98edt

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98edt

99edt →

Prime factorization	2 × 72
Step size	19.4077¢
Octave	62\98edt (1203.28¢) (→31\49edt)
Consistency limit	7
Distinct consistency limit	7

98 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 98edt or 98ed3), is a nonoctave tuning system that divides the interval of 3/1 into 98 equal parts of about 19.4 ¢ each. Each step represents a frequency ratio of 3^1/98, or the 98th root of 3.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	19.408
2	38.815	43/42, 44/43
3	58.223
4	77.631	23/22
5	97.039	18/17
6	116.446	31/29
7	135.854
8	155.262	23/21, 35/32
9	174.669	21/19
10	194.077	19/17, 28/25
11	213.485	26/23, 43/38
12	232.892	8/7
13	252.3	22/19
14	271.708
15	291.116	13/11
16	310.523
17	329.931	23/19
18	349.339	11/9
19	368.746	26/21
20	388.154	5/4
21	407.562	19/15, 43/34
22	426.969	32/25
23	446.377	22/17
24	465.785	17/13
25	485.193	41/31
26	504.6
27	524.008	23/17
28	543.416	26/19, 37/27
29	562.823	18/13
30	582.231	7/5
31	601.639	17/12, 41/29
32	621.047	43/30
33	640.454
34	659.862
35	679.27
36	698.677
37	718.085
38	737.493	23/15, 26/17
39	756.9
40	776.308	36/23
41	795.716	19/12
42	815.124	8/5
43	834.531	34/21
44	853.939	18/11
45	873.347	43/26
46	892.754
47	912.162	22/13, 39/23
48	931.57	12/7
49	950.978	26/15
50	970.385	7/4
51	989.793	23/13, 39/22
52	1009.201	34/19, 43/24
53	1028.608	38/21
54	1048.016	11/6
55	1067.424
56	1086.831	15/8
57	1106.239	36/19
58	1125.647	23/12
59	1145.055
60	1164.462
61	1183.87
62	1203.278
63	1222.685
64	1242.093	43/21
65	1261.501
66	1280.908	44/21
67	1300.316	36/17
68	1319.724	15/7
69	1339.132	13/6
70	1358.539
71	1377.947
72	1397.355
73	1416.762	34/15
74	1436.17	39/17
75	1455.578	44/19
76	1474.986
77	1494.393
78	1513.801	12/5
79	1533.209
80	1552.616	27/11
81	1572.024
82	1591.432
83	1610.839	33/13, 38/15
84	1630.247
85	1649.655
86	1669.063	21/8
87	1688.47
88	1707.878
89	1727.286	19/7
90	1746.693
91	1766.101
92	1785.509
93	1804.916	17/6
94	1824.324	43/15
95	1843.732
96	1863.14	44/15
97	1882.547
98	1901.955	3/1

Harmonics

Approximation of harmonics in 98edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.28	+0.00	+6.56	+8.40	+3.28	+8.11	-9.57	+0.00	-7.73	+1.93	+6.56
	Relative (%)	+16.9	+0.0	+33.8	+43.3	+16.9	+41.8	-49.3	+0.0	-39.9	+9.9	+33.8
Steps (reduced)		62 (62)	98 (0)	124 (26)	144 (46)	160 (62)	174 (76)	185 (87)	196 (0)	205 (9)	214 (18)	222 (26)

Approximation of harmonics in 98edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+3.84	-8.02	+8.40	-6.30	+5.19	+3.28	+6.71	-4.46	+8.11	+5.21	+5.88
	Relative (%)	+19.8	-41.3	+43.3	-32.4	+26.8	+16.9	+34.6	-23.0	+41.8	+26.8	+30.3
Steps (reduced)		229 (33)	235 (39)	242 (46)	247 (51)	253 (57)	258 (62)	263 (67)	267 (71)	272 (76)	276 (80)	280 (84)