November 20, 2019 music

Anytime you want to use intervals based on perfect fifths, you’re multiplying and dividing by 3, but anytime you want to use intervals based on major thirds, you’re multiplying and dividing by 5. Starting from C, it’s possible to produce any note on the piano if you multiply or divide your frequencies by 3 enough times, but those notes won’t be in tune with the notes you’d get multiplying or dividing your frequencies by 5, because 3 and 5 don’t mutually divide evenly. This is not just an abstract mathematical issue. It’s the reason that it’s impossible to have a…