Basic Music Theory in ~200 Lines of Python

So if you pretend that the sharps arent there and that they dont make any difference to anything then its all simple?

We need more "Explain things like I'm a programmer" explanations.

I've tried to grok music theory several times. I've never understood the scale/notes, notations. The 2nd array (with sharps and flats) and couple paragraphs made it "click" instantly. Because it was in a language and presentation I understand.

A fair bit of early music composition is weighted by what is easily sung, more than anything else.

I haven't found an introduction to music theory that makes sense to me.

I vaguely understand that complications arise because we want nice harmonics, ie frequencies whose ratio is a "nice" rational number, such as 2/3 or 3/5 or so.

But our chosen notes should be invariant under doubling of frequencies ("shifting by an octave"), because that's basically the same note.

The problem then is that roots of 2 are irrational, that is, one cannot find (p/q)^2 = 2, or (p/q)^n = 2, or even (p/q)^n = 2^m. Therefore, one cannot find a "nice" interval that, applied several times, wraps around to an octave (or multiple octaves).

However, in a neat coincidence, (3/2)^12 = 129.7463378906... which is close to 2^7 = 128. So, based on that ("Pythagorean comma"), something something something, and we end up with 12 half notes that are basically of frequency f_i = f_0 * 2^(i/12), which are all horribly irrational, but apparently sound "nice" enough, largely (because they are close enough to some "nice" fractions), but only if we pick out some specific 7 of them.

And then the question becomes, which 7 of the 12 do we pick, approximately uniformly distributed. (Why not 6? Every second? I don't know.)

And then, you can transpose them somehow (ie multiply frequencies by 2^(j/12) for some j, but then you change the names for some reason, and everything gets complicated and tonic and Mixolidian double-sharp.

Also, instead of frequencies of the form f_i = f_0 * 2^(i/12) (which, clearly, have the advantage that any multiplication by a power of 2^(1/12) is just a shifting of the index i), you could also use non-equal tuning, with the powers of the 12th root of 2 replaced by some "nice" fraction, which means that any shifting then subtly changes the character of everything, I assume.

This is complicated, admittedly, but for me the nomenclature obscures, rather than elucidates, the issue.

ETA: I sympathise with what irrational wrote: "Is this what it is like when I talk to people who don’t know anything about programming about my work? Pure gibberish?"

Something I wish was more clear in music theory is just how much overlap exists between the various concepts. I think it suffers from having so many names for everything, the learning curve seems much steeper than it really is. Even in this article, much time is spent on the duplicate names of notes and intervals. As a fairly proficient self-taught guitarist, this intimidating perception of theory delayed my learning of it for easily 5-8 years.

For example, you may spend a while learning the major scale, and what can be done with it. Then you learn the minor scale, and it seems like a totally separate scale that sounds completely different. And after that you learn that there are five other scales (modes) to learn about! (Dorian, Phrygian, Lydian, Mixolydian, and Lochrian!). It can seem extremely overwhelming until you learn that they're all the same scale with different relative starting positions. Where major is [1,2,3,4,5,6,7], minor is [6,7,1,2,3,4,5], and the other modes are all the other permutations of starting positions.

My other gripe is that learning theory on piano puts a lot of bias on the notes themselves rather than the intervals. For example, the B major scale has 5 sharp notes (black keys) to remember whereas C major scale has none. These are pretty different shapes to remember. Learning these on guitar means taking the same exact shape and shifting it up a fret (so if you know one major scale, you know them all!). Not to say that guitar is the perfect instrument for learning this - folks will often learn scales as close to the 0th fret as possible, causing you to start on different strings and have slightly different patterns.

That being said, I wish there was a purely linear instrument (a piano with the black keys flattened?) for learning theory. The real magic comes from identifying the shapes and patterns, and how they're similar to each other. Like how major and mixolydian are identical except for one note, so it's very easy to modulate between them, or make a listener think they're in one mode when they're in another. Same with minor and phrygian. Being able to drop the baggage of "the second note of the B major scale is C# which is this black key here" and just focus on a floating set of intervals seems like it would make this all easier and less intimidating.

That all said, I still feel reasonably early in my theory journey. So maybe this is just my bias coming from guitar.