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, vE♭♭
2	24.4898	^^D, E♭♭	78/77
3	36.7347	^3D, v6E♭	45/44, 49/48
4	48.9796	^4D, v5E♭	33/32
5	61.2245	^5D, v4E♭
6	73.4694	^6D, v3E♭
7	85.7143	D♯, vvE♭
8	97.9592	^D♯, vE♭	55/52
9	110.204	^^D♯, E♭	16/15
10	122.449	^3D♯, v6E	15/14
11	134.694	^4D♯, v5E
12	146.939	^5D♯, v4E	12/11, 49/45
13	159.184	^6D♯, v3E	35/32
14	171.429	D𝄪, vvE
15	183.673	^D𝄪, vE	39/35, 49/44
16	195.918	E
17	208.163	^E, vF♭	44/39
18	220.408	^^E, F♭
19	232.653	^3E, v6F	8/7
20	244.898	^4E, v5F	15/13
21	257.143	^5E, v4F
22	269.388	^6E, v3F	7/6
23	281.633	E♯, vvF	33/28
24	293.878	^E♯, vF	13/11
25	306.122	F
26	318.367	^F, vG♭♭	77/64
27	330.612	^^F, G♭♭
28	342.857	^3F, v6G♭	39/32
29	355.102	^4F, v5G♭	16/13, 60/49
30	367.347	^5F, v4G♭
31	379.592	^6F, v3G♭	56/45
32	391.837	F♯, vvG♭	44/35, 49/39
33	404.082	^F♯, vG♭
34	416.327	^^F♯, G♭	14/11
35	428.571	^3F♯, v6G	77/60
36	440.816	^4F♯, v5G
37	453.061	^5F♯, v4G	13/10
38	465.306	^6F♯, v3G	64/49
39	477.551	F𝄪, vvG
40	489.796	^F𝄪, vG
41	502.041	G	4/3
42	514.286	^G, vA♭♭	35/26, 66/49
43	526.531	^^G, A♭♭
44	538.776	^3G, v6A♭	15/11
45	551.02	^4G, v5A♭	11/8
46	563.265	^5G, v4A♭
47	575.51	^6G, v3A♭	39/28
48	587.755	G♯, vvA♭	45/32
49	600	^G♯, vA♭	55/39, 78/55
50	612.245	^^G♯, A♭	64/45
51	624.49	^3G♯, v6A	56/39
52	636.735	^4G♯, v5A	75/52
53	648.98	^5G♯, v4A	16/11
54	661.224	^6G♯, v3A	22/15
55	673.469	G𝄪, vvA
56	685.714	^G𝄪, vA	49/33, 52/35
57	697.959	A	3/2
58	710.204	^A, vB♭♭
59	722.449	^^A, B♭♭
60	734.694	^3A, v6B♭	49/32
61	746.939	^4A, v5B♭	20/13
62	759.184	^5A, v4B♭
63	771.429	^6A, v3B♭
64	783.673	A♯, vvB♭	11/7
65	795.918	^A♯, vB♭
66	808.163	^^A♯, B♭	35/22, 78/49
67	820.408	^3A♯, v6B	45/28, 77/48
68	832.653	^4A♯, v5B
69	844.898	^5A♯, v4B	13/8, 49/30
70	857.143	^6A♯, v3B	64/39
71	869.388	A𝄪, vvB
72	881.633	^A𝄪, vB
73	893.878	B
74	906.122	^B, vC♭	22/13
75	918.367	^^B, C♭	56/33
76	930.612	^3B, v6C	12/7, 77/45
77	942.857	^4B, v5C
78	955.102	^5B, v4C	26/15
79	967.347	^6B, v3C	7/4
80	979.592	B♯, vvC
81	991.837	^B♯, vC	39/22
82	1004.08	C
83	1016.33	^C, vD♭♭	70/39
84	1028.57	^^C, D♭♭
85	1040.82	^3C, v6D♭	64/35
86	1053.06	^4C, v5D♭	11/6
87	1065.31	^5C, v4D♭
88	1077.55	^6C, v3D♭	28/15
89	1089.8	C♯, vvD♭	15/8
90	1102.04	^C♯, vD♭
91	1114.29	^^C♯, D♭
92	1126.53	^3C♯, v6D
93	1138.78	^4C♯, v5D
94	1151.02	^5C♯, v4D	64/33
95	1163.27	^6C♯, v3D
96	1175.51	C𝄪, vvD	77/39
97	1187.76	^C𝄪, vD
98	1200	D	2/1

Music

Bryan Deister

• microtonal improvisation in 98edo (2023)