32. KEYS TO MUSIC

We might notice, rather trivially, that in the C to C octave, there are 5 black notes and 8 white notes making a total of 13 notes – a surprising occurrence of the Fibonacci numbers!

More seriously, Pythagoras disocovered that the tones produced by stretched strings when they are plucked or struck, are harmonious when their lengths are in the ratio of certain whole numbers. For example, a string twice the length of a C-string will sound a C an octave lower. A string 3/2 the length of a C-string produces an F, and so on. You might like to investigate this further. The well-tempered scale gives an interesting variation.


http://en.wikipedia.org/wiki/Pythagorean_tuning

http://paulscott.info/making/ch12pythagA.html