How Does Music Fit into a STEM Program?

As a (former) professional musician, I’m always pleased when my children show an interest in music, and encourage them whenever they want to pick up an instrument and play.  With all of our interest in STEM topics, how does music fit into a STEM program?

No matter where you fall on the STEM vs STEAM debate, music belongs in both camps.  Music naturally fits into the art aspects of STEAM.  How does music relate to the hard sciences?  Simple, the M in STEM can be interchangeable. Music = Math.

Math isn’t the only point where music crosses into STEM territory. We can just as easily find elements of Science, Technology, and Engineering studying music and sound. Let’s explore.

Math and Music

There is a lot of math in music, and we’re not just talking about Math Rock.  You’ll find math in the fundamentals of counting fractions of beats in time signature (especially odd time or poly rhythmic time signatures.)  Though you don’t need to know complex formulas to appreciate or play music, they’re there in the background of harmonics and acoustics. 

Trumpet played in a stairwell

Why do certain things just sound good?  What makes particular tones, timbres, or acoustic spaces pleasing to the ear?  Why does a trumpet sound better when played in a stairwell instead of in a small room?

We can find answers in the math behind the sound. Music and math are related in a number of fundamental ways:

Time Signature and Fractions

A piece of music is equally divided by measures, which are further divided by the beats in each measure.  Time signature informs us how many beats are in each measure and the number we use to count the beat (the numerator) and what note equals a single beat (the denominator.)   Time signature, rhythm, and beats are all about fractions.

Most Western music (rock, pop, country, dance, rap, etc.) is in 4/4 time.  This means there are 4 beats per measure.  The next most common time signature is 3/4, where there are 3 beats per measure.  6/8 time has a similar feel to 3/4, and it should just looking at the numbers; the numerator and denominator are doubled.  The odd time signatures of Waltzes give a push pull kind of feel, especially with an accent on the first beat of the measure. ONE two three, ONE two  three.

Many musicians will tell you they simply ‘”feel the beat,” though at some level there is math at work.

For those interested in teaching time signatures, Kiddymath has some great time signature worksheets for free.

Musical Notes and Divisions of Time

Within each measure of music, we have the notes themselves.  Notes are a series of fractions.  A whole note lasts for a whole measure, a half note for a half measure, a quarter note lasts 1/4 measure and so on. 

We also have rests, which are pauses where a note is not played. Rests still has a defined duration of time within the measure.

A piece of music is made up of many measures. Each measure of music is comprised of fractional notes and rests that make the whole. Music and rhythm con be viewed as fractions of time.

Finding Patterns in Math and Music

Math helps us understand our world through patterns.

Music is organized in patterns.  Classical pieces have repeating motifs, or melodies.  Most modern music is arranged into patterns of verses and chorus, and we all find ourselves waiting for a good “hook” to come around again.

The Science of Sound

OK, so music relates to math.  How about science?  Music is sound.  We hear music as sound waves reach our ears and vibrate our ear drums.  The frequency and amplitude of these sound waves determine how the music sounds.

Frequency and Sound Waves

Not only are the notes divided by length and duration, notes have a pitch, which is how high or low a note sounds. The pitch of a note is determined by the frequency of the sound wave.  Let’s explore.

Sound is created by air molecules colliding and moving apart, which creates motion in the air.  Have you ever been in the front row of a concert or next to a loud speaker and felt the air move?  That’s a sound wave.  Have you ever seen a speaker pulse and vibrate along with the beat of music?  Those pulses are creating sound waves.

Watch sound waves in action as a speaker cone pulses.

A Little Bit Louder Now – Amplitude

Amplitude is simply how loud or soft a sound is.  The higher the amplitude, the louder the sound.  The changes in amplitude represent the dynamics in a piece of music, in other words how loud or soft a passage or part of a song is.  Think “Shout” from the Isley Brothers.  About 2/3 of the way through the song, we hear, “little bit softer now… “as the whole band plays more quietly, and builds back up to “a little bit louder now” until the songs is at its climax.

A little bit softer now… A little bit louder now…

As there are dynamic changes throughout a piece of music, we can also see the volume of individual instruments and sounds. Wait – we hear sound right? How can we “see” the volume of the sound?

Visualizing Sound as Waves

Using a tool like an oscilloscope or sound editing software, we can see sound waves represented visually.  Frequency is how wide and how far apart the waves are.  Lower pitch sounds look larger and wider, while higher pitch sounds are smaller and closer together.

STEM and Music: Amplitude and Frequency

Amplitude is represented by how high the waves are.  The greater the valleys and troughs, the higher the amplitude and the louder the volume.

To see some sound waves in action and the basics on oscilloscopes, check out the video below. You’ll also learn some other applications for analyzing waves.

Assigning numbers to pitch, and tuning.

One full wave, from peak to valley is called a cycle.  The number of these cycles completed each second represents that sound’s frequency (measured in Hertz, or Hz.)  For example, the A above middle C is the note most commonly used for tuning and is often referred to as A440.  440 Hz is the frequency of that note, and how many wave cycles an A makes per second.  If we play an A an octave below, we get a lower pitch with a frequency of 220.   An open E string on guitar is 82Hz .  That same open E note on bass guitar would sound an octave lower, and measure 41Hz. 

Hey – that’s math!

Even something as simple as tuning an instrument is grounded in math and science.

Resonance and Acoustics

Sound can’t exist in a vacuum (In space, no one can hear you scream.) Resonance is how a sound wave’s environment affects the way we perceive the sound.  Clap your hands in the room you’re in right now. Listen to the sound.  Is it loud or soft? Does it echo off of smooth surfaces, or is it muffled by carpet and furniture? Think of how it sounds if you clap your hands in the bathroom, or in an auditorium.

