125/81

Interval information

Ratio	125/81
Factorization	3-4 × 53
Monzo	[0 -4 3⟩
Size in cents	751.1211 ¢
Names	triptolemaic augmented fifth, Trithagorean ultrafifth
Color name	triyo 5th, y35
FJS name	[math]\displaystyle{ \text{A5}^{5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	13.3056
Weil norm (log2 max(n, d))	13.9316
Wilson norm (sopfr(nd))	27
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The triptolemaic augmented fifth or Trithagorean ultrafifth, 125/81, is a 5-limit interva of equal to 25/16 lowered by 81/80, or alternatively the Pythagorean minor sixth 128/81 lowered by 128/125. It also appears as a notable interval in the Trithagorean scale/3.5 subgroup, being the tritave-reduction of 5³. It can be closely approximated by 17/11.

Approximation

Edo approximations for 125/81 (751.12 ¢)
≤ 80edo, relative error ≤ 10%

Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
8	5\8	750.00	-1.12	-0.75
16	10\16	750.00	-1.12	-1.49
24	15\24	750.00	-1.12	-2.24
27	17\27	755.56	+4.43	+9.98
32	20\32	750.00	-1.12	-2.99
35	22\35	754.29	+3.16	+9.23
40	25\40	750.00	-1.12	-3.74
43	27\43	753.49	+2.37	+8.48
48	30\48	750.00	-1.12	-4.48
51	32\51	752.94	+1.82	+7.74
56	35\56	750.00	-1.12	-5.23
59	37\59	752.54	+1.42	+6.99
64	40\64	750.00	-1.12	-5.98
67	42\67	752.24	+1.12	+6.24
72	45\72	750.00	-1.12	-6.73
75	47\75	752.00	+0.88	+5.49
80	50\80	750.00	-1.12	-7.47