A funny example of this I came across recently.

There's a video game called Sonic Chronicles--just before it was completed, the developers were prevented from using the soundtrack they had made and were forced to recompose new songs for the entire game for reasons that remain murky. The result are some almost incomprehensible pieces of minimally instrumentated MIDI music like [this](https://www.youtube.com/watch?v=6o47N-aYd08).

Yet despite sounding like complete ass, those songs were actually lifted from previous Sonic games, where they sound [completely different](https://www.youtube.com/watch?v=t4-DQ4hGRJo) despite being structurally identical.

Well, not all MIDI sounds bad. Have a listen to the Addictive Drummer demos for example. It can sound pretty damn good / real. Still, your point is well taken. MIDI guitar emulations for example are still pretty dang bad. One wonders if this is because a guitar is a more continuous vs discrete instrument compared to drums. Even with all of MIDI’s rich parameters, it’s pretty tough to describe pick angle, materials, etc.

Also, I wonder if there will be a natural “backlash” against generic AI music and towards stuff that has more human imperfection. But then again even the AI will learn to imitate the imperfections so what exactly will make a piece more human in the long run?

The instruments are also mathematical, frequency ratios, spectrums, envelopes ...

MIDI sounds bad because while the notes being played respect a mathematical structure, the MIDI instruments spectrums do not integrate properly into said structure.

I'd really like to understand what you mean by this?

Yes of course, mathematics is used in the design of the instrument but it's not really a "mathematical" / precise device in the same way a calculator is, nor does a good musician conform to mathematics only when expressing themselves using the instrument.

In traditional musics, people use stones which when hit will make a sound that might conform to some frequency, but I wouldn't think the stone is "mathematical"?

I completely understand math is involved in Western and Eastern musical theory, but a saxophone being "mathematical" ? My trumpets and saxophones will only play the correct tones if I work with it to do so.

Disclaimer: been playing sax, trumpet since I was 6.

There is a mathematical structure in the harmonics of a piano note. There is a different one in the harmonics of a sax note. Yes, it's not 100% structure, there is noise too.

This is why the "timbre" of a piano is different from the timbre of a sax, and why the same C note might fit in a song if it's played by a piano, but not in the same song if it's played by a sax.

If you take a higher level view, the mathematical structure of the notes (the chords, ...) needs to fit the mathematical structure of the harmonics of the instruments (the timbres) to get a pleasing sound. Put another way, the timbres of some pairings of instruments might clash on a particular sequence of notes, so you need to search for a different instrument pairing which is harmonious on that sequence.

And then you have synthesizers, which are very mathematical in the way the timbre is generated (oscillators, filters, ...), but this allows you to exactly fine tune the timbre so it "fits"

It seems a bit philosophical to me though, what came first, the music or the maths?

We can use mathematics to describe the theory behind music but the theory isn't the music itself, nor are the instruments, "mathematical".

When a great performer plays live, they're not generally perfectly reproducing what's written in the musical notation either.

Probably not a straightforward thing to argue about, as I said, I think it's mostly a matter of viewpoints.

There was a paper which studied the neurological basis of music.

One of the function of the brain is to predict the future. Neurons and brain systems are rewarded for correct predictions and punished for incorrect ones.

The main theory of the paper was that music is pleasant because it's repetitive nature and simple patterns makes it easy for the brain to predict, thus there is a lot of reward to extract from it. They focused on modern trance music and ethnic african drumming, both which feature very long very repetitive sequences, which reward the brain so much that they can induce a trance like state.

Not any random combination of physical objects is a musical instrument (yes, avantgarde music exists, ...) The sax is built the way it is because it generates a sound spectrum with harmonic relations between the frequencies (integer ratios, ...). Those who originally built the sax didn't use math to design it, but it so happens that the result respects certain mathematical ratios, because those ratios are highly predictable and pleasant to the brain.

“My trumpets and saxophones will only play the correct tones if I work with it to do so.”

I have no opinion either way, but this conflates mathematical with automated, doesn’t it?

what is automated about having to change the shape of your mouth and strength of your exhalation to produce the right tone ?