Music And Measure Theory

You are secretly tricking music lovers into learning epsilon/delta proofs for convergent series and sequences.

I love the fact that you don't expect us to learn it easily, but rather to actively try to understand what you're presenting us. You're one of a kind here in youtube. I have grown sad about the fact that many youtube content providers have given up using maths in their explanation of maths and physics, and when some of them tries to use it, they're hit with a backlash. Maths can be used to help understand itself (that isn't so obvious, even though it's maths for math) and I am certain you're going the right direction. Love your videos!

I knew you were a mathemagician, but I didn't realize you were a mathemusician, too. That's awesome!

You, 3blue1brown guy, are a genius. Never have I seen such beautiful math videos.

Absolutely wonderful. First, I get a MinutePhysics video about approximating harmonics, then you come in and tie it in with interval coverage in Measure Theory. I just have one request: Please, for the love of God, don't ever stop making these. These videos are becoming a major thing I look forward to every month.

My music teacher told the class a story about a music professor he knew that trained himself to always be extremely in tune. As a result of this he began to go crazy because he would always hear the slight out of tuneness in music which made all music sound bad to him.

9:10 "(...) the Proof has us thinking Analytically (...), but our Intuition has us thinking Geometrically (...)." The wisest words I've heard in a long time.

Here in december 2021, the improvement in your animation and recording quality has been massive over 6 year, but I'm impressed to see how you could present such complex and interesting topics even trough less fine tools. Now I need to see every video in your channel. Keep it up!

Could you imagine that my task was to prove that today, when I had watched your video yesterday? I aced my exam of course, thanks to you.

The deal with simple ratios sounding pleasant has to do with something called overtones. If you get a drum vibrating at f1 = 220 Hz, it might also tend to vibrate at modes of 2*f1 = 440 Hz and 3*f1 = 660 Hz and so on. Those higher frequencies, multiples of the fundamental, are overtones. A drum vibrating at f2 = 330 Hz will also have a relatively strong mode at 2*f2 = 660 Hz, so the 220 Hz and 330 Hz tones (separated by the simple fraction r = 3/2) together reinforce each other and have a pleasing effect. Overtones get faint really quickly, which is why fractions with large denominators sound dissonant.

“Suppose there is a musical savant who finds pleasure in all pairs of notes whose frequencies have a rational ratio” ... gotta be Jacob Collier

I liked your presentation on Lebesgue measure. It would have distracted from you narrative but I want to point out to your audience that you actually proved a more general theorem. Every countable subset of the reals has measure zero

The limit of quality when it approaches to perfection is your channel. I totally love your explanations and your animation style. Keep up with the good work! I've watched all your videos and I've already become a fan

Cacophonous is not the same as dissonant. The word you want is dissonant.

Just beautiful. I loved the fact that when you were naming a few rational numbers, the corresponding chord was seamlessly playing on the background. Nice tying up with the Lebesgue measure at the end.

You just helped me solve a topological problem with your approach to measure the rationals in the interval [0,1]. Which made me realize that the rationals, even though they only consist of single point sets that are not adjacent to each other, are not closed under the usual topology of the real numbers, which in turn made me realize that the theorem of Heine/Borel that closed + bounded = compact is something truly special about the real numbers.

Wow, just wow! That is seriously a ridiculously beautiful proof and consequence! Man, I was just sitting staring dumbfounded at my computer screen because of the elegance I was presented. This is why I love and adore math and find it one of the most beautiful things we humans can perceive and understand.

I absolutely love your videos, and everything about them. You perfectly bring out the beauty of mathematics! Keep the good work up :)

13:12 This has helped me get a better grasp of countable vs uncountable infinities far more the many Cantor based videos. THANK YOU!

This was beautiful and mesmerising. Without being cliche, this opened my eyes and made me see measure theory in a way nobody else has explained it (at least to me). And it harmonised with me on a deep level. Your videos are so well thought out and graphically concise. Thank you for all your work, and keep it up 👍