There was a C4 TV series by Howard Goodall recently, which explained the modern tuning of instruments. He started with Pythagoras, who derived his tuning from the nodes of a vibrating string - half giving the octave, third giving the fifth above that (I think - you will notice a certain vagueness - I've got to watch it again). Pythagoras, like Newton, had other interests than the scientific, and seven notes (it is, not eight) fitted the grand theory of the universe, as did Newton's colour divisions. Starting, however, from different points on the scales gave different tunings. G derived as the fifth above the C above middle C would not be the same as G derived from the octave above the G above middle C. I think. This gave all the different feels to the keys, and made playing with different instruments together impracticable. So the tuning was fiddled with, tempered, to form a compromise which allowed orchestral playing, and lost the differences of the different keys. He also gave the origin of middle C, which I have forgotten, and that A was originally lower than 440. Also that some halls now tune higher than 440, and that some singers avoid some of them, because the higher tuning forces them to sing above the break (?) in their voice too much.

Penny