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Monday, 10 February 2003

Consonance / dissonance

It's a small step from equal temperment to total dissonance. Have you ever noticed how all the melodic composers are in to alternate tunings? This because equal temperment is just out of tune. It doesn't sound that way to me and maybe you, because we're used to it. But consonant folks can hear it. So they experiment with just intonation, new tunings, historical tunings, anything to fix the out-of-tuneness of the equally tempered system.

Tuning ought to be built on fractions. This note vibrates three times, during the time this other note vibrates two times. Equal temperment has no fractions. It's based on the twelfth root of two. An octave, from any note, is excatly twice the frequency of the octave below. A chromatic step from a note whose frequency is N, the frequency of the next higher note is N+N*2^^(1/12). Got that? This is not a fraction.

So everyone used to equal temperment is used to tuning that is not fraction based. Every other tuning in the world, as far as I know, is fraction-based. Our tuning is weird and artifical. It always sounds somwhat out of tune, so as to avoid ever sounding completely out of tune. The charecter of older pieces of music suffers for this. But furthermore, we lose a reference point for consonance. A fifth should sound completely consonant. But in equal tempermant, it's not because the fractions are off. It should be a fraction of 3/2, but it's something different. If you graph the frequencies, they don't cross at Y=0, even though they should. Since everything is out of tune, everything is in tune. You lose track of consonance completely. After a while, it sounds just dandy to put a tritone in the bass line. Can't decide on a fourth or a fifth? Go in between! It does sound fine and dandy, because the tuning is encouraging it.

All notes are equally valid, you know, like 12-tone rows, because it's just the obvious direction for equal temerment to go. Tritones are great. minor seconds are great. Sitting in the bass on a minor 6th in a major chord is just as good as anything else.

If you see my band-mates, please pass this along....

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