Post from Mclaren

From: mclaren
Subject: algorithmic composition in non-12
--
Paul Turner asked about Markov processes applied
to computer-controlled composition some
while back. This is an interesting subject & it
relates to microtonality with especial cogency
because as the number of pitches in a just or
equal-tempered scale grows large, it's
attractive (at least in theory) for a computer to
handle at least some of them automatically.
To date, the definitive article on the history of
algorithmic composition is "Composing With Computers:
A Survey," by Gareth Loy, pp. 291-396 in the anthology
"Current Directions In Computer Music Research,"
MIT Press, 1991, edied by Max V. Mathews & John R.
Pierce.
Lejaren Hiller was the first to apply Markov
methods to composition. Hiller was a chemist
by trade: apparently Markov analysis is sometimes
applied to the study of chemical reactions. It is
essentially a rule-based random number sieve.
Markov analysis can be applied to note-groups
of zero length (zeoth-order analysis), length 1
(first-order analysis), length 2 (second-order
analysis), etc. Statistical analysis of a composition
as a first-order Markov process establishes the
probability of a given note following another
note-- for instance the probability that C will
follow D. A first-order analysis can be run for
each of the 12 pitch-classes of 12-TET music,
giving a list of probabilities derived from an input
composition (or group of compositions). However,
such analyses could just as easily be run for a non-12
set of notes--31-TET, 15-TET, Partch 43-note JI,
and so on. Analyzing the composition as a second-
order Markov process establishes the probability
of a given note following two given previous notes;
a third-order Markov analysis yields the probability
of a given note following three previous notes--
and so on.
Thus "the process of composition consisted in
sequentially applying each random number generated
to the appropriate sets of rules. If the number
chosen violated a rule, another number was selected
from the random series until all rules were satisfied,
and the successful number was appended to the end
of the sample being generated." [Loy, G, "Composing
With Computers: A Survey," pg. 310, in Current
Directions Of Computer Music Research, 1991,
ed. Max V. Mathews & John R. Pierce]
Markov methods appear most useful at the level of
the phrase. At shorter time-scales the music sounds
like sample-and-hold white noise, while at longer
time-scales it sounds like a random bricolage of
precomposed sections.
Essentially the Markov analysis reduces the
generation of musical notes & phrases to a single
probability 0< x<1 plus a rule-set. Thus, Markov
composition represents yet another example of the 20th
century's love of extreme reductionism. In
this case, the conceit is that a musical composition
can be reduced to a set of unsigned probabilities
between 0 and 1 mated with some modus ponens
logic tree.
If this sounds ridiculous...well, so do many of the
ideas that have proven popular in the 20th century.
If someone told you that the world's 2 great
superpowers would go hog-wild for a nutty theory
known as "mutual assured destruction," damn near
bankrupt themselves building enough nuclear weapons
to vaporize the biophere and then tear all those bombs
apart and throw 'em out because they they finally
realized it was a terminally stupid idea to begin
with...well, hey--
Welcome to the 20th century, folks!
Markov analysis basically establishes the size of the
sieve through which random numbers will pass,
given some rule-set (i.e., the rule that if notes
X, Y, Z...U, V have already occurred, there is a
probability Q that note W will occur subsequently.)
The advantage of Markov compositional
processes is that [A] they can be scaled
up to the size of the entire composition (in
which case there's a finite probability that
the entire piece of music will occur) or down
to the level of the individual note. Thus,
unlike many other compositional algorithms,
Markov analysis gives the composer some control
over the specific time-scale at which s/he works;
[B] Markov analyses of two radically different
musical styles of composition can be used
to "morph" from one compositional style
to the next, producing striking effects;
abnd [C] Markov analyses can prove useful in
dating and authenticating compositions by
generating a set of note and phrase probabilities
unique to each composer.
