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.

Theory

98edt is related to 62edo, but with the twelfth rather than the octave being just. The octave is stretched by about 3.28 cents, same as in 49edt. Unlike 62edo, which is consistent to the 8-integer-limit, 98edt is only consistent to the 7-integer-limit. The prime harmonics 2 to 23 are all tuned sharp, except for 3.

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 (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+3.84	-8.02	+8.40	-6.30	+5.19	+3.28	+6.71	-4.46	+8.11	+5.21	+5.88	-9.57
	Relative (%)	+19.8	-41.3	+43.3	-32.4	+26.8	+16.9	+34.6	-23.0	+41.8	+26.8	+30.3	-49.3
Steps (reduced)		229 (33)	235 (39)	242 (46)	247 (51)	253 (57)	258 (62)	263 (67)	267 (71)	272 (76)	276 (80)	280 (84)	283 (87)

Intervals

Steps	Cents	Hekts	Approximate ratios
0	0	0	1/1
1	19.4	13.3
2	38.8	26.5	43/42, 44/43
3	58.2	39.8
4	77.6	53.1	23/22
5	97	66.3	18/17
6	116.4	79.6	31/29
7	135.9	92.9
8	155.3	106.1	23/21, 35/32
9	174.7	119.4	21/19
10	194.1	132.7	19/17, 28/25
11	213.5	145.9	26/23, 43/38
12	232.9	159.2	8/7
13	252.3	172.4	22/19
14	271.7	185.7
15	291.1	199	13/11
16	310.5	212.2
17	329.9	225.5	23/19
18	349.3	238.8	11/9
19	368.7	252	26/21
20	388.2	265.3	5/4
21	407.6	278.6	19/15, 43/34
22	427	291.8	32/25
23	446.4	305.1	22/17
24	465.8	318.4	17/13
25	485.2	331.6	41/31
26	504.6	344.9
27	524	358.2	23/17
28	543.4	371.4	26/19, 37/27
29	562.8	384.7	18/13
30	582.2	398	7/5
31	601.6	411.2	17/12, 41/29
32	621	424.5	43/30
33	640.5	437.8
34	659.9	451
35	679.3	464.3
36	698.7	477.6
37	718.1	490.8
38	737.5	504.1	23/15, 26/17
39	756.9	517.3
40	776.3	530.6	36/23
41	795.7	543.9	19/12
42	815.1	557.1	8/5
43	834.5	570.4	34/21
44	853.9	583.7	18/11
45	873.3	596.9	43/26
46	892.8	610.2
47	912.2	623.5	22/13, 39/23
48	931.6	636.7	12/7
49	951	650	26/15
50	970.4	663.3	7/4
51	989.8	676.5	23/13, 39/22
52	1009.2	689.8	34/19, 43/24
53	1028.6	703.1	38/21
54	1048	716.3	11/6
55	1067.4	729.6
56	1086.8	742.9	15/8
57	1106.2	756.1	36/19
58	1125.6	769.4	23/12
59	1145.1	782.7
60	1164.5	795.9
61	1183.9	809.2
62	1203.3	822.4
63	1222.7	835.7
64	1242.1	849	43/21
65	1261.5	862.2
66	1280.9	875.5	44/21
67	1300.3	888.8	36/17
68	1319.7	902	15/7
69	1339.1	915.3	13/6
70	1358.5	928.6
71	1377.9	941.8
72	1397.4	955.1
73	1416.8	968.4	34/15
74	1436.2	981.6	39/17
75	1455.6	994.9	44/19
76	1475	1008.2
77	1494.4	1021.4
78	1513.8	1034.7	12/5
79	1533.2	1048
80	1552.6	1061.2	27/11
81	1572	1074.5
82	1591.4	1087.8
83	1610.8	1101	33/13, 38/15
84	1630.2	1114.3
85	1649.7	1127.6
86	1669.1	1140.8	21/8
87	1688.5	1154.1
88	1707.9	1167.3
89	1727.3	1180.6	19/7
90	1746.7	1193.9
91	1766.1	1207.1
92	1785.5	1220.4
93	1804.9	1233.7	17/6
94	1824.3	1246.9	43/15
95	1843.7	1260.2
96	1863.1	1273.5	44/15
97	1882.5	1286.7
98	1902	1300	3/1

See also

• 62edo – relative edo
• 160ed6 – relative ed6