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by baddox 4261 days ago
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...

1 comments

Yeah, a little bit! What's interesting is that we're so used to equal temperament (i.e. a bit of error added to most intervals in exchange for greater flexibility) that pieces played in just intonation sound "off" to us, even though they're more mathematically correct.

Also, I believe instruments with arbitrary pitch (violin, voice) tend to naturally drift closer to just intonation.

I've been trying to train myself to hear the JI resonances (Harmonic Experience has tons of exercises for this). I can hear the sharpness of the ET major third and the flatness of the ET minor third fairly easily.

Barbershop quartet music (and other a capella music) is a great place to hear just intonation. The consonant barbershop seventh chord was a relevation to me when I first learned of it. It's really close to the dissonant dominant 7th interval, but serves a very different purpose harmonically. The minor seventh is also a different interval. Thus there are actually 3 seventh intervals, all of which are approximated in ET by a single note. This blog post has a good summary:

http://www.garygarrett.me/?p=1575