From: fields@zip.eecs.umich.edu (Matthew Fields)
Subject: GEMS 4 (CANON, FUGUE, ETC.)
Organization: University of Michigan EECS Dept., Ann Arbor, MI
Date: Tue, 17 Nov 1992 18:12:46 GMT

GEMS 4
==== =

Matthew H. Fields

Folks have continued to express enthusiasm for my educational postings.

The story so far:

Shortly after the opening of rec.music.compose, I posted a short note
offering to write articles regarding some of the "gems of
compositional wisdom" that have been passed down to me over the years,
and I received an enthusiastic response.  GEMS 1 dealt with dramatic
shape and the expression of climaxes; GEMS 2 dealt with the concept of
parallel perfect intervals, and their implications for melodic
perception; GEMS 3 was a quick list of heuristics for solving tonal
harmonization homework exercises.

As posted elsewhere, Nathan Torkington has arranged an anonymous FTP site
in New Zealand where these articles are warehoused.  For the time being,
they are also available from me via e-mail.

I have downloaded GEMS 1-3 to my mac, checked their spelling, and
cleaned up some details of grammar, so they are now available from me
in hardcopy (about 15 pages, so far) for a SASE (when figuring
postage, include weight charges for 15 sheets of standard 8.5 inch x
11 inch 20-lb-test paper, and if necessary, figure airmail charges
between your location and the USA).  I don't believe I'm violating any
netiquette here, since I'm not actually selling anything.


The topic for today is:

HINTS FOR COMPOSERS OF CANON, FUGUE, AND OTHER INTELLECTUAL MATERIALS

If you are rigidly opposed to the application of intellect to creative
processes, you may wish to skip this article.  If you expect this article
to take the place of a theory text on contrapuntal devices and conventions,
you will be disappointed, since I will be mainly addressing issues of
interest to composers, and will assume that you can find definitions and
rough descriptions of various intellectual musical procedures in plenty
of existing textbooks.  



Disclaimers:  I am presenting the material here mainly as my opinion.  If
you try to make use of my suggestions and they don't help you write
fabulous music, I don't accept any liability.  Likewise, it is strictly
to your credit and none of mine if you do write fabulous music before or
after reading these posts.  Plenty of the ideas I will be discussing
in this series have been mentioned before, and some theorists may even
wish to lay copyright claim or patent claim to some of them.  However, I
claim that the core ideas have been known to composers and used by them
long before anybody published any writings on them, and these ideas are
therefore basically in the public domain.

On the other hand, I actually sat down and wrote the text of this posting,
and it took me a bit of time and thought, so if anybody were to exploit
this text as a commodity without consulting me, I might get very mad
(standard disclaimer).

All that having been said, I am interested in getting some feedback
on how interesting or useful you find this article.

ABSTRACT

In this article, I will attempt to address the role of intellectual
techniques in the composer's mental toolkit.  Along the way, I will
make some general suggestions that I think may be helpful whether
you're working in serialism, Fibonnacci numbers, canon at the twelveth
at 3-3/4 beat delay, or whatever.  I expect to also explain some
details of specific techniques, mainly to use them as examples of the
general principles I will be describing.


INTRODUCTION

In musician's core theory classes, beyond 4-part harmony, all further
exploration tends to be analytical.  By that dense sentence, I mean that
most people are taught how to analyze music, but not how to go about trying
to construct it themselves.

Occasionally, a theorist will be talented at fugue or serialism, and will
inspire the composers among her/his students to figure out how to use such
materials themselves.  On rare occasions, composition classes are taught
which combine rigorous planning of material with general compositional
strategy.

For those of you who are thirsting for such guidance but have not
found it yet, may this article serve as a primer on the matter.


DEFINITIONS

I'm going to use without definitions a lot of terms from the standard
jargon of classical music theory.  The definitions are omitted mainly to
save space and time.  If you want, you can look up these words in e.g.
the New Grove Dictionary of Music and Musicians:

Canon
Fugue
Sequence
Parallel Motion
Intervals
Serial Music
Fibonacci Numbers
Algorithmic Music
Stochastic Music
Inversion
Stretto
etc.


