Is the Pi melody real or fake? Having seen this video I can't stop wondering whether it is real (which is amazing) or fake. A mathematician-musician polymath opinion needed :-)
 A: It's "real", but somewhat deceptive. The melodic line (the notes that he's playing one-at-a-time with his right hand) does indeed map to the decimal digits of $\pi$. However, the harmony (the notes that he's playing with his left hand), are just arpeggios in A minor and have nothing to do with $\pi$. If you removed the harmony and just listened to the melody, then you probably wouldn't find it to be particularly aesthetically pleasing, and probably no more or less so than a completely random melody composed from the same ten notes.
A: Here is an alternative take on mapping $\pi$ to the diatonic scale. There are probably as many ways to translate $\pi$ to melodies as there are digits in it. And all mappings from digits to notes are arbitrary, as is the base 10 representation of numbers. It might be interesting to use a base 12 representation and map to the chromatic scale.
There have been attempts at using $\pi$ in the construction of tuning systems. The so-called Lucy tuning has a fifth of $600 + 300/\pi \approx 695.5$ cents (in tempered tuning it is 700 cents). A search for this tuning system may soon take you into New Age land, so be warned.
A: This is what can be made from the digits of pi base 12 played in the 12 tones.
https://www.youtube.com/watch?v=0Dwvn73tz8E
