Music theory for nerds

Otherwise, you're right. Historic tunings often tried to optimize for a certain base scale (often times C major), while leaving behind a really bad sounding tuning at the other side of the circle of fifths ( https://en.wikipedia.org/wiki/Wolf_interval ).

Modern pianos are usually equal tempered, which is the strategy of leaving every scale equally bad off - but on the other hand being able to play in all keys without sounding too bad (The famous "well-tempered piano" is referring to this historic change in tuning strategies with small pieces written in all different kinds of keys, all of which would have sounded weird before).

The more I learned about tuning, the more complex, beautiful and sad this topic became for me: http://blogs.scientificamerican.com/roots-of-unity/the-sadde...

It's fascinating and even a little philosophical that we can get so close to perfection with the 12 step tuning - but never, ever completely attain it.

By the way - That's part of the reason why choirs and orchestras often sound so good: As most other non-fixed-string instruments are able to do a slight adjustment in pitch, they can actually play perfect intervals in any chord, dynamically adjusting to any scale.

Wind instruments are necessarily tuned to a specific key, due to the nature of the harmonic series. But most talented wind instrumentalists are capable of modifying pitch to be in tune in any key or chord.

Down the rabbit hole, read on at your own peril:

Even string instruments are tuned to a key, to a certain extent, due to the use of harmonics. It is possible to fine tune the pitch of a harmonic by shortening the string as usual, but it is exceedingly difficult, since shortening the string changes the position of the nodes (the spots on the string that must be touched in order to produce harmonics).

Most musical notation is meant for non-beginners, right? And a lot of the beginner confusion is from features that are useful for advanced users. So there's a tradeoff.

There might, of course, be changes to be had. But a lot of beginner confusion is because the higher-level abstractions are needed.

A good example in mathematical notation is order of operations. Why not just do left to right? Or just going with Polish Notation?

Standard order of operations work well for people working with large formula, because they allow you to write many common things without many parentheses. But mandatory parentheses + left-to-right only would be easier for beginners.

The huge reveal to me was the same - notes doesn't matter - the intervals make the song recognizable. People change notes all the time when singing (jump octaves, start again lower to adjust to others, etc).

So on amateur level it's really just starting on random place on keyboard and guessing which note will sound "right" after that. Everybody hear if the next note is higher or lover, so it's just "was that +1, +2, or +3?" Usually you can guess, if not - start again. Very easy and makes playing instruments so fun.

I never understood why they bother kids with these complicated drawings and hashes and be-mols, if they could've just wrote all songs as "start at this note, and jump by +2, +3, -5, ...".