“Math is a wonderful thing
Math is a really cool thing.
So, get off your ass, let’s do some math
math, math, math, math, math.”
-Jack Black, School of Rock
Math is everywhere. It is used to solve not only the most complex engineering problems, but also the most mundane (like how long it would take to break even after an expensive engineering education). Math and music have always had a very special relationship. Although there is no formal theory relating the two, elements of music like rhythm, meter, pitch, tempo, and beat can be related to the measurement of time and frequency.
For the musically illiterate, here is a bit of music theory. A time signature is basically the number of beats that are contained in each bar of music. Conventional rock and roll music follow a 4/4-time signature, which is four beat-units in a bar. Bored of this convention, musicians in the early ’60s decided to jazz up the stagnant rock and roll scene by incorporating elements of classical music like varying tempos, more intricate song structures, and abstract lyrical themes. This spawned a new genre of music: progressive rock.
In the mid ’80s, progressive rock took a big hit as many influential bands like Pink Floyd and King Crimson fell apart. A group of musicians were passionate enough to try and make progressive rock fresh again, and thus an underground movement was born: math rock!
Math rock songs were characterized by very unusual time signatures (like 7/8 or 13/8), abrupt interruptions, and dissonance (in which a very odd combination of tones were combined tastefully to produce a new tone). Each member of the band played to a different rhythm and meter, but the time signatures they played were often in groupings of 2 or 3 (meaning they were chosen in multiples or clusters).
This genre was not exactly mathematical, but the mathematical symbolism it often contained coupled with the dynamic nature of the songs caused music critics to call it “math rock”.
Something I find very fascinating is the song “Lateralus” by the highly influential and commercially successful progressive rock band Tool. It has many mathematical intricacies that really amazed me when I first listened to it. The lyrics are:
All I see
In my infancy
Red and yellow then came to be
Reaching out to me
Lets me see”
The song itself has little meaning and the first verse is supposed to be the sequence of colors you see when you trip on LSD. But there are some very cool mathematical features about the song. Firstly, the syllables in the main verse follow a Fibonacci series (1-1-2-3-5-8-5-3) in ascending, then descending order.
The vocalist of the band, Maynard James Keenan, was a math major and loved putting these mathematical easter eggs into his songs. In fact, “Lateralus” was initially supposed to be called “9-8-7” because of the 9/8, 8/8, 7/8-time signature sequence it followed. This specific sequence was chosen because 987 is the 16th number in the Fibonacci sequence! Additionally, the song’s intro ends at the 1:37 minute mark or after 1.618 minutes, and this was his touching tribute to the golden ratio.