	11/10
12	177.803	31/28, 41/37
13	192.619	19/17
14	207.436	44/39
15	222.253	25/22, 33/29
16	237.07	39/34
17	251.887	22/19, 37/32
18	266.704	7/6
19	281.521	20/17
20	296.338	19/16
21	311.154
22	325.971	29/24, 35/29, 41/34
23	340.788	28/23, 39/32
24	355.605	43/35
25	370.422	31/25
26	385.239	5/4
27	400.056	29/23
28	414.873
29	429.689	32/25, 41/32
30	444.506	22/17, 31/24
31	459.323	30/23, 43/33
32	474.14	25/19
33	488.957
34	503.774
35	518.591	31/23
36	533.408	34/25
37	548.224
38	563.041
39	577.858
40	592.675	31/22
41	607.492	44/31
42	622.309	43/30
43	637.126
44	651.943	35/24
45	666.76	25/17
46	681.576	43/29
47	696.393
48	711.21
49	726.027	35/23, 38/25
50	740.844	23/15, 43/28
51	755.661	17/11
52	770.478	25/16, 39/25
53	785.295
54	800.111
55	814.928	8/5
56	829.745
57	844.562
58	859.379	23/14
59	874.196
60	889.013
61	903.83	32/19
62	918.646	17/10
63	933.463	12/7
64	948.28	19/11
65	963.097
66	977.914	44/25
67	992.731	39/22
68	1007.548	34/19, 43/24
69	1022.365
70	1037.181	20/11
71	1051.998
72	1066.815	37/20
73	1081.632	28/15, 43/23
74	1096.449	32/17
75	1111.266	19/10
76	1126.083	23/12
77	1140.9	29/15
78	1155.716	37/19, 39/20
79	1170.533
80	1185.35
81	1200.167	2/1
82	1214.984
83	1229.801
84	1244.618	39/19, 41/20
85	1259.435	29/14
86	1274.251
87	1289.068	40/19
88	1303.885	17/8
89	1318.702	15/7
90	1333.519	41/19
91	1348.336	24/11, 37/17
92	1363.153	11/5
93	1377.97	31/14
94	1392.787	38/17
95	1407.603
96	1422.42	25/11
97	1437.237	39/17
98	1452.054	37/16, 44/19
99	1466.871	7/3

Harmonics

Approximation of harmonics in 99ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.17	-5.39	+0.33	-0.74	-5.23	-5.39	+0.50	+4.03	-0.57	-2.59	-5.06
	Relative (%)	+1.1	-36.4	+2.3	-5.0	-35.3	-36.4	+3.4	+27.2	-3.9	-17.5	-34.2
Steps (reduced)		81 (81)	128 (29)	162 (63)	188 (89)	209 (11)	227 (29)	243 (45)	257 (59)	269 (71)	280 (82)	290 (92)

Approximation of harmonics in 99ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+4.54	-5.23	-6.14	+0.67	-0.57	+4.19	-0.51	-0.41	+4.03	-2.43	-5.30
	Relative (%)	+30.6	-35.3	-41.4	+4.5	-3.8	+28.3	-3.4	-2.7	+27.2	-16.4	-35.8
Steps (reduced)		300 (3)	308 (11)	316 (19)	324 (27)	331 (34)	338 (41)	344 (47)	350 (53)	356 (59)	361 (64)	366 (69)