Re: Serial = Random ?

On Feb 3, 12:49 pm, LJS <ljsche...@xxxxxxxxx> wrote:

I thank you for this information and will welcome any comments
concerning my thoughts. I hope that if there is anyone else there that
has seen a different way of approaching this subject, please don't
hesitate to post it.

So far, the discussion has been only of arithmetic, 12-element
duration series. Your criticisms are quite correct, and have been
raised by many others right from the beginning. In fact, the severity
of the difficulties is the reason why most serial composers abandoned
this system almost as soon as it arose.

There are a number of other approaches. Probably the most famous is
Stockhausen's system, made in "...How Time Passes...". He first
observes that a relation between pitch and duration must find some
common element, and he seizes upon the periodicity of tone vibrations
in order to argue that, by projecting this periodicity into the realm
of musical rhythm, it is not duration as such but tempo that is the
relevant analogy. This also provides the modular element missing from
arithmetic duration series. That is, every time you double the tempo,
you reach an "octave equivalence", and start over again. This "tempo
octave" is then divided logarithmically into twelve equal parts, on
the analogy of the logarithmic division of the pitch octave.

Another way of avoiding the problems with arithmetic series is to use
a scale of durations that does not continually diminish in proportions
between the members (that is, 1:2 is a very large proportion compared
with 11:12). The Fibonacci series is one in which the proportion
between consecutive elements is fairly constant, especially as the
numbers increase. Another such series in the incrementing-difference
series (e.g., 1, 2, 4, 7, 11, . . ., where the first two members
differ by one, the second and third by 2, etc.). None of these series,
however, provides the equivalent of an octave modulus, so there is no
point in insisting on twelves.

But this brings me to another important point that has been overlooked
so far, and that is the entire issue of whether "total serialism" is
really an extrapolation of twelve-tone technique or not. In the case
of Milton Babbitt, I think there is no doubt that it is, and his "time
point" system for durations is one means of solving the modulus
problem.

For many European composers, however, serialism is only distantly
related to twelve-tone technique, if indeed it is related to it at
all. (I am thinking above all of Stockhausen, Pousseur, and Nono,
though this also applies in lesser degree to Boulez.) For these
composers the serial principal has to do with scaling the material,
deciding on a suitable size for sets, and then using all the elements
in a set before moving on to the next one. It may also involve nesting
sets. In order properly to illustrate what I am talking about, I would
have to analyze at least a substantial section of a piece, and this
would take a book or at least a long article to do. But the important
thing is that this approach to serialism does not necessarily posit
any recurring *ordered* sets at all--not even of pitches. Commonly
what is found is that each recurrence of a set is differently permuted
(either systematically, or not), and for this reason the term
"permutational serialism" is sometimes used. For durations, the size
of set chosen is usually a matter of practicality, and of suitability
to the particular requirements the composer establishes for a given
piece. In my experience, this usually means sets of between four and
seven elements. Similar considerations apply to serializing
intensities, registers, timbres, and other parameters which cannot
easily form analogies to pitch.

When pitch sets are treated permutationally, the recurring sets (re-
ordered each time) are sometimes collectively referred to as an
"unordered set". Hauer's practice was of this sort, and his term for
the alternating hexachords he used was "trope". Other composers have
used "unordered" sets of different sizes, sometimes of very ingenious
construction (for example, Stockhausen used conjunct trichord pairs to
form pitch sets of five elements each in his Klavierstück II). But I
am straying from the subject, and have gone on long enough.

--
Jerry Kohl
"Légpárnás hajóm tele van angolnákkal."

.

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