54/49

Interval information

Ratio	54/49
Factorization	2 × 33 × 7-2
Monzo	[1 3 0 -2⟩
Size in cents	168.2132¢
Names	Zalzal's mujannab, superpythagorean chromatic semitone
Color name	rr1, ruru unison
FJS name	[math]\displaystyle{ \text{A1}_{7,7} }[/math]
Special properties	reduced
Tenney height (log2 nd)	11.3696
Weil height (log2 max(n, d))	11.5098
Wilson height (sopfr(nd))	25
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Zalzal's mujannab, the interval of 54/49 introduced by Mansour Zalzal, is between 11/10 and 10/9 in size, being 540/539 sharp of 11/10 and 245/243 flat of 10/9. It is the interval between 7/6 and 9/7. Tempering out 540/539 equates it with 11/10 and leads to swetismic chords. Occurring often in JI scales, it is one of the ways 11-limit harmony gets introduced into 7-limit scales.

It is also called the superpythagorean chromatic semitone^{[idiosyncratic term]} since, in superpyth temperament, the minor third is 7/6, the major third is 9/7, and sharps and flats raise and lower by an interval approximating 54/49.

Moving to exotempering, this can be tempered out, leading to the mujannabic temperament equating 7/6 and 9/7. However, it is usually better to temper out 25/24 instead for a similar structural effect.

See also

• 49/27 – its octave complement
• Gallery of just intervals