The disadvantages of Markov compositional
algorithms are [A] the process does not even
remotely model a composer's cognitive
functions; I know of no composer who sets
up a bunch of predetermined rules and then
flips coins to see whether a note is generated.
(Well--no worthwhile composer. There's always
Cage, of course.) This is so alien to the way humans
compose that it's bound to produce musically
unsatisfactory results; [B] The Markov algorithms
remove control of all but continuous "chunks"
from the composer. To use an inapprropriate
term, Markov composition isn't random access--
its strictly sequential. The Markov composer
never knows what's in measure 12 if it's
on measure 2. In the real world, a composer
will typically start by deciding what form
s/he will use--rondo, variations, canon,
etc. Markov methods make it impossible for
the composer to control this highest level of
compositional order. At the other extreme,
human composers will typically jump back and
forth in time, composing the end of piece
before the middle, making sketches, inserting
"extraneous" notes in themes or passages or
chord progressions--yet the theme or passage
or chord progression remains to listeners recog-
nizably thematic. Markov processes are very brittle
in this regard. Toss in one extraneous note,
require the analysis to jump discontinuously
in time from begining to end or vice versa and
the rule-set breaks and the Markov analysis
apart. In particular, Markov processes cannot
handle or model a method of composition in which
the composer jumps discontinuosuly between
various points in time, forward then back,
&c. This is violently contradictory to both
human perception of music (we instantly jump back
in time via memory to the first appearance of
a theme the second time we hear it), and to the way
human composers handle themes and chord
progressions. The final problem is that [D]
because Markov analysis operates only with
pitch classes, Markov analysis is completely
blind to the contour of a melody--yet this is
clearly the most important characteristic
of any melody. Markov analysis is also utter
blind to the "orchestration" of a chord and
to the "contour" of the bass progression
of the set of chords used--thus Markov analysis
destroys the information of where the chord's
component notes are distributed in the frequency
spectrum, and the specific melodic contour of
the bass note in those chords. Now, Stravinsky
clearly thought of one orchestration of a chord as
actually a different chord than another orchestration--
thus he typically said "I was glad to discover that
chord" when speaking of the Firebird. Many composers
think this way. But Markov analysis destroys this
information.
This is another way in which Markov
procedures are violently antithetical to the way
humans think about composition.
It's worth noting that the Markov algorithm is
the earliest compositional method used on
an actual computer. Lejaren Hiller employed
it in back in 1957 to produce the first computer-
composed piece of music, The Illiac Quartet.
Thus Markov processes represent an extremely
early stab at computer composition.
It's also worth noting that Hiller, in his book
"Experimental Music," was careful never to
make the claim that his computer programs
composed actual music. Instead, Hiller
described his efforts as attempts to probe
the cognitive processes of the human mind.
The idea (a typcally grandiose early computer
dream) was that by modelling human music
composition, a series of computer programs
would gradually illuminate the process of
human musical thought to a greater and
greater degree, until finally the process
of composition as a mental activity was
fully understood. At that point (it was fondly
imagined back in 1956) computer programs
could take over and produce music even
more interesting, even more inspiring, and
even more exotic and beautiful than any
human.
Typically, just the opposite has actually
happened.
Instead of illuminating the operation of
the human mind, computer composition
has pointed up how complex and imponderable
human compositional thought actually is.
Thus, what has actually happened with
computer composition is that a series of
musically godawful results inspired researchers
to grab a ragbag of mathematical procedures willy-
willy from other disciplines and press 'em into
service as compositional algorithms. All of these
algorithms have so far *reduced* the composer's
control over one or another vital aspect of the
musical composition, rather than enhancing it.
The net result has typically been a series
of computer compositions about which as Max
Mathews remarked "the music tends to wander,
and with it the listener's attention."
--
What does all this have to do with non-12
tunings?
Because Max Mathews' Music V acoustic
compiler and its descendents allow
total freedom to choose pitches,
xenharmonic composers face what Wendy
Carlos calls "option paralysis." You've
got so many options you spend all your
time trying to decide what to do, until
you've no time left to actually worry
about composing.
