Happy Pi Day! March 14 is the one day of the year where people pretend to care about Pi, perhaps the most essential number in geometry, and possibly existence in general (the gravitational constant is a big deal too). Music has a tendency to be mathematic, as much as we'd like to ignore it. One group puts special emphasis on the science behind its music more than most: Tool. In order to honor both the band and Pi (we guess), we've assembled a brief primer on math 'n' the music of Tool.
The starting point for Tool and progressive rock in general is time signatures. A time signature, or meter, indicates how many notes (and what kind of note) are played during a measure. The average pop song uses 4/4 (four quarter notes per measure), and occasionally a "polka" beat such as 2/4 (two quarters per measure). Many prog and alternative bands choose more obscure measures to create more distinctive/less comfortable music.
Tool decided that just opting for one odd meter wasn't enough for its single "Schism," and ended up switching meters an estimated 47 times during the 6:46 song (hence why your garage band struggles to cover it). Musicologists argue whether the verse meter is 12/8 (compound) or duel cases of 5/8 (complex), a trick some have argued is the "schism" the title refers to. Other oddball meters include the bizarre 6.5/8 (fractional), which can also be interpreted as 13/16. The song features only one bar of simple meter (a 4/4).
Much of the power behind odd time signatures lies in the ability of the drummer, who holds the most math-oriented position in any given band. Tool drummer Danny Carey bases his drum patterns on geometric figures associated with magic and the occult. One example is the unicursal hexagram associated with Thelema, the philosophical law practiced by noted occultist Aleister Crowley among others. Carey can call it what he wants, but we call it math. And it seems to be working for him.
Tool's mathematical songwriting peaks with "Lateralus," a single from the album of the same name. Listeners without context may be slightly confused by vocalist Maynard James Keenan's odd pattern of delivery. Mathematicians and maybe a few musicologists began to recognize that the number of syllables in each bar corresponded with the Fibonacci sequence, a series of numbers that explain the golden ration, or the pattern found in the size and shapes of lifeforms the world over. Keenan's lyrics reference a spiral on multiple occasions, representing the "golden spiral" created by drawing circular arcs across the squares created by the Fibonacci sequence. That, of course, isn't the end of Tool's artful approach to the topic. Keenan travels back and forth through the first several numbers in the sequence, but the rest of the band gets kudos for the trio of time signatures it uses during the song's chorus: 9/8, 8/8 and 7/8. The 16th number in the Fibonacci sequence is 987.
We realize that Pi hasn't actually played into any of this math talk, and we apologize to the number of the day. Unfortunately, we couldn't find anything to pi-ticular in Tool's music so we cheated a bit: Keenan's side project is named A Perfect Circle. And you can't draw a perfect circle without Pi.
