980/729

Interval information

Ratio	980/729
Factorization	22 × 3-6 × 5 × 72
Monzo	[2 -6 1 2⟩
Size in cents	512.23552¢
Names	retrosensamagic fourth, complex sensamagic fourth
Color name	zzy5, zozoyo 5th
FJS name	[math]\text{d5}^{5,7,7}[/math]
Special properties	reduced
Tenney height (log2 nd)	19.4464
Weil height (log2 max(n, d))	19.8733
Wilson height (sopfr(nd))	41
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~4.10482 bits
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980/729, the retrosensamagic fourth or complex sensamagic fourth is a 7-limit interval of about 512 cents, sharp of a perfect 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 Sensamagic dominant 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