Septimagic comma

537824/531441, the septimagic comma or magi comma is a no-fives 7-limit comma measuring 20.7 cents. It is the difference between a stack of five 14/9's and 9/1.

Interval information

Ratio	537824/531441
Factorization	25 × 3-12 × 75
Monzo	[5 -12 0 5⟩
Size in cents	20.66952¢
Names	septimagic comma, magi comma
Color name	sz54, saquinzo 4th
FJS name	[math]\displaystyle{ \text{ddd4}^{7,7,7,7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	38.0563
Weil norm (log2 max(n, d))	38.0735
Wilson norm (sopfr(nd))	81
Comma size	small
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Temperaments

Tempering out this comma gives the rank-3 septimagic temperament in the full 7-limit, and the magi temperament in its minimal prime subgroup of 2.3.7. Magi is the no-five restriction of magic.

Etymology

This comma was named by Xenllium in 2026 as a contraction of septimal magic into a single word.

See also

• Septimagic clan