Music as Numbers

There’s a mathematical way of listening to music that most people aren’t aware of.

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The major and minor scales have seven degrees each. (If you just thought, “but a scale has eight notes from bottom to top!” you’re right, but the eighth tone is actually technically the first note repeated again, an octave higher.)

It doesn’t matter if the scale starts on a C or an Eb or an F#. The seven degrees of the scale will relate to one another in the same way. That’s why we can transpose a tune from one key into another and it sounds basically the same (or it does to the great majority of us without perfect pitch, anyhow).

In music theory, they sometimes refer to each degree of the scale by its number. “Dropping from the five, down to the three …” And each of the seven notes, each number, has its own characteristic feeling within the scale.

-The one is a place of rest.

-The seven is unrest, straining for the one.

-Five and three are also peaceful, though in the end even they long to resolve to the one.

-The four and the six are less urgently restless than the seven, each tending to fall to the more restful degree below itself (the six down to the five, and the four to the three).

-The two is a bit ambivalent, happy to move either down to the one or up to the three.

(Incidentally, I wrote this list to describe the tendencies within a major scale, but it is also true of the harmonic minor.)

Because of this set of tensions and tendencies, it is possible to learn to hear a musical tune as its numbers. We can train ourselves to recognize where a note belongs within the context of a song’s scale when we hear it.

My experience, which I know some others have shared, is that it can be helpful to start by focusing on the deepest notes in a song (e.g. the bass guitar), since they tend to stick out from the rest of the music, inhabiting their own sonic space, and they often (though not always) move around a lot less than the notes of the melody.

Some people will say that learning to hear music like this is a useless exercise. That’s not strictly correct — being able to hear music like this has made me an immeasurably better piano player than I would have been otherwise, for instance, which is a pretty cool skill to be able to pull out at a party.

But for the most part, it’s true, this is a useless ability. But I believe it’s a beneficial and worthwhile useless ability. Sometimes the useless things are also the most beautiful things. Don’t make this a top priority, but don’t be afraid to do it, don’t think it’s out of reach, and don’t ultimately treat it as a waste of time.

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