You're saying its not possible to tune a piano to an arbitrary set of 88 pitches?

Have a look at http://terpstrakeyboard.com/about/ and the janko keyboard

I know neither is about music notation per se (but about fixing the piano), but it is analogous: Music notation has exactly the same problem as the piano -> it defaults to C, which makes everything else relative to C and overly complicated.

For the record, I don't think this means we should switch to a new system, but it is usefull to recognize that it is suboptimal, if only to be able to accept it and continue (because nobody is going to translate everything to some new notation)

Exactly. Music theory is a programming language for musical composition and performance.

Unlike most languages it's inherently two dimensional because music includes both horizontal (time, rhythm) and vertical pitches (chords/colours, harmony) information.

And - especially important - melody is an element that needs both.

You can't represent the same information with text without losing a lot of important content, which is why toys like Sonic Pi are more limited than they seem.

You can kinda sorta represent the same information on a piano roll, but it's not any easier to read than dots - in some ways harder, because you're not going to see the relationship between a bass line and chords as clearly.

Is it a good programming language? It's quite dense, but not denser than some code idioms. The 2D element is unique, and hard to represent in other ways.

The learning curve is steep, but it's probably as good as it can be given the requirements and constraints.

Note that in historical Byzantine musical culture, there are no absolute pitches at all. Their notational form is entirely intervals from some arbitrary root note.

Similarly, in Carnatic and Hindustani classical traditions, the note names (Sa, Re, Pa etc) do not denote pitches - Sa is always the root, whatever it is, and the rest have a somewhat well defined intervallic relationship to it.

I personally would not use "harmonic value" to describe this, since it occurs in music that (broadly speaking) lacks harmony. The key point, IMO, is that what matters are sets of intervals (ratios, if you prefer) rather than actual pitches (as frequencies).

> But it, and the piano black keys with it, are definitely not optimal. It makes playing in C easy, and playing in anything else hard.

I don't think this is true—I was under the impression that, at least on piano, keys other than C major are sometimes chosen specifically to make things easier on the fingers.

I have some great news: you're a nerd ! :))

... or is it geek, i can never remember the difference ...

24, 128, approach infinity -- I know there are microtonal systems, but if you want to understand them, choose the nearest multiple-of-twelve (or really, choose whatever TET contains the closest approximations to the exact notes) TET and look where their intervals land with respect to the symmetries (factors) within that TET, and where those symmetries are broken by a note moving by a perceptual 'slide' (one note 'moves' into the other position) rather than sounding like a new distinct voice.