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TUNING digest 854: further response to Paul

🔗Daniel Wolf <106232.3266@...>

10/4/1996 1:59:12 AM
(1) I think that my musical examples are sufficient to demonstrate that
unless the harmonic situation is static (which is indeed the case for some
repertoires, but I sense that your algorithm is geared to more traditional
western materials) your description will not be musically useful, and
within a static scenario, is is probably meaningless, as any values set by
your algorithm are only in comparison to sonorities external to the music
at hand. "Rootedness" I find to be extremely problematic musically, in the
same way that the Fuxian bass line is simply more convincing musically than
the Rameau basse generale (why is it that all of those dead, white male
composers read Fux and ignored Rameau?). The idea of hearing a single chord
outside of its contrapuntal (voice-leading) context is strikingly
_unmusical_.

(2) I assume that combination tones will have significantly lower
amplitudes than the instrumental tones played. (By the way, I would be
interested in learning how one can calculate the amplitudes of combination
tones if anyone knows). Thus, only pitch complexes constructed from (lower)
harmonic series members will be significantly affected by masking, such
that difficulties in discerning individual tones from the entire complex
occur. (Anyone who has ever tried to dictate ensemble musics has
experienced the masking problem).

(3) I assume that pitch information is mentally processed as frequency
rather than wave length (the ear functioning like a AD transformer): I may
of course be entirely wrong about this, but it is a reasonable assumption.
(An intutionist approach will takes temporal perception over spatial as the
basis of the initial construction (cf Brouwer _Cambridge Lectures_); the
spatial interpretations only follow.) The classical harmonics approach does
not contradict this, as the first visual observation was of different
strings (of different tension or thickness) moving faster and slower and
yielding different pitches (this is immediately observable in gut or wire
strings throughout the frequency ranges presumably used in ancient music),
and then the compared lengths of a single string were then used to quantify
this observation. Oscillatory periods and wave lengths are not observable
as such without special apparati (this is not completely true, but the
perception of wave lengths as physical distances depends on instrumentation
and conditions generally outside of contemporary concert music and well
outside of the ancient setting).

(3a) This is a weak argument, but I give it anyways: why is it that
microtonal music theorist structure their discourse almost universally in
terms of frequency ratios and not stringlengths, wavelengths, or periods?
Either this is just a convention (which I doubt because each individual
theorist seems to like building from first principles), or there is indeed
an intuitive quality to frequency ratios not shared by _alternative_
descriptions.

(4) Indeed, classical harmonics had no definitive _musical_ preference for
subharmonic or harmonic divisions, and their results gave stringlength
measurements for scales constructed in both ways (with preference for the
least cumbersome numerically, and possibly using the physical _boundary_
problem of not being able in practice to divide the string into many parts
as a determinant of their preference), the issue being the prefered
intonation of those (melodic) scales, not their analysis as harmonic
complexes. _Mathematically_, however, the arithmetic divisions (subhamonic)
were recognized as closed segments of the harmonic division; each
individual arithmetic division yielded a finite number of pitches and was
exhausted, while the harmonic division was continuable indefinitely. In
this sense (a kind of set theory), the subharmonic divisions were
considered inferior to the harmonic. The issues we are dealing with -
comparing different pitch complexes - are outside of the narrow framework
of classical harmonics, but I see no contradiction between mine and the
classical approach.

(5) I haven4t a degree in physics but I do recognize that the region
between the smallest particle (10^-33 or so) and the vacuum (null) is not
precisely mirrored by its inversion.

Daniel Wolf

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Date: Fri, 4 Oct 1996 00:54:22 -0700
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