Re: What is this chord in Roman Numerals?


"SleepyHead" <simonharpham@xxxxxxxxxxxxx> wrote in message
news:1178191822.336818.286720@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On 2 May, 21:46, "Tom K." <tkor...@xxxxxxxxxxxxxxxxxxx> wrote:

I think the assumption here is 12 tone equal temperament, so
0,1,2,3,4,5,6,7,8,9,10,11 is the entire pitch universe

OK, well that makes sense from a set-theory perspective, and I suppose
there's nothing to stop the basic idea being extended a little.

It seems to me that if one goal for a serial piece is atonality, then equal
intervals (temperament) becomes a necessity.

This gives rise to interesting questions of notation - why are more than 12
note names necessary if there are only 12 pitch-classes? IIRC, some
composers tried using only flats or only sharps as well as the curious
practice (Stockhausen, I think) of having a sharp or flat affect only the
first instance of a note it preceeds. Notating a measured trill up a
semitone from F for example, would have to be F, F#, Fn, F#, Fn, F#, etc.
(This brief modification of the order rule was specifically allowed by A.S.)
Of course, the real issue is the inadequacy of the 5 line staff for
chromatic music. And the answer is that we notate the best we can so that
the performer can do his/her job - although a lot of folks seemed to lose
sight of this in the 1960's.

(snip)

I can see where the simplification's coming from though. (The next
section is a little wayward, but bear with me). I was thinking about
12-tone and composition techniques in general last weekend, things
like "Augmentation", "Diminution", "Inversion" and so on and so forth
and wondering if I could give any meaningful (or useful) sense to the
idea that any of these composition methods could be applied to any and
all musical elements, even larger-scale elements such as form, style
and so on. For example: the idea that you could either invert a style
by inverting all the elements in that style (invert its characteristic
melodies, harmonies, etc), or by exchanging a given style with another
in a given set around a given member in that set - a bit like harmonic
inversion around, say, the 3rd degree of a scale).


I'm not sure about "style inversion", but one interesting exercise is motive
variation through interval multiplication (augmentation). Take a tonal
motive or larger melody and multiply each semi-tone by a constant. I recall
someone suggesting that you could change a Mozart style into Schoenberg by
this method. Of course, there are pitfalls as C,D,E multiplied by 2 yields
C, E, G# & you'd have too many augmented triads!

This was partly off the back of reading about total serialism and its
parameterisation of any and all musical elements - a goal that seems
attainable until you start listing the number of musical terms and
concepts currently in play - rhythm, pitch, duration, volume, style,
form, harmony, melody, key, tonality, and so on and so forth. Because
music is exactly like a great many fields of investigation in that as
people discover and/or invent (is there really /that/ much difference
between the two?) new viewpoints on old music, and new techniques to
do new music the list of things to which 'basic compositional
techniques' applies spirals out of control and you're left with an
unmanageable plethora of terms.

It's the same with serialism - because the more you look at music the
more you find, in the end you end up with limitless parameters any and
all of which could be controlled serially (or via some other 'auto-
generative' method).

The way out of that kind of impasse (when in philosophy and science
anyway) is usually either to invent some kind of container which
allows control of all its members, or to invent/discover some
fundamental object the control of which automatically implies control
over larger-scale units.

So - to bring this back to my actual point - it's not the human-
perceptible element of rhythms, pitches and what-not and their
differences that makes serialism an unattainable goal, it's that
"total control" is an unattainable goal because "total control"
implies control of any and all elements /including those that haven't
been discovered and/or invented yet/. In that respect "total control"
in music is the analogue of consequentialism in ethics and suffers
from the same problem: No-one knows what's going to happen until it's
happened.

Agreed. To put it in a slightly different way, when control is lost over
the interrelationship of the parameters, the overall effect is
unpredictable. Maybe the serialsts wanted this, but the chance music folks
showed easier ways to achieve it!

Oh I see - not every occurrence of a given tone has to have a
structural function as long as the tone in question has a structural
function overall, and therefore you can pretty much make up your
harmony to suit yourself as long as you keep the order of tones in the
row. Is that right?

That's correct. The only a priori structural function for each tone is it's
order number within a particular row form.

But you raise an important point: you are free to use as many of
Schoenberg's rules as you wish in any way you wish, so the much feared
"12
tone technique" has now simply become another tool in a composer's
technical
arsenal. Of the "Second Viennese School", Berg had a very free way of
using
serialism, Webern was very strict (making his row analyses the easiest)
and
Schoenberg was all over the place, even writing a few tonal pieces
towards
the end of his career.

So - just to bring in something Steve mentioned earlier - the
important thing in 12-tone music would simply be that there is no key
centre and that each note in the row assumes equal structural
importance?

For "strict" 12-tone music, yes it should not have a tonal center. But many
12-tone works are not "strict". I think I mentioned Berg's Violin Concerto
which, although (loosely) based on a row, is pretty clearly G minor/Bb
Major!

Schoenberg even forbade (selective) octave doublings as he felt even a brief
emphasis on one tone would bring back tonal "baggage". In this regard, an
interesting problem arises in Webern's Op. 27 Piano Variations, where he
sets up a registrally symmetrical pitch field with a two voice canon by
inversion. Since the center of the field is A-440, there must be two
instance of the tritone, one above and one below. At one point, the Eb/D#
occurs as note 4 in both rows, and as the canonic time interval is only one
8th note (quarter = 160), they are virtually simultaneous. Webern's
solution was to make these notes grace notes to minimize their impact, and
he notates one as an Eb and the other as D#, so the performer isn't to think
of them as an octave doubling!

I think a case may be made that the structural importance of (for example)
note 11 (as penultimate) is greater than note 5 in many 12-tone pieces, but
again, this is due to order, not content.

Ah! To paraphrase The Terminegger: there isn't any form in 12-tone
music, except that which we create for ourselves? Ironic really, given
that the ordering of notes was supposed to be the thing which brings
structure to the piece!

But isn't it always the responsibility of the composer to structure a piece
by either appropriating/modifying an existing form or creating a new one?

Tom K.


.

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