Schoenberg

>From Tuning Digest 1385 -- Reinhard:
>On Tue, 14 Apr 1998, Paul H. Erlich wrote:
>> >
>> >} In his "Harmonielehre" [1911], p. 24-25, Schoenberg
>> >} explained...
>
> This sounds to me like 5-limit just intonation as a basis for
> conventional harmonic theory, a further developing of
> Helmholtz in using the overtones as a foundation for
> harmony. Illustrating partials up to the 12th or further
> merely underlines the exactness inherent in the series.

Monzo:
First, it was I and not Erlich who gave the Schoenberg
citation quoted above.

It's true that Schoenberg envisioned the basic scale as
a 5-Limit just system. But what did you mean in that
last sentence, about underlining exactness? Is this a
reference to the fact that as you go higher in the overtone
series, the partials divide the pitch-space into ever-smaller
increments?

Reinhard:
> ...Shoenberg defined dissonances as corresponding
> to the remote overtones. His was an open theory that
> may have accounted for jazzy, pop, and other interval
> invasions to previous theory. Forgive me for speculating.

Monzo:
Indeed, Schoenberg's tonal theory is almost exactly the same
as much of the established basics of jazz harmony. His
most important (and controversial) idea was this very one.
"Dissonances" did not have to sound quickly according
to rules, but could be used as regular chord members,
because several higher overtones come close to these
(12-eq) notes.

Note that Schoenberg hedges his bets by saying at the
outset that his exposition is "based on the _possibly
uncertain_ overtone theory" [emphasis mine], and that
he used it because it seemed, in his experience, to
agree best with the facts of musical usage by the
German masters (who are the only ones important
to Schoenberg).

Reinhard:
> Schoenberg describes temperament as an
> indefinitely extended truce (Harmonielehre p.25) and says
> the chord is the synthesis of the tone. Would either
> Partch or Erlich disagree?

Monzo:
Hey, don't leave me out of this! I've written a _lot_ on
the rational implications represented in Schoenberg's theories.

I _do_ think Partch would disagree with this: as I pointed out,
he emphazed that the undertone series _as an acoustical
phenomenon_ was not a part of his theory, but the mathematics
involved in calculating it was.

Erlich would probably disagree too, just because he likes to
disagree (-- but that's OK by me, Paul; in fact it's healthy in
this forum).

Reinhard:
>
> Frankly, this is more tomfoolery than it is decisive. Schoenberg
> never pretended to understand the mathematics, preferring to
> let the music speak for him and to apply intuition and the
> reservior of theory as it existed at that time.

Monzo:
I must agree wholeheartedly with the second sentence here.
Schoenberg expressed in several of his writings that he usually
composed very spontaneously, and a notorious tidbit of Schoenbergian
musical history is that he wrote his opera "Erwartung" in 17 days
(summer of 1909), and even though I believe scholarship has found
this to be somewhat exaggerated, the piece was still written in
a very short time, no longer than a couple of months. To have
written what I consider to be the most experimental piece of
his career (a career which lasted another four decades!) and
the one furthest removed from any conception of what a piece
of music was up to that time, in such a short fury of inspiration,
underlines to me how far Schoenberg trusted his instincts.
In fact, his whole speculative theoretical output (i.e., that other
than what he considered to be tutoring in "composer's basic
training") is merely an attempt to provide some kind of rational
[note well that word! -- but used here in its sense of "logical",
not as referring to ratios] underpinning for the radical sonic
structures he wrote into his pieces.

Reinhard, from Tuning Digest 1379:
> Schoenberg did imagine music microtonally. And
> with his gift of musicianship he could imagine much
> more than is usual. He wrote of 53ET to Busoni...

Monzo:
In "Harmonielehre", on the pages we are here discussing,
Schoenberg cites both Busoni's musings on 36-ET and a
certain Dr. Robert Neumann on 53-ET. He first maintains
that at some future date the world will be ready to accept
such enlarged scale resources, then scoffs at the idea that
musicians in 1911should be bothered with such
number-play, as "12 x 12 notes provides more than
enough to explore" for the forseeable future, and never
mentions microtonal intervals again (or possibly mentions
them only once more in passing).

In several places throughout his theoretical writings,
Schoenberg (seemingly proudly) announces his ignorance
of musical mathematics, until one finally finds a footnote
explaining some simple ratios in his "Preliminary Exercises
in Counterpoint" [1963], written near the end of his life.

Judging by all accounts I've read, both Partch and Schoenberg
each must have had a profoundly sensitive ear for pitch.
Schoenberg, after all, is the person who came up with the
idea of "tone-color melodies", that is, instruments of several
different timbres playing succesively the same note, with the
different overtones of the different timbres providing a sort of
"melody of overtones". This is the last idea in "Harmonielehre"
(and was actually explored on chords in the middle piece of
"5 Pieces for Orchestra" [1909]), and was surely the most
far-out idea presented in a harmony book up to that time.

Reinhard, from Tuning Digest 1381:
> Most troubling for me was the basis of Helmholtz for
> Schoenberg's theories, but with nary a mention.

Monzo:
As has been pointed out before (in a JMT article, possibly
also in the translator's preface to the 1978 English edition
of "Harmonielehre"), although Schoenberg professed to being
"self-taught" with the exception of his lavishly-credited
instruction from Zemlinsky, he does use many concepts
from several different turn-of-the-century theoretical treatises,
which _can_ be identified along with their authors, and
Schoenberg gives no references by name, with the single
exception of a focused attack on Schenker.

Although this is possibly just an attempt by Schoenberg
at assuming credit for as much as possible in his book, he
does address the lack of references early in the book by
saying that he only read the other books casually and
retained the good ideas without the extraneous information.

There's another perplexing aspect to Schoenberg's lack
of interest in using ratios in harmony. There is a book
published recently which I saw in the library -- I have
neither title nor author, but I think it's called "The Composer
as Numerologist" -- which purports to explain Schoenberg's
pre-compositional techniques as being based on
numerology. It has been quite definitely reported
(see Stuckenschmidt's biography) that Schoenberg
was a believer in numerology, and it seems that this
was passed on to his pupil Berg. (I'm not sure about
Webern in this regard -- anyone out there know?).

The argument in this book seems pretty plausible to
me, but it astonishes me that a composer so hung
up on numbers _and_ on explaining "dissonant" chord
tones as high overtones, would fail to see the relevance
and importance of using ratios as a notation for pitch.
I got into a small debate with Sandy McCroskey over
this, and he emphasized Schoenberg's conception of
the "democratization of the 12 tones". This sounded
reasonable to me, but surely someone with an ear
as good as Schoenberg's could tell the difference
between the 12-eq notes and their supposed rational
implications. So why not use ratios, and play with
_those_ numbers instead of the ones representing
the 12-eq pitch set??????

Joseph L. Monzo
monz@juno.com
4940 Rubicam St., Philadelphia, PA 19144-1809, USA
phone 215 849 6723

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