source file: m1385.txt
Date: Tue, 14 Apr 1998 13:52:19 -0400 (EDT)

Subject: Re: TUNING digest 1380: Schoenberg, over-/undertones

From: Johnny Reinhard <reinhard@IDT.NET>

On Tue, 14 Apr 1998, Paul H. Erlich wrote:
> >
> >}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.

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.   

> >}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".

That Schoenberg was confused by just intonation as it regards to higher
primes should not be surprising.  Partch never composed with 13th limit
intervals -- even though he included a fairly exhaustive 3 page list of
13-limit ratios in Genesis.  

When I first came across Schoenberg's rationale that 7/4 was a minor
seventh when simple arithmatic would account for the 16/9 I felt a duty to
jump on this error, as Partch did.  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.

> >}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. -- Monzo

This sounds like Partch was flexing.  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?  

> >Me - Paul:
> >Please continue, to where Partch shows that two notes which Schoenberg
> >assigns to the same 12ET note are in fact 99 cents apart. I lent my copy of
> >Genesis to a friend, so I don't have the reference handy.

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.   

> >Reinhard:
> >
> >>> }Partch did Schoenberg one better by explaining the minor
> >>> }through an undertone series.

I guess much of this comes down to whether one believes in the undertone
series, as I do.  Partch's use of the utonality clinches it for me
regardless intellectual machinations. I'd love to hear from those on the
list regarding this matter.

Undertone "series: singing by Tibetans?  Allen Strange's wife wrote a
thesis on the subject regarding the violin, I believe.  Is it not the
anti-matter of the matter?

I find it hard to believe either Schoenberg's "artificial" explanation for
minor, or Partch's numerological inversions.  There's something there
(IMHO).

Johnny Reinhard
Diretcor
American Festival of Microtonal Music
reinhard@idt.net

MicroMystery Tour '98 -- May 7 and 8 at 8 pm in NYC at
Columbia University's St. Paul's Chapel

PS
April 20th LA MicroFest at Pierce College at 7:30

April 21st lectures at CalArts in the afternoon (check with CalArts)

I'll be cack on the list following my return from LA