Septimagic comma

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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
Open this interval in xen-calc

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