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Music & Math

Music & Math

Have you ever noticed that many great musicians or composers are also mathematically inclined–and vice versa? Leonardo DaVinci, Albert Einstein, Herbie Hancock, Johann Sebastian Bach, John Coltrane. At first, music and math might seem like the two farthest disciplines from each other: in math, there is one right answer and not much of the human involved; in music, on the other hand, passion, humanity and creativity are essential ingredients. But if you look a little closer, you’ll see that there is a very precise, mathematical system underneath those wild rhythms and soaring melodies that can be harnessed to create original compositions. There is math in the music!

Thelonious Monk famously said, “All musicians are subconsciously mathematicians.” What did he mean by that? Well, when you are first learning an instrument and learning to read music, you are very likely simply rote memorizing the tune of a song, how to get from one note to the other, which comes when and how your fingers make that happen. This system definitely works! And it’s a great way to learn when you’re just starting out. But as you progress, and perhaps start to write your own music, you may find yourself wondering why one note sounds better than its neighbor, or why a certain combination of notes sounds dissonant.

The first thing you have to remember when you start getting into the link between math and music is that music travels to our brains as sound waves, and sound waves have different frequencies (for example, the E above middle C reverberates at a frequency of approximately 329.63 Hz). So when you start thinking of notes as frequencies, the distance between notes can then be understood as fractions: An article published by Kent State’s Hugh A. Glauser School of Music on the connection between math and music explains that in a middle A major interval, for example, “which is A (440 Hz) and E (659.25 Hz)…with A on the bottom and E on the top…the frequency of E is approximately 3/2 larger than that of A, making an easy, digestible fraction.” In other words, beautiful harmonic chords are collections of notes that reverberate in similar frequencies and therefore whose distance away from each other in the musical scale can be expressed by simple fractions (rather than complicated, abstract ones).

Hopefully I haven’t lost you with all the fractions and frequencies! The important thing to note is that there is reason in the rhyme: that if you want to create complicated, impeccably structured polyphonic fugues like Bach, you can. But you can also stick with what just sounds right. Either way, math and music lend themselves to each other–especially in the classroom–and this link is becoming more and more clear. In fact, Herbie Hancock, one of the polymaths mentioned above, helped start https://mathsciencemusic.org, a website that offers teachers resources and lesson plans to use music as a vehicle to teach other disciplines. His passion to “figure things out” is what drove him towards engineering and jazz.

One obvious way music and math can work together in the classroom is by helping students learn fractions, as is evidenced above. Relating fractions to music can help make these often dry mathematical staples more interesting and show students that they have a real-world application. Beyond that, a student who plays a musical instrument has to be able to recognize patterns–in notes, rhythm, etc. And patterns are essential building blocks of math, as well, so learning these two disciplines simultaneously can reinforce the concepts. Scientific American posits that music enhances executive functioning, a cognitive processing skill: “Playing a musical instrument recruits these functions through, for example, constantly adjusting your motor movements to changing tempos and key signatures.” And because executive functions “are known to be a strong predictor of academic achievement, even more so than general intelligence,” there may be a correlation (not necessarily causation, though!) between playing music and excelling in math.

So let yourself get a little mathy when learning or listening to Beethoven’s Moonlight Sonata; and let yourself get a little rock and roll when you’re solving for x. You may find that you’ll excel a little bit more in both.

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