A MODEL OF A COMPOSITIONAL PROCESS

Many composers have spoken of a search for the El Dorado of algorithms,
the rigorous method which, if applied, always yeilds great music.  The way
I compose certainly feels methodical to me, but when I consider the
oft-voiced goal of automating my work on a computer, I realize that what
I do is very hard to quantify or describe in clear categories---that is,
clear enough categories to form the basis of a computer program.
Why might this be so?

It helps to remember that two of the most widely accepted measures of
"good" music are that it is A) entertaining to people who don't already
know all about it, and B) memorable.  Entertainment value, by which I
mean entertainment in the widest sense--not just light entertainment
but also tragic, spiritual, and other kinds of entertainment---is
essential if the listeners are going to pay much attention.
Memorableness is essential if you hope the listener will ever seek to
hear your piece a second time.  As it turns out, both entertainment
value and memorableness are tricky quantities which psychologists are
still just starting to classify, so I don't expect anybody to turn up
a mathematical formula mapping patterns of notes or sounds to specific
values in either domain.  You're just going to have to try to judge
for yourself how well your music meets these goals.  So any serious
methodology which I propose for composition is going to have to incorporate
these unexplained, unquantified judgements.

So, let's suppose that I'm doodling with a melody, and I decide that it
might be neat to try to make a convincing piece in which this melody is
a subject of a four-part fugue.  If I'm not really all that knowledgeable
about fugue, I

1) STUDY THE CATEGORY OF MATERIALS that I'm thinking of using, to see whether
it stimulates my imagination.  At about the same time, I may begin to

2) PLAY WITH THE MATERIALS that I might use, and try to learn as much as I
can about their qualities.

In the case of my fugue subject, I may decide that I'm looking for 3 counter-
subjects, so when all four parts are playing, they are all playing material
that can be heard elsewhere in my piece.  Soon, I realize that these subjects
not only have to form decent 4-part harmony with each other, but also, to
be interesting and to be easily recycled into other parts of the piece, they
have to form decent harmony when parts are exchanged (counterpoint is inverted)
so lower parts become upper parts, outer parts become inner parts, etc.
(this means that music is transposed by, e.g., an octave or two when it is
assigned to a different player or melodic strand).

Now, depending on my mood and the nature of the materials, I might
either want to 2a) refamiliarize myself with (or learn) the principles
resulting from my decision, or 2b) begin immediately trying to
construct music based on the ideas in my head, then fix it as I go
along.

If, in the example of the fugue, I choose No.2a, I'll go back to look
at invertable counterpoint at, e.g., the octave, and find out its
consequences for parallel fifths: parallel (or direct) fourths become
parallel (or direct) fifths after revoicing, so if I'm trying to avoid
parallel fifths, I better not allow any parallel fourths either.
Knowing that ahead of time can save me some time on process No.2b,
which I'll eventually have to confront anyhow.

So now I'll try to build the first such countersubject, by laying out
my main subject on a stave, with a blank staff above and another one below.
I can now go into the following cycle:
                  2b1) Have I written enough music for this subject?
                       If so, I can quit this cycle, else I continue.
                  2b2) Add a note to the subject.  Put it in the upper
                       staff, and at the same time, transpose it down an
                       octave and put it in the lower stave.
                  2b3) Consider, in isolation, my countersubject so far.
                       Does it groove? Does it sound ok? If not, erase this
                       note from both staves, and go back to 2b2.
                  2b4) Consider the music in the upper two staves. Does it
                       violate any of the rules I've discovered in step 2a?
                       Does it violate any aesthetic rules (like the
                       avoidance of parallel fifths and octaves) that I've
                       decided to stick to?  Is it in any way less than optimal
                       in grooviness or some similar nameless quantity that I
                       want to preserve?  If the answer to any of these
                       questions is yes, erase the note and go back to 2b2.
                  2b5) Apply the same rules as from 2b4 to the music in the
                       lower two staves (remember, we have 3 staves here:
                       countersubject above, main subject, and countersubject
                       below).
                  2b6) If we get to here, this note is one we're going to
                       try to stick with, for now. Go back to step 2b1 to
                       continue building more of the countersubject.

