88/81

Interval information

Ratio	88/81
Factorization	23 × 3-4 × 11
Monzo	[3 -4 0 0 1⟩
Size in cents	143.4979¢
Names	2nd undecimal neutral second, Alpharabian artoneutral second
Color name	1o2, ilo second
FJS name	[math]\displaystyle{ \text{m2}^{11} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	12.7993
Weil norm (log2 max(n, d))	12.9189
Wilson norm (sopfr(nd))	29
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88/81, the 2nd undecimal neutral second, is an interval of about 143.5 cents. It is 352/351 (4.9 cents) sharp of 13/12 and 243/242 (7.1 cents) flat of 12/11. It is also the interval between 9/8 and 11/9. In Alpharabian tuning it is known as the Alpharabian artoneutral second.

Approximation

Edo approximations for 88/81 (143.50 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
8	1\8	150.00	+6.50	+4.33
9	1\9	133.33	-10.16	-7.62
16	2\16	150.00	+6.50	+8.67
17	2\17	141.18	-2.32	-3.29
25	3\25	144.00	+0.50	+1.05
33	4\33	145.45	+1.96	+5.38
34	4\34	141.18	-2.32	-6.58
41	5\41	146.34	+2.84	+9.72
42	5\42	142.86	-0.64	-2.24
50	6\50	144.00	+0.50	+2.09
51	6\51	141.18	-2.32	-9.87
58	7\58	144.83	+1.33	+6.43
59	7\59	142.37	-1.13	-5.53
67	8\67	143.28	-0.21	-1.20
75	9\75	144.00	+0.50	+3.14
76	9\76	142.11	-1.39	-8.82

See also

• 81/44 – its octave complement
• Gallery of just intervals