Music and Measure Theory (2015) [video]

I love 3B1B, but it's a little disingenuous to attribute small integer ratios being are consonant to our brains/taste because of the simple polyrhythms. Our brains never receive the waveforms in that way; the ear performs a mechanical fourier transform, first. Small integer ratios mean many harmonics overlap, so the frequency-space signal from the ears is also relatively simple. The simpler the picture in freq-space, the more consonant (not necessarily more beautiful or pleasant, but specifically consonant)

Unfortunately, that reality is a very poor setup for the math he wants to demonstrate -- he needs to imagine someone for whom all ratios are consonant to motivate the measure theory question. So I'm not sure music was the best road to the goal.

This is one of the few people who connects math and music in a way that's both useful and interesting. I followed this channel back when I found the video on Fourier transforms[1], but never looked at other videos. I've never really thought about the math of consonance and dissonance, but I use it all the time without realizing it.

For example: a hypersaw. That's 7 saws slightly detuned played at the same time. The more you detune them, the worse it sounds. If you own Serum, you can hear this in realtime if you make a 7 voice saw and play with the detune knob.

You can use an LFO to modulate this and get a sound that's a little uneasy while still somehow being harmonious. It's perfect for dark/spooky music.

[1] https://www.youtube.com/watch?v=spUNpyF58BY

It's a fun personal discovery in mathematics when you realise there are different degrees of infinites.