This procedure looks like a backtracking algorithm, but notice that none of
the aesthetic judgements are quantified.  With a little struggle, it can
probably be adapted to quite a wide variety of musical structures.  I've used
a sort of variant on it as a way of working out serial music, and as far
as I can tell, it hasn't failed me there.

The important test: DOES IT SOUND GOOD? DOES IT GROOVE? is the glue that
holds this method together.

3) SOLVE THE MOST INTELLECTUALLY DIFFICULT OR COMPLICATED PART FIRST.

In the case of my four-part fugue, I'm going to try to construct music
in which the subject and all three countersubjects sound together, and verify
that every pair of them fits in good invertable counterpoint together.  In
so doing, I'm going to use all the tricks I have from steps 1 and 2.

4) CONSIDER EXPLOITING YOUR SOLUTION FROM STEP 3 when constructing other
parts of your piece.

Now, by simply copying this music to a fresh sheet of paper (or a
fresh range of measures in my notation program, or a fresh notelist
file in my sequencing program, etc.), maybe transposing it, maybe
revoicing it, maybe erasing one or more voices, I can come up with an
incredible number of musics with slightly different feelings to them,
different textures and densities, but all with a sense of relatedness
to each other.  I don't have to be at all careful about (e.g.)
parallel fifths because I already arranged that they wouldn't arise
back at step 3.  So, out of my quartet texture, I can pull 23 other
quartets by merely rearranging the voices; 24 trio textures,
constructed by erasing one voice and permuting the others; and 12 duet
textures, obtained by erasing two of the voices, and optionally
inverting the counterpoint of the two voices I have left.  Plus, I can
try putting the music in a different mode (e.g. major or minor),
transposing it, etc.  In all these cases, I'm taking advantage of all
the work that went into step 3, so I don't have to work hard to get
any of these materials.

Since the materials are so closely related, if I construct a piece mainly
out of these materials, it will have a sort of redundancy that may help drive
the melody into the listener's memory in a more effective manner than mere
repetition.

4) Sooner or later, I've got ENOUGH MATERIAL, and it will be time for me
to STOP PLAYING WITH MATERIAL AND START ORGANIZING A COMPOSITION.

Under this heading I include all the ideas from GEMS 1, including top-down
planning of a dramatic push towards a climax, choosing an assertive gesture
to start the piece, finding a convincing and special-sounding ending to the
piece, prolonging the climax, etc.  I already have a sketchbook loaded
with both explicit materials and ways I've found to make materials that I
want to use, so now it's merely a matter of choosing among these materials,
linking them together, and taking a step back to look at the big picture.

DOES IT GROOVE?  If not, it doesn't matter how perfectly I've applied my
intellectual technique: I'm going to have to go back and adjust the
eigenvalues or coefficients, prolong the climax a bit more or less, and
maybe throw in a contrabass clarinet solo for good measure---whatever it
takes to make it finally sound good.

5) REMEMBER, BY MECHANICAL MEANS IT'S EASY TO PRODUCE MORE VARIANTS
THAN YOU'LL NEED.  If I systematically presented all the duets, trios,
and quartets that I could extract from my 4-part fugue exposition, my
piece would probably get to be quite long and boring.  I may only want
3, or 5, or 7 or 8 of the variants that I've found.  That may be
enough to build a fairly long, dramatic piece.  It's all right for me
to know that all the other variants exist and all work perfectly well
as counterpoint or whatever, but I don't get any brownie points for
cataloguing them all to the audience.  So I'm going to have to just
learn to let go of, cross out, and ignore most of the variants which I
have generated, once I've used all the ones that fit my piece.  Or, I
might separately create another piece out of some of the leftover scraps
of fabric.  But unless I'm incredibly clever, I should never have both
of these pieces played on the same concert.


MATT RANTS ON
While I'm on the soapbox, let me remind folks that our listeners hope
to be entertained.  We can't count on them reading program notes, so
they're going to have to get something out of the music without any of
the knowledge that could be imparted there, whether it amounts to an
explanation of poetic allusions, an intriguing essay on the
intellectual techniques underlying your piece, a story that the music
is supposed to tell programmatically, or whatever.  If the listeners
are interested enough in the music, they may be a bit more likely to
read the program after hearing it, and if they're really interested in
the music, they may pour over the program looking for information on
how to buy a recording of the music.  At that time, they may learn
something about the music which may, after the fact, enhance their
appreciation of it.  But you just can't count on them gleaning the
important fact from the program notes which turns their listening
experience from a mystified sitting through a wash of sound into an
enlightened experience of a scientific principle.  The music has got
to draw them in and get them interested all on its own.

