Musical Thoughts On Teaching Physics

TL;DR There are many lessons physics teachers can learn from music teachers about teaching one’s discipline. Many, and perhaps most (all?), concepts in music have analogs in physics and mathematics.

I have a background in music, spefically percussion. Marching band was my life in high school and that carried over into my college years. I considered double majoring in astronomy and physics but decided against is for some reason. If I had it to do over again, I might major in percussion performance (if I decided to go to college at all, that is). Music continues to be an important part of my life, and my next career will be either standup comedy or playing drums in an ’80s cover band.

During my years in academia, I have come to recognize that there are many examples from music education that can, and probably should, carry over into physics education. I will describe as many of these as I can think of in this post.

Disclaimer: By “music” I specifically mean Western music. Apologies to readers from other cultures, but Western music is the only kind with which I am familar.

Another Disclaimer: All analogies are imperfect, and I have no doubt invoked some imperfect anglogies in this post. Don’t beat me up for doing that; I’m aware of it.

Learning To Care For The Instrument

Unfortunately, in most introductory physics courses (and other science courses too), we begin the course by jumping directly into discipline content and I have come to see that this is perhaps the most inappropriate thing we can do. We do this because we feel the urge, indeed the necessity, to “cover” as much material as possible to prepare students, with no regard for the rate at which students learn. We arrogantly think there are topics that simply must be included and we think that unless we explicitly mention these things in class students have no hope at all of thinking about them or learning anything about them. Of course, these assumptions on our part are so obviously false that it’s embarrassing that we ever treat them as true. We know better.

If you have ever taken instrumental music lessons, you know that you did not begin by ripping a Neil Peart drum solo or an Orianthi guitar feature. Instead, you began by learning how to care for the instrument (e.g. piano, clarinet, voice, etc.). You learned how to assemble it if necessary. You learned how to clean and maintain it. You learned how to hold it properly. You learned proper embouchure (stick grip for drumming, finger positioning for guiter, etc.). You learned proper way to create a note (percussionists learned to strike a surface). You learned scales (percussionists learned rudiments). You learned études. You learned exercises. The list goes on, but we all know you did not immediately perform for an audience.

The takeaway is that we must take the time to demonstrate how to care for the “instrument” and in this case, the “instrument” is the intellect. This foundation is what most people would call critical thinking. In science courses especially, we must take the time to address the very definition of science becuase if students take subsequent courses, those instructors will (rightly) assume students understand what science is (and what it is not) but will not necessarly address that.

Musical Terminology Is Precise

In science, we talk of “theories.” We know that scientists and laypersons use this word differently, and yet it seem that despite our best efforts this problem persists. It makes me wonder whether or not we are really doing our best to eliminate it or if the problem is so pervasive we should give up and either ignore it or find a better word so we don’t have to keep trying (and failing) to fix the problem.

In a jazz theory class, students never sit around discussing whether or not jazz exists, if it is real, or if it merely an idea in someone’s brain. In music, “theory” has a very specific meaning and I have never encountered a music student who didn’t understand that.

The takeaway is that we must be careful to consistently use precise terminology. Mean what we say, and say what we mean. It’s difficult, but it can certainly be done.

Musical Notation Is Precise

Take everything I said about terminology and apply it to notation. Musical notation encodes musical thought. There is one way to notate a C major scale. That which is notated that way is immediately recognizeable as a C major scale.

Physics notation and mathematical notation encode physics thought and mathematical thought. In science, we have standardized units with accompanying symbols so why not have standardized symbols for physical quantities and use them consistently? Yes, it would be difficult to impose, but we all know it can be done. Okay, well then let’s at least shoot for consistent notation that emphasizes subtle differences. For example, we should agree on how to notate a vector’s magnitude differently from the vector itself so that there is never any ambiguity. That’s probably easier for us to agree on.

The takeaway is that notation should help students articulate physical understanding. Notation should be consistent, especially across introductory textbooks.

A Musical Composition

A physical system is a conceptually complex entity. It contains momentum, energy, angular momentum and possibly other things. They’re all related, and yet each can be studied separately from the rest.

A musical composition or arrangement is a conceptually complex entity too. It contains tone, harmony, rhythm, tempo, dynamics, melody, and a host of other things. They’re all related, and yet each can be studied separately from the rest.

