Eureka!

[telerib]

It started out with a brief perusal of the UMD campus rag, The Diamonback. I came across this little gem:

He's [a music graduate student] talking about "just intonation," which is a kind of temperament, or tuning, in which intervals are spaced - that is, flattened or sharped - so there's no dissonance between them; that's different than the widely used 12-tone equal temperament, in which the pitches aren't in tune with each other.

Whatever is this person talking about? I wonder. Obviously, there has been a loss of data from the grad student to the 'journalist.' I have heard of Pythagorean tuning, "The Well-Tempered Clavier," and have a vague notion that there are other ways to tune than the modern one, but saying that the modern equal temperment is "not in tune"? Huh?

Mystified, I turned to that source of all information, Google. Google kindly referred me forward to the Wikipedia's article on just intonation. Now the vague outlines of a geometry problem are starting to take shape, with the Least Common Denominator being a pain in the butt. That article gave me a whole list of temperments or tunings I'd never heard of. And there - a link to Pythagorean tuning!

It finally makes some sense! What it is, why it was used, and why it is largely no longer used. I am happy to see that all the reasons it is not used do not apply to me or to my harp! On the other hand, tuning my harp in this way will put me out of tune with just about any other instrument I'd care to jam with. (Never mind that my tuner is hard-wired for equal temperment; I'd have to get a new one that shows Hz.)

I'm just absurdly pleased that I finally have a handle on this, or at least have located the handle. Early music theory is on my list of private research projects that get worked on sporadically as time allows, and I always wish I had more time for them. A little bit of unexpected enlightenment just makes my day.