75/64

Interval information

Ratio	75/64
Factorization	2-6 × 3 × 52
Monzo	[-6 1 2⟩
Size in cents	274.5824¢
Name	classic(al) augmented second
Color name	yy2, yoyo 2nd
FJS name	[math]\displaystyle{ \text{A2}^{5,5} }[/math]
Special properties	reduced, reduced harmonic
Tenney norm (log2 nd)	12.2288
Weil norm (log2 max(n, d))	12.4576
Wilson norm (sopfr(nd))	25
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75/64, the classic(al) augmented second, arises as 9/8 sharpened by 25/24. It can also be created by stacking nine 3/2's, octave reducing, and subtracting two syntonic commas. It is the unchanged interval (eigenmonzo) for 2/9-comma meantone. In terms of interval regions, it can be treated as a subminor third.

Approximation

Edo approximations for 75/64 (274.58 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	1\4	300.00	+25.42	+8.47
9	2\9	266.67	-7.92	-5.94
13	3\13	276.92	+2.34	+2.54
22	5\22	272.73	-1.86	-3.40
26	6\26	276.92	+2.34	+5.07
31	7\31	270.97	-3.61	-9.34
35	8\35	274.29	-0.30	-0.87
39	9\39	276.92	+2.34	+7.61
44	10\44	272.73	-1.86	-6.80
48	11\48	275.00	+0.42	+1.67
57	13\57	273.68	-0.90	-4.27
61	14\61	275.41	+0.83	+4.21
70	16\70	274.29	-0.30	-1.73
74	17\74	275.68	+1.09	+6.74
79	18\79	273.42	-1.16	-7.67

See also

• 128/75 – its octave complement
• Gallery of just intervals