51/40

Interval information

Ratio	51/40
Factorization	2-3 × 3 × 5-1 × 17
Monzo	[-3 1 -1 0 0 0 1⟩
Size in cents	420.5967¢
Name	diatismic major third
Color name	17og4, sogu 4th
FJS name	[math]\displaystyle{ \text{d4}^{17}_{5} }[/math]
Special properties	reduced
Tenney height (log2 nd)	10.9944
Weil height (log2 max(n, d))	11.3449
Wilson height (sopfr(nd))	31
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In 17-limit just intonation, 51/40 is the diatismic major third. It exceeds the Pythagorean major third (81/64) by a diatisma (136/135), hence the name.

It is approximated by:

• 7\20 (420 cents)
• 1\3 (4\12) (400 cents)
• 6\17 (12\34) (423.529 cents)
• 13\37 (421.622 cents)

See also

• 80/51 – its octave complement
• 20/17 – its fifth complement
• Gallery of just intervals