980/729

Interval information

Ratio	980/729
Factorization	22 × 3-6 × 5 × 72
Monzo	[2 -6 1 2⟩
Size in cents	512.2355¢
Name	sensamagic fourth
Color name	zzy5, zozoyo 5th
FJS name	[math]\displaystyle{ \text{d5}^{5,49} }[/math]
Special properties	reduced
Tenney height (log2 nd)	19.4464
Weil height (log2 max(n, d))	19.8733
Wilson height (sopfr(nd))	41
Open this interval in xen-calc

980/729, the sensamagic fourth is a 7-limit ratio of about 512 cents, sharp of a just fourth 4/3 by a sensamagic comma 245/243.

It arises in just intonation as the difference between the supermajor third 9/7 and the semidiminished seventh 140/81, making it a critical tempering target in the Canovian chord. However, its distinction from 4/3 is emphasised in the canou family of temperaments, through its accessibility by two steps of the 81/70-generator.

See also

• 729/490 – its octave complement
• Gallery of just intervals