Neil's Post in 980

G'Night John Boy-
Neil Haverstick stated that the harmonic series is a natural
phenomenon, and that deviation from it is deviation from the "pure"
in some way. I disagree, and I agree. In nature, there are no physical
objects that vibrate with a pure harmonic series of partials above the
fundamental. The harmonic series is a construct of our mathematical
minds, modeling a phenomenon first observed with our nonlinear hearing
mechanism, and later with lab instruments. The harmonic series is an
idea, just as is the beatlessness of simultaneously sounding simple
tones.
Making a scale from a pitch set of harmonic partials divided down
into the octave is no more natural than making a scale from a pitch set
whose elements are related by small number ratios. They are both
constructs of the mind, and in my view perfectly natural things (we are
not in the world, we are the world).
We may have, hardwired into the structure of our brains, an innate
musical understanding of the harmonic series, but we may be hardwired
for understanding small number ratios as well. For that matter, we may
be hardwired for mathematical understanding of all that we can understand
mathematically, and that may spill over into musical understanding, even
of tempered and non-octave scales.
In short, I don't think we are in any position to say what is
natural to our musical understanding and what is not. Further
psychoacoustic research may shed some light on what musical
structures are more primal, but I haven't seen anything convincing
yet. I'll bet Brian Mclaren has an opinion on this.

John Starrett

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M.L.West's Ancient Greek Music (Oxford Univ Press, if I remember right).

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