Over-/Undertone series

Just to clarify the point of the controversy over undertones:

The question is not whether or not it is possible to create a harmonic
series of pitches _under_ a "root", as the converse of those over it,
with which we are already very familiar -- as Joseph Downing (and Partch)
described, it can be easily demonstrated.

The controversy is over the concept of the undertone series _as an
acoustical phenomenon_ -- and this is something that, as Max Meyer
pointed out clearly, cannot exist.

I think this was the main confusion I had over the whole argument for a
long time.

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

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>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?

The first comment is vague. I don't know what the war was that resulted
in the truce. If it was the war between temperament and just intonation,
then one side clearly won the war; there was no truce. Partch would
probably say he was rebuilding just intonation from its ashes. Of course
meantone gets forgotten in this dichotomy.

The second comment is vague too, but let me interpret it to mean that a
chord is an approximate harmonic series so that every chord implies a
synthetic tone whose pitch is that of the fundamental of that harmonic
series. Clearly this view of harmony fails to account for minor and
other utonal chords, which, if viewed as a part of a harmonic series,
imply a fundamental that musically speaking is clearly a non-harmonic
tone. But by a Helmholtz/Plomp/Sethares analysis, utonal chords are at
least as consonant as otonal ones. So on this interpretation, yes,
Partch and I would both disagree with Schoenberg. However, there is
nothing wrong with a musical style based entirely on otonalities, which
(it is my understanding) characterizes the spectral school of
composition.

>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.

Can you elaborate as to how this is a response to Schoenberg's comments?

>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).

Anyway, thanks to Daniel Wolf and Joe Monzo for some good history
lessons. I agree with both of them!

>> Reinhard:
>>> Schoenberg describes temperament as an
>>> indefinitely extended truce (Harmonielehre p.25)...

> Erlich:
> The first comment is vague. I don't know what the war
> was that resulted in the truce...

Monzo:
Schoenberg continually speaks of "problems" in connection
with learning the craft of composition and also in connection
with the act of composing itself. After spending years trying
to divine as much as possible what Schoenberg had in mind
as regards chromaticism, intonation, ratios, 12-eq, and
pantonality (his term for what most of us know as
his "free atonality" period), I have come to the conclusion
that what Schoenberg meant in referring to "problems"
is that given the acceptance of the 12-eq scale as a
compositional medium, there are _many_ different ratios
(both higher-prime "overtone" relationships in vertical
sonorities as well as traditional 3- and 5-limit relationships
in melodic movement) that can be represented
by each 12-eq pitch-class, and the composer's task
is to understand what those rational relationships sound
like (and also to understand their psychological and
emotional effects) and how to represent those sounds
(and feelings) by notes available in the 12-eq scale.

The relevant passage is quoted below:

> Schoenberg [Theory of Harmony,1911, English trans.,
> 1978, p.25, in reference to the 5-limit diatonic major scale]:
>
> This scale is not the last word, the ultimate goal of music,
> but rather a provisional stopping place. The overtone series,
> which led the ear to it, still contains many problems that
> will have to be faced. And if for the time being we still
> manage to escape those problems, it is due to little else
> than a compromise between the natural intervals and our
> inability to use them -- that compromise which we call
> the tempered system, which amounts to an indefinitely
> extended truce.

Monzo:
I will continue the quote from this spot because it is
pertinent to the discussion we've been having of Schoenberg
[p. 25 and 26]:

> Schoenberg:
> This reduction of the natural relations to manageable
> ones cannot permanently impede the evolution of music;
> and the ear will have to attack the problems, _because
> it is so disposed_. Then our scale will be transformed into
> a higher order, as the church modes were transformed into
> major and minor modes. Whether there will then be quarter
> tones, eighth, third, or (as Busoni thinks) sixth tones, or
> whether we will move directly to a 53-tone scale that Dr.
> Robert Neumann has calculated, we cannot foretell.
> Perhaps this new division of the octave will even be
> untempered and will not have much left over in common
> with our scale. However that may be, attempts to compose
> in quarter or third tones, as are being undertaken here and
> there, seem senseless, as long as there are too few
> instruments available that can play them. Probably,
> whenever the ear and imagination have matured enough
> for such music, the scale and the instruments will all at
> once be available. It is certain that this movement is
> now afoot, certain that it will lead to something. It may
> be that here again many digressions and errors will have
> to be overcome; perhaps these, too, will lead to
> exaggerations or to the delusion that now the ultimate,
> the immutable has been found. Perhaps here, once
> again, laws and scales will be erected and accorded
> an aesthetic timelessness. To the man of vision, even
> that will not be the end. He recognizes that any
> material can be suitable for art -- if it is well enough
> defined that one can shape it in accordance with its
> supposed nature, yet not so well defined that the
> imagination has no unexplored territory left in which
> to roam, in which to establish mystical connection
> with the universe.

Monzo:

(Many people have noted the similarities between
Schoenberg and Partch -- if I didn't know better, I'd
be ready to swear that Partch must have read this
passage and used it as the catalyst for his life's work.)

Schoenberg _clearly_ realized that composers (and
performers) would eventually tackle the problems
of using more complex scale resources. It is obvious
that he knew that music would keep evolving, in
ways which could not even be imagined at the time
he wrote this.

