dots in the shark

Imagine somebody were to argue that Kool-Aid’s convenience outweighs the superior taste of real grape juice, and convinced society to switch en-masse to Kool-Aid. Imagine further that we grew so accustomed to Kool-Aid that grape juice began to taste somehow wrong, and we now preferred the taste of Kool-Aid. Sick, no? It happened, in music:

The twelve-tone equal-temperament (12-TET) system that we use today developed as an approximation to the first few elements of the harmonic series. The ratio of any two distinct tones in 12-TET is an irrational number, some power of the twelfth root of two (the half-step), and that irrationality creates dissonance. By contrast, scales whose frequencies are related by small whole-number fractions are minimally dissonant, because they synchronize – but we wouldn’t know, because we never hear such scales.

Fortunately, there now exists computer software that allows one to play in harmonically perfect scales from the computer keyboard. (“Harmonically perfect scales” = “just intonation” = “rational temperament” and other combinations thereof.)

I did a little experiment over Christmas, subjecting a few family members to blind taste tests of the two scales. I would play a major seventh chord (e.g. C, E, G, B) first in 12-TET, then in a scale for which the tones were perfect consonances (1, 5/4, 3/2, 15/8). Very consistently, everybody preferred the approximation to the real thing!

12-TET is a recent phenomenon, dating to around Bach, whose series of compositions, The Well-Tempered Clavier, was intended to showcase 12-TET’s capacity for modulation to any of twelve identical keys – all of them slightly wrong. Bach and others eventually convinced Europe and most of the world that the novel ability to modulate “freely” was worth the sacrifice of perfect harmonic intervals.

But that is not what my family preferred about 12-TET, because I never changed key. They thought a single, static chord sounded better in 12-TET than with just intonation. Moreover, that reaction is typical of people who have just been exposed to harmonically perfect scales (according to I don’t remember who; sorry).

My uncle Steve, an occasionally-professional musician, said the 12-TET chord had more “soul”, while the other was “too consonant”. Too consonant to sound good. His comment, while provocative, is not a good defense of 12-TET: dissonance should be intentional, not ubiquitous.

Before 12-TET, composers had to be conscious of the frequency relationships between tones. Now they don’t – almost all of them identify the pitch spectrum with the piano keyboard, as if the latter begets the former. Composers have largely lost sight of the mathematical origins of the pitches they work with.

I think we have screwed ourselves out of a lot of good music. Can you imagine restricting dance to a lattice – and not just some abstruse branch of dance, but almost all the dance in the world? Or can you imagine visual art limited to 16 colors – and no longer because it is convenient, but because we have come to perceive colors from outside the grid as wrong? Can you imagine math restricted to some excruciatingly small subset of the real line? That last example actually happened, although we eventually saw our way past it. It is hard to imagine how we could see our way past 12-TET.

I realize I am being quixotic, but I really think this is sad.

Ways I might change my tune

I have so far complained about the near-total domination of 12-TET over more conscious tuning systems. Might there be a few silver linings?

(1) A few years back, I bought some music in just intonation, from the Just Intonation Network. It is indeed sublime. Perhaps exposure to such artistic heights, and frustration with my own instrumental resources, will conspire to drive me away from what has been a blood-sucking hobby.

But really, I’m not going to stop playing music, so that’s dumb.

(2) Maybe the 12-TET system prevents musicians from wasting time. There are, after all, a lot of other parameters musicians can work with – the words, the instrumentation, the cultural context – and the Pandora’s Box of true freedom might lead one to spend so much time on harmonic questions that the music is left too poor in orchestration, lyrical content, or social midwifery to accomplish anything. Indeed, much of the music I got from the Just Intonation Network could be accused of such faults.

Alas, argument (2) is also lame, because although it’s true that some people would be wasting there time working with just intonation (e.g. Bob Dylan), there will exist others whose time would be best spent there, given appropriate accomodations. Comparative advantages differ. I would like a world in which someone whose comparative advantage might lie in the exploration of rational scales would have access to keyboards made for its exploration. Presently, such people have to learn how to program, or else how to build instruments. That difficulty drives most of them to other pursuits.

Which sucks.

# posted by Jeff Brown @ 12:56 AM