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	19.212
2	38.423
3	57.635	30/29, 31/30
4	76.847
5	96.058	19/18, 37/35
6	115.27	31/29
7	134.482	27/25
8	153.693
9	172.905	21/19
10	192.117	19/17
11	211.328	35/31
12	230.54
13	249.752	15/13
14	268.963	7/6
15	288.175	13/11
16	307.387	37/31
17	326.598	35/29
18	345.81	11/9
19	365.022	21/17, 37/30
20	384.233
21	403.445
22	422.657	37/29
23	441.868
24	461.08
25	480.292	29/22, 33/25
26	499.503
27	518.715
28	537.927	15/11
29	557.138	29/21
30	576.35
31	595.562	31/22
32	614.773
33	633.985
34	653.197
35	672.408	31/21
36	691.62
37	710.832
38	730.043	29/19
39	749.255
40	768.467	39/25
41	787.678
42	806.89	43/27
43	826.102	29/18
44	845.313	31/19
45	864.525
46	883.737	5/3
47	902.948
48	922.16	29/17
49	941.372	31/18, 43/25
50	960.583
51	979.795	37/21
52	999.007	41/23
53	1018.218	9/5
54	1037.43
55	1056.642	35/19
56	1075.853
57	1095.065
58	1114.277
59	1133.488	25/13
60	1152.7	35/18, 37/19
61	1171.912
62	1191.123
63	1210.335
64	1229.547
65	1248.758	35/17, 37/18
66	1267.97
67	1287.182
68	1306.393
69	1325.605
70	1344.817	37/17
71	1364.028	11/5
72	1383.24
73	1402.452
74	1421.663	25/11
75	1440.875
76	1460.087
77	1479.298
78	1498.51
79	1517.722
80	1536.933	17/7
81	1556.145	27/11
82	1575.357
83	1594.568
84	1613.78	33/13
85	1632.992	18/7
86	1652.203	13/5
87	1671.415
88	1690.627
89	1709.838
90	1729.05	19/7
91	1748.262
92	1767.473	25/9
93	1786.685
94	1805.897
95	1825.108	43/15
96	1844.32	29/10
97	1863.532
98	1882.743
99	1901.955	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)