> On Fri, 16 Sep 2011, Michael Smith wrote:
>
> > I'd be curious to know what makes one style of music more 'rational'
> > than another. In what way is say a Haydn symphony more rational than a
> > ricercar by Frescobaldi or a motet by Ockeghem?
>
> Solving the pythagorean comma thingy?
I would have said the syntonic comma was more of a problem, at least since thirds became popular as harmonic intervals. In any case, all the tuning theorists of the xvii and xviii ss. (Kirnberger, Werckmeister, Young etc.) seemed to be mostly worried about that one.
But I assume the reference here is to equal temperament. Funny how that should be regarded as a triumph of rationality -- funny even on the etymological level. Equal temperament works by making all the keys equally out of tune, and out of tune in the same way. Equal-tempered intervals are literally irrational (since the square root of 2, and by implication all the even roots of 2 out to 12 and beyond, are irrational numbers, as Pythagoras famously observed). Details available on request, but the short of it is that equal-tempered tuning is all fudge and blur; nothing rational about it. It's a kind of Solomonic rough justice that splits the baby in twelve. (Perhaps that's rational in a Swiftian sense.)
> After that, the circle of fifths
> exactly chimes with the octaves, making modern harmony possible (because
> now you can modulate using the same instruments rather than needing to
> grab new ones).
This is kinda muddled, I fear, and conflates a number of different practical problems that confront working musicians.
Unfretted string instruments (violin, cello etc.) don't need equal temperament to play in tune, nor does the human voice. Swapping instruments (or crooks) used to be an necessary technique for brass players, but it was valves rather than equal temperament that obviated that requirement; and brass instruments by definition can't play in equal temperament, since they depend on the natural, 'rational' harmonics of a resonating tube. (Well, they could if they had twelve valves; but they don't).
Brass players tune, more or less -- usually less, in my experience -- to equal-tempered instruments, by 'lipping' the pitch up or down. Which is to say, by de-tuning their instruments. Trombone to be sure is the exception; because of the slide, it falls into the voice/unfretted string category, and can realize any interval, rational or not.
> I'm perfectly open to the idea that you can define rationality differently
> (and that sufficient unto every culture is the rationality unto). But I
> think what mostly matters here is the "sound of regularity" for Joanna,
> who has grown up in that system, and who seems attracted to music that
> sounds less regular by its criteria -- which unites middle eastern music
> with Renaissance motets.
Ah well, but that's just provincialism, isn't it? "Rational" simply means "what I'm used to".
> Another ways to think of it are parts that seem (to the modern listener,
> socialized as we are) more independent and less subordinated to, and
> contrained by, the pattern of the whole.
I would have said just the opposite -- if you compare, as I suggested earlier, Haydn and Ockeghem. Alto lines in the 'modern', 'rational' world of music are generally so boring that it's no wonder altos are such notorious substance abusers. (Brahms is the great exception; was Clara Schumann an alto, I wonder?)
-- --
Michael J. Smith mjs at smithbowen.net
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