On 2018-01-31 17:40, Bill Gosper wrote:

On 2018-01-31 08:22, Henry Baker wrote:

...

I'm curious as to what others think about this Fourier Transform video (1/26/2018).

http://www.3blue1brown.com/

https://www.youtube.com/c/3blue1brown

I wish, very early on, when he's visualizing those simple chords, that he'd make a point of sliding around the relative phases, making visually dissimilar waveforms that sound the same. --rwg

Reminder: Try playing with Howard Cannon's http://hichacks.is-a-geek.net/triangles/artcircle *These are Fourier series: All the rotors (harmonics) remain constant in length and turn at constant angular velocity. Yet inhttp://hichacks.is-a-geek.net/triangles/?a_=besser&radiusPct=90&nRotors=23&d... <http://hichacks.is-a-geek.net/triangles/?a_=besser&radiusPct=90&nRotors=23&dtPct=20&rotorSort=1&=7&cmn_=32&cmt_=highcontrast&cmabs_=false&stepsPerCycle_=1&delayMS_=0>* the vector sum runs back and forth seven radians around the rim of a circle. Try reducing the number of rotors. And in *http://hichacks.is-a-geek.net/triangles/?a_=incirc&radiusPct=42&nRotors=23&d... <http://hichacks.is-a-geek.net/triangles/?a_=incirc&radiusPct=42&nRotors=23&dtPct=20&rotorSort=1&cmn_=32&cmt_=highcontrast&cmabs_=false&stepsPerCycle_=1&delayMS_=0>* the vector sum runs alternately around an equilateral triangle and its inscribed circle. --rwg