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>2. On Hindemith. Having never studied with him, I can only report his book
>Unterweisung im Tonsatz, translated as The Craft of Musical Composition.
>This is the book in which he builds up a new harmonic theory based on the
>harmonic series and then treats everything as 12-tET. Hindemith discussed
>the 7th harmonic at some length but did not, as far as I can tell,
>understand it. His book is to me a historical curiosity: it almost did
>something right, perceived something of an abyss at really paying
>attention to the harmonic series, and then retreated into the familiar.
>
>I'd be interested in others' opinions.

I think this evaluation is on the mark. Historically, the tidy-minded
Hindemith was looking for some objective way to counter opposing techniques
like the 12-tone method. He saw, quite rightly I think, that tonality is
inherent in the harmonic series, but then destroyed his own argument by
off-handedly saying that of course temperament was inevitable. He also
tried to use "undertones," if I recall correctly, without much
justification, to fill out the 12 tone system.

I thought I would report on what I perceive as a kind of contemporary echo
of this point of view. While at the 4th Symposium and Festival on
Intercultural Music in London last April, I had the pleasure of meeting Roy
Travis, professor emeritus of UCLA. While he was a warm and gracious man, I
can't say that I agree with the principles of paper he gave.

A student of Schenker student Felix Salzer and a defender of the
Schenkerian faith, Travis endeavored through his career to apply find ways
of applying such analysis to twentieth-century works of extended tonality,
such as those of Bartok. His claimed insight was to allow the construction
of "tonic chords" based on higher-order harmonics.

In an analysis of the Bartok 4th string quartet, for example, he showed how
a particular sonority consisting of the 1st, 5th, and 11th harmonics (C, E,
and F# in his analysis) could function as a "tonic chord" the same way a
major or minor triad had in the common-practice period. Like Hindemith, he
then casually remarked that the compromises of temperament were, of course,
necessary.

Now, I have no problem with Bartok's well-established use of non-triadic
sonorities, but I proposed to him in the question-answer session that
compromises of temperament (especially with regards to the 11th harmonic)
invalidated the justification of the harmonic series. His reply was, as
best as I can paraphrase, "I can only tell you that if the major triad,
which is also compromised by temperament, is justified through its
proximity to the tones in the harmonic series, why not the 7th, 9th, and
11th harmonics?"

I told him that,to me, the 11/1 ratio was a beautiful and consonant
interval, but that the equally-tempered tritone was quite a different
sound. He said that he thought that the tritone, in a given context, could
be heard as consonant, and suggested that perhaps people just hear
differently.

I hope I haven't misrepresented his point of view, but I thought it would
be of interest to the subscribers here.

Bill

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^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
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Interchangeable fretboard guitars

🔗John Chalmers <non12@...>

🔗alves@osiris.ac.hmc.edu (Bill Alves)