www.sonic-arts.org/darreg/dar30.htm

USING TWO-PART COUNTERPOINT FOR

NON-TWELVE-TONE MUSIC

Ivor Darreg (1988)

The 20th Century is nearly over with. We have spectacular progress in all the arts--except
music, alas. I have done something about this--will you?

Stand near a downtown street-corner for a moment--everybody is in such a hurry that you
can't do that for more than a few seconds: cars and people will be rushing past, and every
so often--too often indeed--there will be a siren proclaiming another accident. It will
happen because both parties are in a hurry--almost every incident.

If you are quite downtown, you will see some joggers or actual runners hurrying down
the street with no real destination. You can't escape this even by going out in the country:
aircraft will whiz by overhead! Now contrast this with the average instruction in music
that most of will have gone through: rule after rule after rule, repeated and repeated to
intimidate us. DEAD COMPOSERS EXCLUSIVELY! Moreover: dead composers of the
19th century in central europe, not here in the USA. Nostalgia beyond belief. Why, it
amounts to Musical Necromancy--maybe Necrolatry.

Put on the radio or TV--"Golden Oldies" some stations say they are broadcasting. Well,
of course I know that doesn't mean the compositions of the Romantic Period in the 19th
century, but logically it could. In truth and in fact, much of the popular music of this
century is a reprocessed stylized permutation of the Romantic standbys all the way from
Europe in 1830 or 1850 or 1870. Dead but not buried; transported by H. G. Wells' Time
machine into 20th-century America and set down in the music textbooks and the How To
Play the Piano o Guitar or Violin or Ukelele books at your music store, or in more
dignified form, given out in conservatory and college courses throughout our fair land.

Walk into your neighborhood supermarket--look on the shelves and you will find Freeze-
Dried This and Old Country That. Well, if Atonal Twelve-Tone Serialism and similar
styles of music taught in our colleges and universities and discussed at great length in the
musical journals isn't Frozen and Dried from the Old Country, what better description
can YOU concoct for it? I dare you to come up with anything more apt. and to make
matters more annoying, the so-called avant-garde or ultramodern music many students
are taught to compose at the piano, which is the epitome of 18th-century technology,
engineering, and design, not even the 19th. Why, the very notes and clefs, accidentals,
and symbols used to print today's music whether serious/academic or popular/light, were
designed in Central Europe during the middle of the 19th century, nothing whatever to do
with today's ideals of graphic design. I might as well cut out a few and paste them in
here.

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The piano and that standard notation are holding back progress and so are most orchestral
conventional instruments--not quite all of those. The new electronic keyboards have been
imitating conventional ones so closely as to be mere clones in many cases. The new
samplers--well, that's emulation. However, this need not be that had: the cloning and
slavish emulation of old instruments is mostly the fault of the performers and their not
knowing the possibilities of these new instruments, rather than of the instruments
themselves. They simply haven't been told of what they CAN NOW DO!

Recent visits to demonstrations of synthesizers and other new instruments, discussions
with certain people in new music movements, recent demonstrations of computer music
software in action, and recent tapes from various sources, have usually exemplified built-
in constraints and limitations slavishly copied from mid-19th-century music and
instruments of that period or even earlier. In some cases these limitations can be
circumvented or defeated; in other cases they are impossible to alter. The music software
for computers is just as bad as the new hardware: and this goes for the graphics programs
which print out conventional musical notation--often they cannot do any new symbols
such as microtonal accidentals or various avant-garde expression-marks or some
composer's graphics inventions.

Maybe some of you think I am yelling and screaming about trivia--but consider the
consequences of impersonal soul-less corporations and conglomerates most of whose
business sis not music-related at all, and programmers and software houses which have
not consulted composers alive and experimenting with new music right now, and money-
managers and engineers and record companies and bankers and media experts and
manufacturers of assorted equipment who couldn't care less about any advancement or
progress or change or experiment in the art of music or its tools and means. Consider that
they, consciously or innocently and subconsciously, are telling you and me and all the
other persons that we MAY NOT COMPOSE this or that innovative melody or harmony.
(As a matter of cold hard fact: some of the new music software cannot play 5/4 meter, let
alone 7/4 or 2 notes against 3, so this built-in limitation extends to Rhythm.)

