Tool

The {7/2} heptagram is not only a symbol. It is a traversal algorithm over seven beat positions. Because 7 is prime, that traversal never gets trapped in a sub-orbit.

Danny Carey calls it sacred geometry. Gauss proved it non-constructible. They are, unexpectedly, describing the same object.

Alongside physics and astronomy, two other things have occupied an unreasonable share of my attention since adolescence: mathematics and music. Lateralus by Tool — released 2001, still in rotation — is the piece that most conspicuously occupies the intersection. The song is structurally built around the Fibonacci sequence, from the syllable counts in Maynard Keenan’s vocals to the time signature pattern that concatenates to F(16). This post works through the mathematics in some detail and asks why it works musically.