I wondered in my last posting why Schoenberg placed
so much importance on numbers but manipulated them
as 12-eq pitch-classes rather than as ratios. That last
phrase about "unexplored territory" is probably the
key: the 12-eq scale _in relation to its supposed
representation of ratios_ is indeed "not so well defined"
by Schoenberg, and apparently, purposely left so, in
order to leave room to explore those "mystical
connections".

>> Monzo:
>> ...
>> 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:
> Can you elaborate as to how this is a response to Schoenberg's
> comments?
>

Monzo:
Simply that Schoenberg (as well as Oettingen, Riemann, et al.)
was using the _acoustical_ phenomenon of the overtone series
as a basis for explanation, while Partch denied this single
acoustical archetype as a basis for harmony, and emphasized
instead the properties inherent in _numerical_ comparisons.

> Erlich:
> Anyway, thanks to Daniel Wolf and Joe Monzo for some
> good history lessons. I agree with both of them!

Monzo:

In particular, I found Daniel Wolf's quoting of Schoenberg's
letter to Yasser to be invaluable. I've never seen it before,
and it clearly explains Schoenberg's position regarding
the 12-eq scale and its rational implications.


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

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Trying to understand the 12ET overtone Schoenberg discussion - Are we saying
Schoenberg recognized that the tempered scale's ratios were a bit off, but if
you pay attention to the overtones created by the tempered scale (which will
reflect the natural harmonic series), you can include that aspect into your
music? Was he trying to connect the equal tempered system to the pure
intervals you would associate with just intonation? And would Partch's
response be - that's nice, but why don't we just start off with the pure
ratios?

> Graham Breed wrote:
>
> > Was [Schoenberg] writing for, and being
> > performed by, string ensembles when making the progression towards
> > atonality?
>
> Verklarte Nacht, and two string quartets (Nos. 0 and 1) preceded the
> famous 2nd Quartet - with soprano, who sings 'I sense the air of
> other planets'. The 2nd Quartet is nominally in F# minor but is
> usually considered Schoenberg's first 'atonal' work (whatever that
> means).
>
> I say 'whatever that means' because in many so called 'atonal' works
> (obviously not all), tonality is very much _implied_but_not_stated_
> but also, which is confusing, frequently shifting and ambiguous.
> This is one reason why atonality can generate such tension:
> sometimes so much that it immediately and continually collapses.
> Many listeners find this incomprehensible, and/or frustrating. Other
> listeners, who don't feel the implicit tonality of 'atonal' works,
> either don't enjoy them at all, or seem to listen in radically
> different way (focussing on texture, colour etc).
>
> > As regards the possibilities of 11- or 13-equal,
>
> Tune your keyboard/soundcard/piano to 11-ET; doodle around a bit,
> and write a melody (or harmonise a melody) using at least all 11
> chromatic notes; distil this material to an 11 note row from
> which it may be derived; write out the conventional (44) permutations
> of the row; then try to compose a piece with this material using
> harmonic timbres... After that experience, try arguing that
> Schoenberg could have been able to write as fluently and rewardingly
> as he did, given his millieu, experience, aesthetic projects etc.
>
> > Applying these
> > rules in 19-eq would give entirely different results, as it's
> > easier to avoid keys without using all 19 notes. Did Schoenberg
> > ever consider this?
>
> Pass. Does anyone know if S had any further correspondence with
> Yasser not already mentioned on the list?
>
> But I'm not entirely clear about your argument. Having written quite
> a bit of (what you would probably call) 'serial' and 'atonal' music
> in 19-ET I am very aware of how difficult it is to structure a 19
> note series that works well - I tend to use series of less than 19
> notes. But whether this supports the _principle_ (?) behind your
> point I don't know.
>
> > "The Berg Violin Concerto is said to be the first fully serial
> > concerto, though it has many tonal twists to it. The soloist
> > announces the series, a succession of rising thirds, topped by
> > a tritone: G, Bb, F#, A, C, E, G#, B, C#, Eb, F."
>
> This should read: G, Bb,***D***, F#, A, C, E, G#, B, C#, Eb, F."
>
> You can see immediately that this row contradicts at least one
> of your definitions of atonal (not that you said it is atonal, but
> it is often called atonal music). It's sort of dodecaphonic tonal
> atonal. But in my experience the violin concerto would not normally
> be called a 'serial' work. You are right that the term serial is
> (of course) derived from the series, but the term 'serial' is
> commonly retained for music in which the serial principle is applied
> to other parameters ('total serialism' merely being an extreme
> instance of this). For example, Schoenberg Op 25 might be called the
> first dodecaphonic work, rather than the first 'serial' work - which
> would normally refer something written in the 40's.
>
> However, maybe someone on the list could identify when the terms
> 'series' and 'serial' were first applied?
>
> > I think Wozzeck................... as a whole is atonal.
>
> Do you think it does not have stunning tonal passages? Like
> Marie's Lullaby? Do you think the end is 'tonal' or 'atonal'? What
> in your view is the point of making the verbal distinction?
>
> But maybe we're getting off-topic, and should take this elsewhere?
>
> Patrick O-L