On the other hand, even the worst concert-goers (with the exception of
a few psychotics) go to concerts to have a good time, and will try to
have a good time with your piece.  So, your relationship with your
audience is not necessarily adversarial...although some listeners will
bring a healthy skepticism (or a pathological fear of anything new) to
their listening.  While it's certainly reasonable to simply not worry
about the few who have already prejudged your music on the basis of
the fact that it's new to them, and to not worry about reaching the
few who will groove simply on the fact that any sound is being made at
all, it would not be a good idea to ignore the middle of the audience,
the folks who don't yet know whether they can dig your music.  If you
can guide them into your way of hearing things, it doesn't matter
whether they can describe your piece in theoretical terms: at some
human level, they're following along with the course of your musical
argument, and they stand a chance of getting something out of it.


LISTENING ASSIGNMENT

Here I list some of my favorite examples of beautifully passionate but
rigorously intellectually-structured music.  Most emphatically, let me
repeat that you can gain a great deal by looking at the score while
listening.

I recommend two compositional publications by J.S.Bach as informative
sources on musical intellection (and sources of delight and
wonderment, as well): The Well-Tempered Clavier, which is a set of 48
preludes and 48 fugues arranged in two sets of 24 each, where each set
cycles through all 12 major and all 12 minor keys; and Art of Fugue, a
collection of some 16-odd fugues and 8-odd canons for unspecified
instruments (plus an arrangement of two of the fugues for keyboard
duet), all based on variants of a single melody (and a fairly small
set of counterpoints to that melody).  If you really cannot read
music, for about twice the price of the scores to these works, you can
acquire CD's of performances of them (on WTC, I recommend the
harpsichord performances of Gustav Leonhard or Kenneth Gilbert; on Art
of Fugue, I recommend the performance by Musica Antigua Ko"ln, who have
also produced a superb recording of another recommended Bach piece,
The Musical Offering--but unfortunately, this recording is out of print
now).

Other great examples that come to mind are Bela Bartok's Music for
Strings, Percussion, and Celeste, and Arnold Schoenberg's Variations
op.31.

Part of what I hope listeners to these works will come to realize is that
for composers who use such intellectual material all the time, the
intellectual structure eventually becomes so basic to their art that the
focus of the art is on how they improvise expressive shapes in, with,
and around these materials, rather than how they assemble these materials
themselves.


WRITTEN ASSIGNMENT
For those inclined to think harder when there's a written assignment,
here is a short one.  But don't forget to work on your current opus!

Compose a piece of 8-40 bars in two melodic lines, using one of the
following: invertable counterpoint of the octave, twelveth, or tenth.

Decide whether to work in tonality or not.  Decide what rules to apply.

After some number of bars, swap parts betwen the melodic lines.

Add whatever is needed to the beginning, the middle, or the end to
make a convincing piece.  Consider only using additional material that is
relatively simply derived from the other material of your piece.

Sculpt this music to provide a convincing climax, where applicable.

Choose a keyboard, or, preferrably, two voices and/or instruments to
play your piece; if necessary, either adjust your choice of
instruments to meet the demands of the piece and the availability of
players, or adjust your music to meet the demands of writing for these
players, or both.

Stage a performance of the piece.  Perhaps record it.



CONCLUSION
I hope some of these ideas are useful to some of you out there.  The
only way to learn to use them is to play with them constantly until
they become an automatic part of your musical personality.

For at least a while I will be keeping a copy of this article here
in my disk directory.  As long as the volume of "reprint" requests
is reasonably manageable, I will offer to send copies out by e-mail.

I can't really tell you when the next article will be ready for
posting, since I haven't written it yet.  The next and final article
in the GEMS series will address the concept of serial materials: what
they are, where they come from, how they're used, and how they relate
to the art of composition.

17 November 1992  Matthew H. Fields, D.M.A.




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