Computer-controlled composition offers
a way out of "option paralysis." It's
inherently attractive to let a computer
handle all the Dedalaean complexities
proferred by all those notes--thus one
might well understand why a composer
would prefer to have a computer handle
composition (or some aspect of composition,
such as, say, chordal accompaniment, or
melodic episodes) in 53 tones or 171
tones per octave.
--
Future generations will look back with wonder
and astonishment at the peculiarly 20th-century
conceit that computers could generate music
even remotely as interesting as a composition
written by a human.
People used to drink coal tar in the 1870s as a
cancer cure because there was a lot of coal
tar around, the oil business was glamorous, and
nobody could think of much else to do with coal
tar. A lot of composers probably use computers
to make music nowadays for the same reason--
there are a lot of computers around, anything
connected with computers is automatically
glamorous and hi-tech, and the composers likely
can't think of anything better to do with their
PCs.
Thus algorithmic composition is fashionably
trendy nowadays, very chic, and highly "in,"
and it's yet another example of the kind of
musical tulipomania that has periodically deluded
groups of otherwise sane composers since 1948:
row-based serialism, pitch-class matrix methods,
aleatoric composition, neo-dadaism, and so on.
Algorithmic composition may well be another fad,
like the miniskirts of the 60s and the men's
platform shoes of the 70s.
Time will tell.
Because computer algorithms never permit the
composer to simultaneously control large
and small time-scales of the composition,
and systematically prevent composers from
assigning emotional values to sets of chords
or notes, algorithmic computer composition has
never produced much music worth listening to.
Typical computer compositions fade in from nowhere
and fade out after some indetermine length of time,
giving the impression of sonic wallpaper. Algorithmic
compositions can work very effectively as background
music, however.
The net musical result is generally a very low-quality
Muzak, or a particularly dull & repetitive kind of
fusion jazz. This applies with especial
force to Tod Machover's computer-generated
hyperinstrument noodlingsm, although the problem
is endemic through the computer composition
field.
Why spend so many millions of man-hours and so
many trillions of CPU cycles to generate sub-par
Muzak and boring fusion jazz? Well...why did so
many composers spend so many millions of
man-hours composing row-based serial music
in the 1940s and 1950s? As Charles Mackay
pointed out in his classic book "Extraordinary
Popular Delusions and the Madness of Crowds"
(1843): "Men, it has been said, think in herds,
and they go mad in herds, while they only
recover their senses slowly, and one by one."
The essential problem is one of mapping. All
computer composition programs either sieve (from
the top down) or generate (from the bottom up)
random noise, then assign values to that subset
of random noise. In the case of Markov-type and
other top-down noise-sieve algorithms, the mapping
is determined by the rule-set pre-entered by the
composer. In the case of cellular automata and
MAX-type recursive shift-register algorithms,
the mapping is out of the composer's control and
is determined by the emergent order of
the cellular automaton or that paritcular
topology of feedback shift register.
In both cases, the essential problem (other than the
fact that composer loses control over either the
very large or the very small time-scale in
a piece of music) is that no one has yet determined
how to meaningfully map a chord or note to an
emotional affect. Thus the mappings have to date
been extra-musical and the results thus trivial.
There is no sign that the mapping problem will be
solved any time soon, since the same chord or note
can have *many* different emotional affects
depending on its context. To determine what emotional
impact a chord or note will have, you have to *listen.*
And this, computers can't do. Lejaren Hiller addressed
this concern in his 1957 book "Experimental Music:"
"The composer is traditionally thought of as guided in
his choices not only by certain technical rules but
also by his `aural sensibility,' while the computer
would be dependent entirely upon a rationalization
and codification of the `aural sensibility.'" [Hiller, L.,
Experimental Music," 1957] To date, no such
rationalization and codification has proven
musically successful.
--mclaren





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