TUNING digest 1380: Schoenberg, over-/undertones

>> }Schoenberg . . . completely recognized the overtone series as the
>> }basis for 12ET.
>>
>> Are you aware of the extreme inconsistencies in this position that
>> Partch pointed out?
>
>Please elucidate.

In his "Harmonielehre" [1911], p. 24-25, Schoenberg explained
the diatonic major scale as deriving from the three triads
(i.e., the first five, and five strongest, partials) built on "I, IV
and V", and said that as the higher overtones are a part
of the sound of music, they must also be taken into account
in harmonic theory, and he illustrates partials up the the 12th in
his diagram as representing chromatic tones, but without any
further explanation.

In the article "Problems of Harmony" [1934] (reprinted in
"Style And Idea", p. 268-287), he derived the 12-eq chromatic
scale from the first 13 partials of the "I, IV and V".

In "Genesis of a Music" [2nd Edition, 1974], p. 418, Partch
criticized these statements by comparing the cents values of these
partials with those of the 12-eq scale, noting that the 7th partials
are 31.2 cents flatter than their supposed 12-eq representations,
the 11th partials are 48.7 cents flatter, "very nearly a 'quartertone'",
and the 13th partials are 40.5 cents flatter.


>> }Partch did Schoenberg one better by explaining the minor
>> }through an undertone series.
>>
>> The "undertone" explantion of minor dates back long before
>> Schoenberg. But Partch scoffed at any reference to
>> "undertones" or the like, calling them "hallucinations" or worse.
>
> Where does he say this? I am more familiar with his use of what he
> called "Utonality" - which was intervals formed from inversions of
> "Otonality" ie. Otonal intervals were derived from the overtone series,
while
> Utonal intervals were derived from the Undertone series.
>
>(Just re-read Genesis a couple of months ago)>
>

I thought I remembered Partch saying that too, but I've looked
for the citation and can't find it. On pages 75 and 89, however,
he does note the controversy surrounding the theory of an
"undertone series" and says that it is not a part of his theory.

Partch explained O- and Utonality not in terms of over- or undertone
series, but as an inherent dualistic numerical property of the ratios
themselves. It so happens that these properties *do* explain the
over-/undertone series, but Partch did not use these as a basis
for his harmonic theories.

The theorist most associated with dualism was Hugo Riemann,
an Austrian who formulated his theories based on over-/undertones
in the late 19th century, but he too was uncomfortable with the
idea of an undertone series, and by the early part of this century
he had discarded it.

PS. Anyone who gets hold of a copy of "Style and Idea" and
thinks of Schoenberg as being serious and having no sense of
humor should read the short "Sleepwalker" (as well as its longer
and more sober sequel "The Music Critic") -- it's a stinging
(and hilarious) attack on a critic who published a bad review
of a Schoenberg concert, even though he apparently saw only
about half of it!

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

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