Exploring the Complex Relationship Between Math and Music

Music is expressive, it is simultaneously immediate and timeless, diverse yet universal. Music can lift us to a higher form of communication. (Think of humans and aliens learning to communicate at the end of “Close Encounters.”) And – like most human experience – music is also very mathematical. A caveat- there is a danger in associating music and math. For starters, it’s a bit on the nose for an actuary to make the comparison; am I an actuary who loves music, or am I a music lover who just happens to be an actuary? Does it matter? There’s also the (clearly crazy) idea that equating music and math is somehow a disservice to music. When we identify and explore the quantitative structure of sound, are we dehumanizing it, robbing it of its expressive power?

Here’s the thing: the mathematics exists, however we choose to feel about it. We can barely talk about music without invoking numbers. Musical intervals happen in thirds, fourths and fifths (and more). Music in three time gets you a waltz. Four? That’s a foxtrot. And, of course, once a song gets to 100 beats per minute, it’s disco. Eleven is a prime number, and also the name of a song by the Grateful Dead; a fantastic piece of music with 11 beats per measure (3 * 3 + 2). Dave Brubeck has an album called “Take Five,” whose title track is one of the most well-known compositions in jazz. (Though I prefer “Blue Rondo a la Turk”, which is an amazing thing in 9/8 time.)

A twelve-bar blues has a repeatable structure – it’s very simple, but it’s structure all the same – just like an equation. We can change the values we plug into the parameters and get a dazzling array of composition. Don’t let the “blues” in twelve-bar blues distract you. It can mean anything from Howlin’ Wolf’s “Killing Floor,” “Can’t Buy Me Love” from the Beatles, “Rehab” by Amy Winehouse, Pink Floyd’s “Money,” U2’s “Where the Streets Have No Name” and so on. I can never think about linear models without thinking of twelve-bar blues. It’s a simple thing that means so much.

Math is about rules and what we can and can’t do within that system. When we need to, we break the rules or make new ones. It took a while, but we eventually got imaginary numbers, division by zero, the infinity of spaces between numbers. Music does the same thing. Schoenberg, Webern and others threw out the idea of a tonal center, giving equal weight to 12 tones. John Cage challenged the very definition of music in his avant-garde composition “4’ 33”.“ No instruments are played. The audience hears the ambient environment in which the piece is performed. Neither musician nor composer has control over what the listener will experience. Both Cage and Karlheinz Stockhausen were proponents of aleatoric music, composition which encompasses randomness. Imagine that, actuaries: stochastic music.

Aleatoric music isn’t the only time that music has taken cues from math. Charles Dodge began with data from the Earth for his piece “The Earth’s Magnetic Field.” Sonification of data permits us to listen to fractals. There’s an entire genre called “math rock,” whose bands draw from minimalists like Steve Reich and Phillip Glass. Is it music or math? Can it be both? What’s the difference between art and math? They’re both beautiful manifestations of the universe.

I can’t close this without acknowledging something. I don’t yet know how to play in instrument, but I have performed music in public. I’m a shameless karaoke singer (is there another kind?) and more than a few former work colleagues have witnessed me in action. Some lucky members of the pricing team at CNA Re got to see my version of “Mack the Knife” in Chicago one night. Across the Atlantic, the CRO of Munich Re talked me and another colleague into singing that same song in both English and the original German (“Mackie Messer”). At another offsite work function, someone had the wisdom to rent an actual karaoke machine. I was first in line with my take on the Ramones’ “I Wanna Be Sedated.” A colleague and I gave a heartfelt duet on some Beastie Boys later that evening.

I’ll be in New Orleans (birthplace of jazz!) in a few weeks. They probably have a few karaoke bars. Maybe I’ll see you there.


About Brian Fannin

Brian Fannin is a research actuary at CAS. He is also the founder of PirateGrunt LLC, a boutique consulting firm based in Durham, North Carolina specializing in predictive modeling in the property casualty markets. Fannin has been an Associate of the CAS since 2002 and a Certified Specialist in Predictive Analytics (CSPA) through The CAS Institute since 2017.

One Response to Exploring the Complex Relationship Between Math and Music

  1. avatar Bill Mech says:

    I think of the combination of time signature, tempo, chord progression, instrument and melody as the variables underlying the music as it’s heard in performance. Change any one of them and the performance is altered. They’re rather like the parameters of a loss distribution. It would be interesting to see if sampling the catalog of a large record company could make the variables stochastic, and result in a statistical distribution of music. Wonder what the expected value would be? Probably not “Blue Rondo a’la Turk”! Maybe more like “Mary Had a Little Lamb” played by the Boston Pops.

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