music theory is witchcraft

In alchemy, the moon is represented with this symbol. Isn't that strange? The ground intersects the most obvious cycle in the sky, and the resulting symbol represents the second most obvious cycle in the sky.

It's a pretty direct visual reference, but generally, cycles are represented with circles. And that makes sense. What's more cyclical than a circle?

One of the most fundamental kernels of knowledge, one that everybody seems to intuitively  understand, is that music is movement. And that journey is often cyclical. You need to establish a home, then travel away.

Then, usually, but not always, you come back home. This applies to harmony, but it also applies to melodies. A melody that doesn't leave home is just a tone.

When I say music is about the  journey, this is what I mean. If C is the destination, how do we get there? You could plot a melody as a trip around a circle.

Just as you can only travel halfway into a forest, you can only go halfway into an octave. anything past F#, up or down. .

. it's going to bring you closer to C. That's circles.

This. . .

is salt. A perfect bisection. In our circle of notes, it depicts a tritone.

A rather dissonant pair. Every obvious shape does this. Triangle?

That's an augmented chord. Square? Diminished chord.

or really just two tritones. These shapes show the liminal areas of our circle. You can travel here, but it takes tremendous effort to  stay here.

the tritone wants to bend, to resolve. The augmented chord wants to scalene, to resolve. The square, or more commonly the isosceles, wants to move forward.

I guess there's one more shape you can add here: two triangles. But now we're just hitting every other note. I think I saw someone expand on this once.

. . Ah, but you can pull magic from this arrangement.

Just rotate the star. That's the circle of fifths: a cornerstone of music theory and analysis. And it's built on a lie.

See, the power of the circle of fifths, the reason that musicians keep coming back to it, is in its name. Each note is a fifth away from the last, and they circle back around after visiting all 12 notes. A fifth is defined as a frequency ratio of 3/2, but the fifth that we use?

It's off by a third of a percent. Less, actually, but it adds up. Look.

And we're back at C, right? Wrong. We're off by 24 cents, give or take.

A Pythagorean comma, formerly. The "circle" of fifths is actually a spiral. There's this weird, shockingly prevalent notion that music theory is a hard-bound set of rules that you must follow to make your music sound good and boring.

I want you to know that's just not true. Music is squishy witchcraft. Theory is a popular way of navigating that, but you can write your own spells.

You'll probably end up reinventing several wheels, but who cares? Have fun first.