Music is like the art of math. The playing of musical instruments is art, but the writing of it and the instrument design and the understanding of how those instruments operate is all math. Music can be created without art, but music cannot be created without math; not even in the slightest aspect of it. It is the only major form of classical arts to which that claim can be prescribed. A drum requires a calculation to generate reverberation to make itself heard. A scale must be calculated from its underlying frequencies. Strings must be measured in length, thickness, and tension to determine their resonance. The hole spacing and size of wind instruments must be calculated. Even something as simple as humming while alternating between high and low is a binary expression of either volume or frequency. It is only over the course of several millennia that we have developed the ability to teach an artistically gifted person to generate music without learning a bit of math. But that person still owes their artistic creations to the mathematicians of history. The connection is not at all tenuous. It is a very clear case of cause and effect.

Whether it's simply a rhythm, or playing a melody, or adding a harmony, every part about playing music engages the math part of the brain.

That doesn't mean you need to understand calculus to play. It's simply addition and basic translations, but it's a constant barrage of adding things and subtracting things.

If it's a piano or guitar, or even a voice, you have to know that do re me fa, is whole step - whole step - half step. The fretboard or keyboard is a large numerical puzzle. It's right in front of you, and what makes a good singers is someone who mentally works in that musical puzzle. Adding steps and half steps. You never really add past 12, because you can start over then. You don't need an advanced mathematics degree to solve the puzzle, but your brain is doing (simple) math constantly.

Not only that, but music is, since the beginning of time, the essential example of how to train your brain, to do without doing. The brain patterns of jazz musicians in performance resemble those of meditating monks.

The idea that the connection is tenuous may suggest you don't play music. If you've never made a beat before, try this:

openmusicgallery.appspot.com/drums.htm

Now keep in mind, this is just telling the program when to play a beat. If a human were to try to play these beats, they'd be doing math the entire time (not differential equations, but still math). Making sure beats are evenly placed is just counting. Once you've done it enough, you don't literally need to count "1,2,3,4" but I know many professional drummers that do exactly this, and are nearly flawless because of it.

I'm a professional musician, I also do creative coding for artists. One interesting tension is that some artists don't think that music is art. I agree with them 99% of the time. You can get paid a few hundred bucks to play Lynryd Skynrd song, which ends up being paint by numbers.

Music on the whole is just paint by numbers. Occasionally it breaks into the realm of genuine art. In any case, like programming, I find that it is merely a vehicle for expressing things.

Playing in time, and in key are pretty objective. You want unforgiving, try to sing the Star Spangled Banner out of tune at some event.