The takeaway is that we must demonstrate how many concepts come together to make a beautiful and stirring picture of physical reality.

A Song Is Independent Of Key Signature

Physics textbooks, especially introductory ones, are full of coordinate systems. David Hestenes calls this the coordinate virus. Yet, physics independent of our choice of coordinate systems becuase the Universe is similarly coordinate independent. We need to do a better job of teaching students how to reason with physics independent of coordinate systems. This will probably require some (extensive?) modifications to the existing mathematal foundations we expect introductory students to have, but there is no reason why we can’t introduce these modifications into the physics courses. Why shouldn’t we, especially of a new foundation will help students better understand the physics. Choosing a coordinate system involves choosing an origin and a set of numbers for identifying points in space. Yet, Newton’s laws or the Maxwell equations can be written in a form that doesn’t require us to do this. Physics is valid in all coordinate systems, but some coordinate systems are preferred for their simplicity or symmetries.

Pick any well known song. I choose Do-Re-Mi for reasons that I hope are apparent. You and I can sing this song simultaneously by starting on arbitrarily different notes, but the starting note isn’t important becuase it is the intervals between the notes that make the melody recognizable. In musical terms, we can sing the song in different key signatures. Choosing a key signature specifies a root, but the intervals are the same for, say G major and C major (all major scales are defined by the same pattern of intervals). Perhaps a musical transposition corresponds to a transformation from one coordinate system to another. Do-Re-Mi is Do-Re-Mi in any key, but some keys are preferred for the emotion they evoke or their tonality.

As an aside, I distinguish between a frame of reference (a state of motion against which other states of motion can be analyzed) and a coordinate system (a way of labeling points within a frame of reference). I can see musical transposition as an analog of either of these. Is there something more specific to which I can appeal? Tempo perhaps? Hmm…

The takeaway is that we shouldn’t restrict introductory students to just one coordinate system or reference frame. We should exploit symmetries when we can, and we should emphasize that coordinate systems aren’t even required at all.

Class Is For Rehearsal

No professional musician performs for an audience without prior rehearsal. It takes hours of rehearsal for the final performance to meet the musician’s standards (hopefully). Musicians may become frusted by mistakes during rehearsal, but they understand that making mistakes is essential to creating a better final performance. I have never heard of a professional musician leaving music because of mistakes made during rehearsal.

In teaching, it is customary to distinguish between “formative” assessment and “summative” assessment. Formative assessment is directly analogous to rehearsal. It is necessary to build proficiency in anticipation of a formal performance.

The takeaway is we should devote more time to formative assessment, with no penalties incurred for learning.

Class Is For Performance

If rehearsal is that which is done prior to a performance, then the performance is that which showcases a musician’s skill and proficiency of music (in whatever form the musician has chosen).

In teaching, the analog of a performance is a summative assessment. It is here where students can shine, and show off what they have learned.

The takeaway is that we should treat summative assessment as a performance, with all the customary adulation and positive reinforcement due the performer.

Mathematical Operations Have Musical Analogs

Any musical note can be adorned with a sharp (\sharp), which raises its pitch by one half-step (one semitone), or a flat (\flat), which lowers its pitch by one half-step (one semitone). This is sometimes done to distingush one key signature from another or to temporarily create the desired pitch in a key signature where it is not normally present (an accidental). As discussed above, Do-Re-Mi is Do-Re-Mi regardless of the key signature to which we choose to transpose it.

In physics, we deal with mathematical objects endowed with the geometric properties of covariance and contravariance, and these properties are notated respectively with subscripts and superscripts. Contravariant components can be transformed into covariant components, and the converse is true. In coordinate-free language, vectors can be transformed into one-forms by contracting with the metric tensor. Some mathematicians call this operation a musical isomorphism. Physicists call it raising and lowering indices. The physics is independent of our choice of contravariance of covariance.

The takeaway here is that it may help students to relate certain mathematical operations to musical analogs.


There are probably other analogies applicable here. I have found that students with music backgrounds understand these analogies and I think that helps build some confidence that what they’re trying to learn in physics.

As always, comments and feedback are welcome!

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