This is a pretty big question with lots of potential answers, but the answer you're probably looking for is the rules of harmony.

https://en.wikipedia.org/wiki/Harmony

tl;dr: Frequencies that are related by some simple ratios are defined as "intervals" which are organized into scales. A handful of those make up the vast majority of popular western music and "sound good together".

The rules are different for different styles, and they're hard to get right, because musical structures are holistic, and multi-layered. The domain of interest is at least as long as a phrase, and can be as long as the entire piece - which means that potentially every note is related to every other, and the data structures you use have to understand how and why.

I'm finding the tunes the least successful element here. They sound like a fairly naive Markov sequence/chord spine mashup, with none of the character of really good tunes.

The sounds/production are much better. The drum parts are midway between the two.

>I find an interesting parallel between 1/2/4/8 repeating beats/parts in songs, and binary...

There's more to it than that.

Good algo-comp is PhD-level work. Kemal Ebcioglu, who made one of the best efforts to date, had to add a lot of hand-rolled heuristics to an expert system that was trying to produce classical counterpoint. He was last seen working for IBM research on compilers and architectures for parallelism - a very smart guy.

It's easy to underestimate how hard the problem is.

My background is in music theory, and, as others have commented here, this is a question that there's no clear, agreed-upon answer to yet. Music theory can tell us what composers tend to do - which chords they choose should follow each other, which notes to use when - but it's not as good at telling us why those chords / notes sound good together.

In building Jukedeck, we're applying our own theories about what makes good music. And, like any musical composition, it's an experiment!

> In building Jukedeck, we're applying our own theories about what makes good music.

Have you thought about applying also common patterns found in the best selling hits? Hooktheory has a nice DB for this:

https://www.hooktheory.com/api/trends/docs

the parallel is divisibility by 2.

re: what determines what sounds good, in some sense you can read up on music theory for this (scales / keys). in a more basic sense ("why is this sad and this happy?") it's actually an open and actively researched question in the physics of music. it's anyone's guess, really, why certain melodies are pleasant. is it a physical/structural/formal feature of the sound itself? is it a feature of our psychology or neurological makeup? who knows.