The link that Pythagoras supposedly discovered between math and music is that the most basic consonant intervals (octave, fifth, fourth) correspond to the most simple of superparticular ratios (1:2, 2:3, and 3:4 respectively). This basic understanding is the beginning of all music theory.Dunbar wrote:i was under the impression that maths and music theory, or harmony, were closely linked. I think Pythagoras is credited as the first chin-stroker to work out the math behind scales and the harmonic relationships of notes.
Equal temperament (the way the modern keyboard is layed out) is a bit of fudge, it doesn't follow the maths (that's because the maths sounds bad when followed to the letter). But there is method to musics maddness.
The problem is that if you use these mathematically pure intervals, and ascend through the circle of fifths (c,g,d,a,e,b,f#,etc) the 'c' that you arrive at will be slightly different than the c you arrive at if you start at the same low c and cycle upwards by octaves.
This difference is called the pythagorean comma. And it is the reason for all of the different temperaments western music has gone through.
All of these are an attempt to compromise between the need for music to have perceived consonances, and the need for a tuning system that allows all of the different instruments, with their increasingly large ranges, to interact with singers and with each other without a major trainwreck. It is not because equal temperament sounds better. On the contrary, acoustically pure 'Pythagorean' intervals sound absolutely gorgeous compared to their tempered counterparts, which sound sort of 'off' after listening to the others.
For more information on acoustically pure intervals, look here: http://www.justintonation.net
