| Out of curiosity, have you studied just intonation? I'm currently reading the mostly excellent Haromonic Experience [0]. I'm reasonably well educated on music theory, but I had never looked into just intonation and the way frequency relates to our perception of pitch and harmony. I'm finding this stuff enlightening. An ideal string (or any oscillator) when disturbed (e.g. plucked) will tend to vibrate at a fundamental frequency of x Hz as well as modes of 2x, 3x, 4x, etc. These higher frequencies at integer multiples of the fundamental frequency are called harmonic partials. This is a physical phenomena unrelated to music and human hearing. But the basic elements of harmony come from the fact that our auditory system seems to be "tuned" to identify harmonic partials. If we start with a fundamental frequency x Hz (let's call it C), the first partial is 2x Hz, and it is another C an octave above (multiplying or dividing a pitch by a power of 2 will give you the same pitch in another octave). The next partial is 3x Hz, and it sounds like a G. This is the interval called a perfect fifth, and is the strongest, most stable sounding interval (other than the octave). The next partial is 4x Hz, which is just another C, two octaves above the C we started with. The next partial is 5x Hz, which sounds like an E. This is a major third, which is another strong and stable interval which is ubiquitous in most music. [0] http://www.amazon.com/gp/product/0892815604/ref=oh_aui_detai... |
Also, I believe instruments with arbitrary pitch (violin, voice) tend to naturally drift closer to just intonation.