7 The fundamentals of Schenker's analytical method: the harmonic series in myth.
Schenker's Free Composition is a curious document, in which assertions, of a
more or less obscure character, greatly outnumber arguments. [23]
Such a
document depends for its credibility upon the authority of the author. To some
extent this can be assessed by consideration of those arguments he deigns to
supply, but for lack of many of these, the accuracy or otherwise of his
assertions in areas of which this writer has substantial knowledge carries much
of the weight.
An example of Schenker's style of argument appears in his
Introduction, where he purports to counter the question: But did the masters
also know about all this? [24]
His first response is an ad hominem attack
(This objection ... only betrays a lack of education). He continues to argue
that the masters had no need to write about the laws of art, which is true
enough, but scarcely to the point, since some of them did, and finally suggests
that the reader must concede that conformity of a composition with Schenker's
ideas shows that the masters had a keen awareness of such relationships. The
last seems to this writer not to follow at all, because of the many examples of
human behaviour which stem from unconscious motives. The entire paragraph is
consistent with the view that the masters' ground plan for music was
substantially different from Schenker's, which is why he is unable to find a
good answer to the question.
Schenker's description of his fundamental
structure is introduced by the curious phrase In nature sound is a vertical
phenomenon. [25]
Since in the open air, and in the absence of wind, sound is a
radial phenomenon, this is a peculiarly unfortunate phrase, which, this writer
has been told, sounds no more plausible in the original German. The figure to
which the phrase refers shows the first five notes of the harmonic series, so
what Schenker appears to mean is that the occurrence of the harmonic series as
a chord in music is a natural phenomenon. Unfortunately, this is still not true,
at least not in the sense that Schenker intends, in two aspects. The trivial
one is that on the majority of vibrating objects, it is much easier to
demonstrate multiple resonant frequencies sequentially than simultaneously. The
more serious objection is the one demonstrated above, that those musical
instruments which sound harmonic, or approximately harmonic, do so because of
the efforts of their designers and the choice of musicians, not because of the
inherent nature of music, either in the human central nervous system or in the
universe at large. Indeed, in a culture in which only percussion instruments
existed, it is conceivable that a completely different art of music might have
arisen, based on a dominant instrument with non-harmonic partials. The latter
would have been the foundation for a completely different harmony and
counterpoint, and the design of all other instruments would have had to
conform to it.
Schenker appears to have had some difficulty in finding a
reason to exclude the interval of the fourth from consideration as candidate in
some part of his fundamental structure. His basic thesis requires him to find a
way to deny to the interval of the fourth the same status in the fundamental
line as that given to the octave and the fifth.
[26] His argument appears
dangerous to this writer, for whom the chord generated by the harmonic series
reveals both the fourth and the fifth more readily than it reveals the double
octave, and for whom any argument concerning the fourth applies equally well to
the fifth. Moreover, if one attempts to derive harmonic laws from the harmonic
series, one could as reasonably derive melodic ones; but this leads to the
embarrassment of finding two minor thirds of different sizes before one finds
the tone, and of the latter the lowest one in the harmonic series is larger
than any tone used in conventional Western music, despite Kirnberger's attempt
to introduce the harmonic seventh in 1771.
[27]
These three examples do not seem,
to this writer, to demonstrate that Schenker is an author whose accuracy one can
reasonably take for granted. On the contrary, he appears to be ignorant of many
of the characteristics of sound which are of importance in music and
contemptuous of the means by which they can be discovered. He is also
inconsistent in the application of his arguments.
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