"Pythagoras surmised that there might be a divine reason behind our tendency to find specific harmonies and note intervals more pleasant to the ear than others. He pointed out that there were mathematical congruencies behind these notes – a phenomenon he first observed when he passed by a blacksmith's shop and noticed that the pings of the various hammers fell along common musical intervals. Why? It was the proportions of the varying weights of the hammers – a twelve pound hammer and a six pound hammer produced pings an octave apart. Similarly, a string stopped at 3/4 of its length produces a note that is 1/4 above the octave. This fourth harmony is extremely common and we find it pleasant. If the stop is 2/3 the length of the string, then the note is a perfect fifth. A stop at half the length produces a note that is an exact octave higher than the full length of the string.
Needless to say, this is somewhat uncanny. Spooky, even. Why should this be? Pythagoras surmised that the gods generally prefer small numbers such as occur in these fractions, because simplicity is always profoundly more elegant. Pythagoras was a bit of a numbers nut, so the fact that there were mathematical underpinnings to the most common musical harmonies was very exciting for him. It was like unlocking a key to the universe. He further identified three kinds of music: instrumental, human and celestial. [...]
The celestial music, the music we attempt to imitate – where the divine harmonies come from – actually does exist, Pythagoras said, and this music has its source in the spheres that 'hold' the planets. He believed that the planets were attached to revolving crystal spheres (how else could they stay up?) and that each planet, along with its crystal sphere, produced its own unique tone as it whistled through the cosmic ether. [...]
Pythagoras was convinced that each musical scale has profound, specific and unique effects on people. The Hypophrygian mode is one of the many variations of the diatonic scale where the intervals between notes have been altered. According to Pythagoras, a tune in the Hypophrygian mode could totally sober up a drunk young man. In his day, the power of music was commonly accepted, and there were music-based healing centres throughout Greece. The notes of the basic scale were associated with the Muses, and each tone had its own attributes and temperament. The seven planets that the Greeks could see had associations with the seven vowel sounds of classical Greek, which were also considered sacred. The various names of God were formed out of recombinations of these vowels and harmonies. The cosmic harmonies informed every aspect of life – our speech, our bodies and our state of mind. These musical and mathematical correspondences among all things were out there, and the idea was that we needed only to discover them."