88CET #17: Voice Spacing in Counterpoint

In nonoctave tunings, chord-tone spacing is no longer independent of chord
quality (sonority). In 88CET, you can't, for example, have a subminor triad
spanning more than an octave, or a major triad spanning less than an octave.
The subminor third is only available within the first octave's span, and the
major third is only available in the second-octave's span as a major tenth.

What does this mean to a composer, other than the obvious fact that you have
to plan spacing and quality each in light of the other? Does this pose
problems? Certainly it can complicate some situations. For example in
chorale-like, first-species counterpoint (and thus in a lot of small ensemble
compositions) you usually want most voices to move in small, smooth steps.
Suppose that all voices are closely spaced, forming a subminor triad. It would
clearly be impossible to expand that subminor chord in small step-wise motion to
a major chord.

Still, that certainly doesn't prevent you from presenting the essential
sonority of a subminor chord moving to a major chord. First of all, adding a
bass note at a fifth below the root of the subminor triad, doesn't change the
essential sonority of that triad very much. That chord would then span over a
range of a major ninth, which can expand step-wise to a major tenth. The root
of that subminor chord could even be a common tone between the two chords.


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Brian's writings are a little like plastic explosives. They come in many
shapes and forms, but no matter what shape they take, they detonate with
explosive force! Usually this explosive force is one of amusement. (Although I
think he's putting too much effort into pointing out who rather than what his
research disagrees with, but let's not get into that.)

I think it's important to listen to his research carefully, because the
points he's raising are definitely meaningful. But recall what I've mentioned
about Brian before: When he gets into something, it becomes his entire world
for a while, and he sometimes loses perspective on the big picture.

It's worth asking exactly how the information in Brian's psychoacoustics
postings affects the art of composition. I think that it helps in important,
but in more peripheral, ways than Brian seems to be suggesting.

Consider his points about whole-number-ratio harmony. What did composers
know before? We knew that whole-number ratios, up to a point, outline
meaningful harmonies. And after all of these statistics about stretched
octaves, low-frequency effects, neuron firing rates, basilar membrane anatomy,
and so forth, what do we now know? We find that whole-number ratios, up to a
point, outline meaningful harmonies. Hmmm... Sounds familiar, eh?!

What matters, I believe, is that we now know more detail about that point
exactly where the just-intonation model breaks down. We shouldn't conclude from
this that the JI model is worthless. I think it's pretty obvious from thousands
of years of history and individual exploration that it is meaningful. But it's
only a model, and every model has its limits. Brian's posts may help us find
those limits.


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