The size of the space, shape of the space, reflective surfaces, are only a few of the factors that affect the sound.  When designing stages, theaters, concert halls, amphitheaters, and other structures where sound is important, acoustics are often considered in the architecture.

The Musikverein concert hall in Vienna is regarded as one of the world’s best acoustic spaces.  What makes it so great?  The shape of the room and ornate details in the architecture reflect the sound waves and help diffuse the sound.  Though the magical acoustic properties of this space were not fully planned, architects use the science behind it to replicate some of these properties.

Harmonics and Instrument Design

Take a basic recorder or flute.  Each hole sounds a certain note.  The spacing between the holes to produce the correct tone is math based. Think of a flute, made from bone, say 40,000 years ago.  How did our ancestors know where to place the holes?  Same question if you wanted to do a STEM project to make a simple flute out of PVC.  Here’s a great article from Michigan Technological University that explains the math and formulas behind the hole placement.

Similar, we can look at stringed instruments like a guitar, and where the frets are placed on the neck. If we look at a fretless instrument like violin or cello, where the musician places their finger is critical to determine the length of the string that is vibrating to produce the correct pitch.

Music and STEM in the Classroom

This teacher brought a guitar into the classroom to demonstrate some of these concepts to his Physics class. This is a great way to use music as a teaching tool, especially for STEM topics. Some of the hard science concepts become more relatable if we think of them in relation to the guitar in this lesson.

Everyone may not know how to find harmonics, or may get lost when talking about the relationship with shortening distance and its effect on frequency – but they can follow along easily when those concepts are put in context with something as familiar as a guitar. It suddenly become more tangible.

Still not convinced that music fits into STEM programs? If you don’t think there is some heavy duty science in music, check out the section at about 4:10 in this video talking about harmonics on guitar strings.

Okay, I’m fairly technical and can geek out on this kind of stuff, but I’ll admit that even I zoned out a bit on that one.

Technology and Engineering in Music

We dipped into how Math and Science relate to music. What about Engineering  and Technology?  Music’s connection to STEM touches on all of the STEM topics. 

Flip on the radio or pull up your favorite band or song online.  Chances are everything you’re hearing has an attachment to STEM in some way.

STEM and Music Hardware Design

Acoustic instruments depend on their capability to produce sound waves in a range of pitch.  As we’ve advanced in technology, the instruments we use have changed dramatically.  Pickups in electric guitars make magnetic pulses that are translated into sound.  Guitar effects (analog or modeled)  are designed to process and change the original sound. Synthesizers are widely used to create sounds not possible with natural instruments.  Samplers started as a way to mimic natural instruments and went far beyond.  

Guess what?  Someone designed and engineered all of this technology.  

Remember the sound waves we discussed up above?  Amplitude is a measure of how loud a sound wave is.  It’s no coincidence that Amplifiers were developed to make instruments (or vocals) louder and therefore easier to hear.  The audio amplifier market alone has grown into a multi billion dollar industry. Some amps are coveted for the way they color the sound, especially among guitarists (I’m partial to old Fender amps myself.)  Someone engineered those amplifier circuits too.

Programming Music Software

The bloops and beeps of 8 bit video games are music to a generation of gamers. This music was largely was programmed, not performed (as, arguably, is much of today’s pop music.)

Before we had the capability to digitize music, we had the early forerunners: Player Pianos and music boxes. Placements of the bumps on the piano rolls were an early method of programming, much like computers that were programmed with punch cards.

Digital Audio Workstations (DAWs) such as Protools, Cakewalk, etc. are virtual studios that all but replaced multitrack tape recording.

Synthesizers have found their way to virtualization as “soft synths.” Some of the most popular analog synthesizers have been digitally recreated – or modeled – through software.

Digital effects are everywhere, whether they are dedicated hardware modules or a piece of software (hello reverb and autotune.)

Like any other software or app, creating these requires people with skill sets in programming and coding.

Audio Engineering

Even if we completely disregard any kind of electronic instrument,  we can’t escape the science in music recording.  There are acoustics involved in the space where the music was recorded, and audio engineers have an arsenal of techniques to capture characteristics of sound. 

How? With Technology, of course. Microphones, mixing consoles, effects racks, computers, software, are some of the tools used by audio engineers to capture the music we hear.

Music Playback

We’ve spent some time discussing the science of sound and the math of music.  What about just simply listening and enjoying some music?

There are different technologies for playing back music.  Every shift from wax cylinders, vinyl records, cassettes, 8-tracks, CDs, mp3s, and streaming represents a change in technology. Someone had to start with an idea, then design and engineer each aspect of each platform we’ve used to record and enjoy music.

STEM concepts surrounded every step of development, long before STEM was a ‘thing.’

Conclusion: Music and STEM programs

Wow. There’s more to the music we hear than just artistry and song craft. So, how does music fit into a STEM program? We find art in the music itself, we find science in the sound waves and frequency and pitch that make the music. Technology brings us advances the way music is played, recorded, and delivered. From primitive bone flutes to the most complex synthesizer, we find engineering in the instruments themselves and creation of the acoustic spaces designed for music. And math gives us the beat, the notes, and ties all of the other aspects of STEM together.

Music (and, by extension, sound) touches on all aspects of STEM and STEAM.

Related Post: See our top picks for STEM music gear


H. Evan Miller is as dedicated to fatherhood as he is to life long learning. Musician, Photographer, Educator, Consultant, Entrepreneur, Blogger, and founder of STEMtropolis, where you can share his adventures in STEM and STEAM with his family.

Recent Posts