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	19.4
2	38.8	43/42, 44/43
3	58.2
4	77.6	23/22
5	97	18/17
6	116.4	31/29
7	135.9
8	155.3	23/21, 35/32
9	174.7	21/19
10	194.1	19/17, 28/25
11	213.5	26/23, 43/38
12	232.9	8/7
13	252.3	22/19
14	271.7
15	291.1	13/11
16	310.5
17	329.9	23/19
18	349.3	11/9
19	368.7	26/21
20	388.2	5/4
21	407.6	19/15, 43/34
22	427	32/25
23	446.4	22/17
24	465.8	17/13
25	485.2	41/31
26	504.6
27	524	23/17
28	543.4	26/19, 37/27
29	562.8	18/13
30	582.2	7/5
31	601.6	17/12, 41/29
32	621	43/30
33	640.5
34	659.9
35	679.3
36	698.7
37	718.1
38	737.5	23/15, 26/17
39	756.9
40	776.3	36/23
41	795.7	19/12
42	815.1	8/5
43	834.5	34/21
44	853.9	18/11
45	873.3	43/26
46	892.8
47	912.2	22/13, 39/23
48	931.6	12/7
49	951	26/15
50	970.4	7/4
51	989.8	23/13, 39/22
52	1009.2	34/19, 43/24
53	1028.6	38/21
54	1048	11/6
55	1067.4
56	1086.8	15/8
57	1106.2	36/19
58	1125.6	23/12
59	1145.1
60	1164.5
61	1183.9
62	1203.3
63	1222.7
64	1242.1	43/21
65	1261.5
66	1280.9	44/21
67	1300.3	36/17
68	1319.7	15/7
69	1339.1	13/6
70	1358.5
71	1377.9
72	1397.4
73	1416.8	34/15
74	1436.2	39/17
75	1455.6	44/19
76	1475
77	1494.4
78	1513.8	12/5
79	1533.2
80	1552.6	27/11
81	1572
82	1591.4
83	1610.8	33/13, 38/15
84	1630.2
85	1649.7
86	1669.1	21/8
87	1688.5
88	1707.9
89	1727.3	19/7
90	1746.7
91	1766.1
92	1785.5
93	1804.9	17/6
94	1824.3	43/15
95	1843.7
96	1863.1	44/15
97	1882.5
98	1902	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)