99edt

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99edt

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Prime factorization	32 × 11
Step size	19.2117¢
Octave	62\99edt (1191.12¢)
Consistency limit	2
Distinct consistency limit	2

99 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 99edt or 99ed3), is a nonoctave tuning system that divides the interval of 3/1 into 99 equal parts of about 19.2 ¢ each. Each step represents a frequency ratio of 3^1/99, or the 99th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	19.2
2	38.4
3	57.6	30/29, 31/30
4	76.8
5	96.1	19/18, 37/35
6	115.3	31/29
7	134.5	27/25
8	153.7
9	172.9	21/19
10	192.1	19/17
11	211.3	35/31
12	230.5
13	249.8	15/13
14	269	7/6
15	288.2	13/11
16	307.4	37/31
17	326.6	35/29
18	345.8	11/9
19	365	21/17, 37/30
20	384.2
21	403.4
22	422.7	37/29
23	441.9
24	461.1
25	480.3	29/22, 33/25
26	499.5
27	518.7
28	537.9	15/11
29	557.1	29/21
30	576.4
31	595.6	31/22
32	614.8
33	634
34	653.2
35	672.4	31/21
36	691.6
37	710.8
38	730	29/19
39	749.3
40	768.5	39/25
41	787.7
42	806.9	43/27
43	826.1	29/18
44	845.3	31/19
45	864.5
46	883.7	5/3
47	902.9
48	922.2	29/17
49	941.4	31/18, 43/25
50	960.6
51	979.8	37/21
52	999	41/23
53	1018.2	9/5
54	1037.4
55	1056.6	35/19
56	1075.9
57	1095.1
58	1114.3
59	1133.5	25/13
60	1152.7	35/18, 37/19
61	1171.9
62	1191.1
63	1210.3
64	1229.5
65	1248.8	35/17, 37/18
66	1268
67	1287.2
68	1306.4
69	1325.6
70	1344.8	37/17
71	1364	11/5
72	1383.2
73	1402.5
74	1421.7	25/11
75	1440.9
76	1460.1
77	1479.3
78	1498.5
79	1517.7
80	1536.9	17/7
81	1556.1	27/11
82	1575.4
83	1594.6
84	1613.8	33/13
85	1633	18/7
86	1652.2	13/5
87	1671.4
88	1690.6
89	1709.8
90	1729.1	19/7
91	1748.3
92	1767.5	25/9
93	1786.7
94	1805.9
95	1825.1	43/15
96	1844.3	29/10
97	1863.5
98	1882.7
99	1902	3/1

Harmonics

Approximation of harmonics in 99edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-8.88	+0.00	+1.46	-0.62	-8.88	-6.78	-7.42	+0.00	-9.50	-1.60	+1.46
	Relative (%)	-46.2	+0.0	+7.6	-3.2	-46.2	-35.3	-38.6	+0.0	-49.4	-8.3	+7.6
Steps (reduced)		62 (62)	99 (0)	125 (26)	145 (46)	161 (62)	175 (76)	187 (88)	198 (0)	207 (9)	216 (18)	224 (26)

Approximation of harmonics in 99edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.63	+3.55	-0.62	+2.92	-5.98	-8.88	-6.42	+0.84	-6.78	+8.74	+8.63
	Relative (%)	-13.7	+18.5	-3.2	+15.2	-31.1	-46.2	-33.4	+4.4	-35.3	+45.5	+44.9
Steps (reduced)		231 (33)	238 (40)	244 (46)	250 (52)	255 (57)	260 (62)	265 (67)	270 (72)	274 (76)	279 (81)	283 (85)