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	14.8
2	29.6
3	44.5	38/37, 39/38, 40/39, 41/40
4	59.3	29/28, 30/29, 31/30
5	74.1	24/23
6	88.9	20/19, 39/37, 41/39
7	103.7	17/16, 35/33
8	118.5	15/14
9	133.4	40/37, 41/38
10	148.2	12/11, 37/34
11	163	11/10
12	177.8	31/28, 41/37
13	192.6	19/17
14	207.4	44/39
15	222.3	25/22, 33/29
16	237.1	39/34
17	251.9	22/19, 37/32
18	266.7	7/6
19	281.5	20/17
20	296.3	19/16
21	311.2
22	326	29/24, 35/29, 41/34
23	340.8	28/23, 39/32
24	355.6	43/35
25	370.4	31/25
26	385.2	5/4
27	400.1	29/23
28	414.9
29	429.7	32/25, 41/32
30	444.5	22/17, 31/24
31	459.3	30/23, 43/33
32	474.1	25/19
33	489
34	503.8
35	518.6	31/23
36	533.4	34/25
37	548.2
38	563
39	577.9
40	592.7	31/22
41	607.5	44/31
42	622.3	43/30
43	637.1
44	651.9	35/24
45	666.8	25/17
46	681.6	43/29
47	696.4
48	711.2
49	726	35/23, 38/25
50	740.8	23/15, 43/28
51	755.7	17/11
52	770.5	25/16, 39/25
53	785.3
54	800.1
55	814.9	8/5
56	829.7
57	844.6
58	859.4	23/14
59	874.2
60	889
61	903.8	32/19
62	918.6	17/10
63	933.5	12/7
64	948.3	19/11
65	963.1
66	977.9	44/25
67	992.7	39/22
68	1007.5	34/19, 43/24
69	1022.4
70	1037.2	20/11
71	1052
72	1066.8	37/20
73	1081.6	28/15, 43/23
74	1096.4	32/17
75	1111.3	19/10
76	1126.1	23/12
77	1140.9	29/15
78	1155.7	37/19, 39/20
79	1170.5
80	1185.4
81	1200.2	2/1
82	1215
83	1229.8
84	1244.6	39/19, 41/20
85	1259.4	29/14
86	1274.3
87	1289.1	40/19
88	1303.9	17/8
89	1318.7	15/7
90	1333.5	41/19
91	1348.3	24/11, 37/17
92	1363.2	11/5
93	1378	31/14
94	1392.8	38/17
95	1407.6
96	1422.4	25/11
97	1437.2	39/17
98	1452.1	37/16, 44/19
99	1466.9	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)