mathNEWS Issue 114.2: Friday, October 08, 2010

Spiral Out

The numbers in Tool's Lateralus

For some reason, a surprisingly large number of Mathies seem to be fans of Tool, one of the most popular progressive metal bands in the world. It could be because of the band's virtuosity, their affinity for prime time signatures, or the fact that their music is impossible to dance to, thus saving Mathies from the inevitable embarrassment of dancing in the first place.

One of the band's most mathematical songs is (somewhat surprisingly) also one of their most popular. Lateralus, from their 2001 double-platinum album of the same name, contains dozens of time signature changes seamlessly integrated with deep philosophical lyrics and powerful instrumentation. On first listen, the song flows beautifully and seamlessly from bar to bar while the lyrics evoke imagery of spirals and metamorphosis. However, when analyzed, the mathematical brilliance of the song becomes very clear.

The song begins slowly and quietly, until the lyrics start almost exactly 1.618 minutes (or φ, the golden ratio) into the song. The syllables of the verse's lyrics, when grouped by pauses, form the start of the Fibonacci sequence (from 1, 1, ..., 13 then back down). The song's chorus then follows a pattern of time signatures: 9/8, 8/8, 7/8 — a slowly descending pattern that brings a sense of convergence to the beat. This pattern of 9/8/7 also happens to be the 17th number of the Fibonacci sequence (987).

Although it would be amazing if all of these mathematical properties were purely coincident, Tool is known for using a lot of mathematical and geometric properties in their music. I would highly recommend their entire discography to any Mathie looking for some intellectually-stimulating (or just really awesome) music.

seven-eight



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