Every year, without fail, I have students ask me “What do I need this for?”. I am attempting to give just one possible answer through my guest blogger, Matthew Williams. Matthew is an accomplished musician and computer programmer. He has played at Hard Rock Live and at a street festival in downtown Orlando in front of thousands of people as well as many other venues. Currently, most of his recording has taken place in his home studio. He also happens to be my husband. I hope you enjoy his entry as much as I did.

**Why Math Is Important In Music**

There is no denying the intertwining that exists between math and music. Math plays an enormous part in music including the way it is written, how it is performed, and even how we hear it. Music can even open the listener up to learning math by stimulating the parts of the brain involved in comprehension.

Written music consists of notations that symbolize time, rhythm, pitch, and dynamics, all of which can be broken down into simple mathematical representations. Time is shown in several different ways: tempo (typically measured in ‘beats per minute), time signature (shows how many beats comprise a measure and which note duration receives each beat), and note durations (shown as whole notes, half notes, quarter notes, etc). All of these together determines the basic rhythm of the song, the length of the song, and the length of each note played. All of these also represent measurements that use basic math skills to understand, such as counting, adding, multiplication, and division.

The tone, or pitch, of each note is represented on a musical staff that includes lines and spaces that represent notes. In Western music, these notes are a part of a 12-tone scale. Each tone represents a certain musical frequency, measured in Hertz. In most Western music, the note “A” is 440 Hertz. The next “A” in the scale is then determined by either doubling (up one octave) or halving (down on octave) the frequency. The other notes in the scale are calculated based off of a ratio calculation that takes into account the desired pitch value and your base scale frequency, such as the aforementioned “A” at 440 Hertz. The result is numeric intervals in frequency that also sound pleasing to the ear.

Dynamics determine how loudly or softly a note or passage is played. While in performance, these dynamics can be very subjective (one person’s “loud” may be another person’s “medium”), the measurement of a sound’s “loudness” is typically measured in decibels. In acoustic music, the decibel level of music denotes how much sound pressure is being generated. Decibels are also used in audio electronics to signify how much power is being applied to the electronics, which results in how loud the resulting broadcast is perceived.

Moving beyond the written or theoretical language of music, math still plays an important part in the music we hear. Waveforms that are calculated on a synthesizer can shape the instrument’s sound to be like a piano, a violin, or even percussive instruments, all based on predetermined algorithms. Electronic effects can be applied to instruments that alter its basic sound, such as an overdrive effects pedal on a guitar. These effects utilize electronic components that shape and alter the source sound using a variety of mathematical equations to affect that sound. Utilizing MIDI, a computer language that represents a musical performance in mathematical terms, devices can recreate musical passages from a previous performance.

While it is not necessary to have a deep understanding of math and its relationship with music, it is quite obvious that math plays a vital part in the music we create, listen to, and enjoy on a daily basis.

Matt,

Thank you for your insight. It is great to hear how professionals use math in their “real life”. As a math teacher, I was not aware of how much math was incorporated into music.

Matt,

Thanks for that excellent break down of the relationship between math and music. The irony for me is that I consider myself a fairly accomplished musician, however I barely made it through high school math. (I think the only reason I passed Math 11 was because I gave the teacher’s son some free saxophone lessons!)

-Barry

Matt, I have to be honest and say that this is a connection that I would not have made on my own (beyond the logical thinking aspect that makes math useful to so many other areas). An interesting perspective.

Matt,

The math- music is so interesting and important to consider for integrated instruction. I found this quote that seems fitting to your post: “Music is a secret exercise in arithmetic of the soul, unaware of its act of counting.”

–Gottfried Leibniz, philosopher and mathematician.

Excellent post. A similar conversation recently played out between my son and his band director and percussion specialist regarding his Accelerated Math 2 grade and his desire to stay in music long-term!

Thanks, everyone, for the positive comments. I initially had thought of writing about the strong relationship between math and computer programming, since my day job is in software development, but the more I thought about it the more I realized that that connection is quite obvious. The ties to music, in most conversations I’ve had on the subject, is far less obvious, especially to the casual listener.

Even as a musician, I don’t ‘consciously’ process music as a function of math, it’s more on a subconscious level. It wasn’t until several years ago when I delved deeper into relative pitch theory that I started recognizing the relationship. It deepened even farther when I started exploring audio engineering and learning to apply gain, compression, EQ, and effects to recorded audio paths. There, the link between math and the resulting audio you hear is much more apparent.

It’s my belief that most of the musicians and composers we’ve come to understand as geniuses or virtuosos (Bach, Paganini, Mozart through to modern day acts like The Beatles, Hendrix, Miles Davis, my personal faves John Petrucci and Steve Vai) have an analytical ability in math that they didn’t or don’t realize.