98edo

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98edo

99edo →

Prime factorization	2 × 72
Step size	12.2449¢
Fifth	57\98 (697.959¢)
Semitones (A1:m2)	7:9 (85.71¢ : 110.2¢)
Consistency limit	3
Distinct consistency limit	3

98 equal divisions of the octave (abbreviated 98edo or 98ed2), also called 98-tone equal temperament (98tet) or 98 equal temperament (98et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 98 equal parts of about 12.2 ¢ each. Each step represents a frequency ratio of 2^1/98, or the 98th root of 2.

The patent val has a flat 3, a sharp 5 and a slightly flat 7, and tempers out 81/80 in the 5-limit, making it a system of meantone family with a 4-cent-flat fifth. In the 7-limit it tempers out 1029/1024, 1728/1715, supporting mothra temperament, in the 11-limit 176/175 and 540/539, supporting mosura, and in the 13-limit 144/143 and 196/195. It provides the optimal patent val for 13-limit mosura temperament.

Harmonics

Approximation of odd harmonics in 98edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	-4.00	+5.52	-1.48	+4.25	-0.30	+4.37	+1.53	+5.25	-3.64	-5.47	-3.78
	relative (%)	-33	+45	-12	+35	-2	+36	+12	+43	-30	-45	-31
Steps (reduced)		155 (57)	228 (32)	275 (79)	311 (17)	339 (45)	363 (69)	383 (89)	401 (9)	416 (24)	430 (38)	443 (51)

Intervals

Steps	Cents	Ups and downs notation	Approximate ratios
0	0	D	1/1
1	12.2449	↑D, ↓E♭♭
2	24.4898	↑↑D, E♭♭	78/77
3	36.7347	↑3D, ↓6E♭	45/44, 49/48
4	48.9796	↑4D, ↓5E♭	33/32
5	61.2245	↑5D, ↓4E♭
6	73.4694	↑6D, ↓3E♭
7	85.7143	D♯, ↓↓E♭
8	97.9592	↑D♯, ↓E♭	55/52
9	110.204	↑↑D♯, E♭	16/15
10	122.449	↑3D♯, ↓6E	15/14
11	134.694	↑4D♯, ↓5E
12	146.939	↑5D♯, ↓4E	12/11, 49/45
13	159.184	↑6D♯, ↓3E	35/32
14	171.429	D𝄪, ↓↓E
15	183.673	↑D𝄪, ↓E	39/35, 49/44
16	195.918	E
17	208.163	↑E, ↓F♭	44/39
18	220.408	↑↑E, F♭
19	232.653	↑3E, ↓6F	8/7
20	244.898	↑4E, ↓5F	15/13
21	257.143	↑5E, ↓4F
22	269.388	↑6E, ↓3F	7/6
23	281.633	E♯, ↓↓F	33/28
24	293.878	↑E♯, ↓F	13/11
25	306.122	F
26	318.367	↑F, ↓G♭♭	77/64
27	330.612	↑↑F, G♭♭
28	342.857	↑3F, ↓6G♭	39/32
29	355.102	↑4F, ↓5G♭	16/13, 60/49
30	367.347	↑5F, ↓4G♭
31	379.592	↑6F, ↓3G♭	56/45
32	391.837	F♯, ↓↓G♭	44/35, 49/39
33	404.082	↑F♯, ↓G♭
34	416.327	↑↑F♯, G♭	14/11
35	428.571	↑3F♯, ↓6G	77/60
36	440.816	↑4F♯, ↓5G
37	453.061	↑5F♯, ↓4G	13/10
38	465.306	↑6F♯, ↓3G	64/49
39	477.551	F𝄪, ↓↓G
40	489.796	↑F𝄪, ↓G
41	502.041	G	4/3
42	514.286	↑G, ↓A♭♭	35/26, 66/49
43	526.531	↑↑G, A♭♭
44	538.776	↑3G, ↓6A♭	15/11
45	551.02	↑4G, ↓5A♭	11/8
46	563.265	↑5G, ↓4A♭
47	575.51	↑6G, ↓3A♭	39/28
48	587.755	G♯, ↓↓A♭	45/32
49	600	↑G♯, ↓A♭	55/39, 78/55
50	612.245	↑↑G♯, A♭	64/45
51	624.49	↑3G♯, ↓6A	56/39
52	636.735	↑4G♯, ↓5A	75/52
53	648.98	↑5G♯, ↓4A	16/11
54	661.224	↑6G♯, ↓3A	22/15
55	673.469	G𝄪, ↓↓A
56	685.714	↑G𝄪, ↓A	49/33, 52/35
57	697.959	A	3/2
58	710.204	↑A, ↓B♭♭
59	722.449	↑↑A, B♭♭
60	734.694	↑3A, ↓6B♭	49/32
61	746.939	↑4A, ↓5B♭	20/13
62	759.184	↑5A, ↓4B♭
63	771.429	↑6A, ↓3B♭
64	783.673	A♯, ↓↓B♭	11/7
65	795.918	↑A♯, ↓B♭
66	808.163	↑↑A♯, B♭	35/22, 78/49
67	820.408	↑3A♯, ↓6B	45/28, 77/48
68	832.653	↑4A♯, ↓5B
69	844.898	↑5A♯, ↓4B	13/8, 49/30
70	857.143	↑6A♯, ↓3B	64/39
71	869.388	A𝄪, ↓↓B
72	881.633	↑A𝄪, ↓B
73	893.878	B
74	906.122	↑B, ↓C♭	22/13
75	918.367	↑↑B, C♭	56/33
76	930.612	↑3B, ↓6C	12/7, 77/45
77	942.857	↑4B, ↓5C
78	955.102	↑5B, ↓4C	26/15
79	967.347	↑6B, ↓3C	7/4
80	979.592	B♯, ↓↓C
81	991.837	↑B♯, ↓C	39/22
82	1004.08	C
83	1016.33	↑C, ↓D♭♭	70/39
84	1028.57	↑↑C, D♭♭
85	1040.82	↑3C, ↓6D♭	64/35
86	1053.06	↑4C, ↓5D♭	11/6
87	1065.31	↑5C, ↓4D♭
88	1077.55	↑6C, ↓3D♭	28/15
89	1089.8	C♯, ↓↓D♭	15/8
90	1102.04	↑C♯, ↓D♭
91	1114.29	↑↑C♯, D♭
92	1126.53	↑3C♯, ↓6D
93	1138.78	↑4C♯, ↓5D
94	1151.02	↑5C♯, ↓4D	64/33
95	1163.27	↑6C♯, ↓3D
96	1175.51	C𝄪, ↓↓D	77/39
97	1187.76	↑C𝄪, ↓D
98	1200	D	2/1

Music

Bryan Deister

• microtonal improvisation in 98edo (2023)