HN Theater @HNTheaterMonth

Hah! Now this is why hacker news is hacker news. Here's an interesting and related 3Blue1Brown video: https://www.youtube.com/watch?v=cyW5z-M2yzw

⬐ 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

⬐ 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.

⬐ dia80

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

⬐ daviddaviddavid

Totally agree! When I was in school, I took a logic class that used Boolos & Jeffrey's "Computability and Logic", which is a really great book. Chapter 2 is a very clear presentation of Cantor's diagonalization proof that there exist uncountable sets. It blew my mind.

⬐ ogogmad

The theorem in the video (that countable subsets of R have Lebesgue measure zero) can be used to show that the real numbers are uncountable in a way that's different from Cantor's proof. Essentially, the real numbers cannot have Lebesgue measure zero.

⬐ 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-...

⬐ 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).

⬐ 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.

Perfect octave is doubling the frequency.

For better and much deeper explanation: 3Blue1Brown: Music And Measure Theory https://www.youtube.com/watch?v=cyW5z-M2yzw

Here is much better theory:

Music And Measure Theory – A connection between a classical puzzle about rational numbers and what makes music harmonious. https://www.youtube.com/watch?v=cyW5z-M2yzw