
Music and Measure Theory (2015) [video] - ogogmad
https://www.youtube.com/watch?v=cyW5z-M2yzw
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diiq
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.

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Kye
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](https://www.youtube.com/watch?v=spUNpyF58BY)

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nicetryguy
A little detuning goes a long way! It gives it that full warbly phase sound.
5-10 cents down is usually my sweet spot for synth plugins. I even detune one
string on each key on my piano about 5-10 cents down, it gives it some life!
Natural phasing sounds awesome.

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dia80
It's a fun personal discovery in mathematics when you realise there are
different degrees of infinites.

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ogogmad
The fact that all countable subsets of the real numbers have Lebesgue measure
zero (as proved in the video) implies that the real numbers are uncountable.
Otherwise the real numbers would have Lebesgue measure zero, which is absurd.

This approach to proving R uncountable is carried out more formally here
(proof A.3):
[https://link.springer.com/content/pdf/bbm%3A978-1-4614-8854-...](https://link.springer.com/content/pdf/bbm%3A978-1-4614-8854-5%2F1.pdf)

~~~
shitgoose
Speaking of absurd. I remember when I found out that Cantor set (uncountable)
has measure 0, my mind was blown. No wonder Cantor ended up in an institution
(as I heard).

