729/490

Interval information

Ratio	729/490
Factorization	2-1 × 36 × 5-1 × 7-2
Monzo	[-1 6 -1 -2⟩
Size in cents	687.7645¢
Name	complex sensamagic fifth
Color name	rrg4, rurugu 4th
FJS name	[math]\displaystyle{ \text{A4}_{5,7,7} }[/math]
Special properties	reduced
Tenney height (log2 nd)	18.4464
Weil height (log2 max(n, d))	19.0196
Wilson height (sopfr(nd))	39
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~3.95741 bits
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729/490, the complex sensamagic fifth is a 7-limit ratio of about 687 cents, flat of a just fifth 3/2 by a sensamagic comma 245/243.

It arises in just intonation as the difference between the semidiminished fourth 35/27 and the supermajor seventh 27/14, making it a critical tempering target in the Sensamagic dominant chord. However, its distinction from 3/2 is emphasised in the canou family of temperaments, through its accessibility by two steps of the 81/70-generator.

See also

• 980/729 – its octave complement
• Gallery of just intervals