Some composers and some music-theorists have written volumes saying that nobody has
the right to compose in the 13-tone equal temperament or to use more 12 pitches at a time
out of the 1/4-coma meantone temperament, or to use any resources of a non-twelve-
tone-equal-tempered scale beyond what the rules of the ordinary textbooks permit for use
in standard Romantic or Classical piano compositions. Others claim they have tried this
or tried that and rejected it because they could not do anything worthwhile with it;
therefore you and I are also forbidden to try either.

The worst instance of this at present is the offering by some manufacturers of alternative
tunings which do not permit using more than a twelve-pitch-class subset of a scale at any
one time. When somebody is trying to perform in just intonation this because very
irritating and exasperating. I have had to wait for sixty (60) of my 72 years for non-
twelve-tone instruments and adequate recording equipment and cannot wait one minute
longer!

Another dreadful imposition upon us is the Acoustical Instruments Only Attitude--that
composers of anything, to be taken seriously, must not use electronic instruments or new
recording studio technology or samplers or effect-boxes or computers, but must stick to

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the instruments of the 19th century in Europe and never anything else--not even
saxophones or marimbas or vibes or kazoos for that matter. The idea of someone in a
modern home or apartment playing recordings, let along making their own, or playing an
electronic instrument or a guitar refretted to a new scale--why that would be a Mortal
Sin! Ironically enough, electronic instruments have aided and abetted the revival of the
clavichord and harpsichord and have acquainted millions of people with their sounds
who would never have heard them onstage.

Performers have intimidated composers all through the last century and almost killed
compositional progress. I have received letter DEMANDING that I never write a non-12-
tone-tempered note. This when I was past 50 and the writer was maybe 30! "No
performer will play it" this guy said. Now the tables are turned--most any composer can
get or borrow recording equipment to produce high-quality copies of recordings without
needing to impose on any narrowminded run-of-the-mill performers. Performers still
denounce improvising and any kind of do-it-yourselfery, and keep on demanding that
every single note be written down before it is ever heard, and they are happy if they can
keep others from composing anything that has the slightest chance of ever being heard by
other persons.

Listeners for centuries have had to attend performances often at great distances from their
homes or do without. The 19th-century in Central Europe is not the End of the Twentieth
Century in this country, so times have changed and nothing is gained by denying one-self
opportunities out of Purism. So why should I or any other composer alive today have to
pretend that only professional performers at public concert-hall can convert my musical
ideas into sound?

Now I am ready to get into our main subject: why two-part counterpoint in non-twelve-
tone scales? To make the listener have an easier, more enjoyable time with the
compositions in a scale that he or she has never heard before. For the sake of new
listeners. For people to understand and analyze the new composition and its scale--make
it simple! For a composer who decides to de-twelvulate it is just plain common sense to
begin with pieces that they can do well without a heavy investment in preparation and
from my own personal experience this is where and how to begin!

It's quicker and it's cheaper. It's more "transparent." Also, it is more appealing to certain
other musical cultures where one might find listeners or grounds for discussion; and it
permits beginning with one moving voice against a drone or very slowly-moving second
part.

Overdubbing only two tracks is much easier than overdubbing 3 or more. Playing only 2
notes at once or two voices at once is much easier than playing heavy block chords or 4-
part harmonies in a new scales. Some scales are not harmonic! How about that? THINK.

Some people have rejected the 13-tone temperament, for example, after scarcely trying it.
Others never bothered to try it at all, or snorted in haughty disdain, usually on theoretical
grounds. OK, let's begin there. 13-tone equal temperament is not harmonious. However,
if you want new melodies, they are there in great abundance, and it's all free of charge.
Consider the reason why somebody rejected 13-tone: it has no fifths, it doesn't have a
consonant triad, it deviates so far from just intonation, you have to go to the 11th and

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13th harmonics in the overtone series before you get any reasonable match. Another
argument you will hear if you dare mention 13 to the average musician is "How would
you write it down?" We can take that one up later.

Why do you have to write it down? Set an instrument to 13 and try melodies out till
something appeals to you. Turn on the tape machine and record that. Where's the
problem? Holy Jumping Catfish! Program a computer to generate random notes in 13--
this is possible with several existing kinds of software. Why use 13? Somebody will ask
you. Because it's different. We all need new experiences. My reason and somebody else's
might be "wounded Pride;" Look, man--the resources of 12-tone equal temperament are
just about exhausted--just about everything worthwhile that can be said in 12-tone has
been said already, and probably better than you or I could. It is humiliating to think that
not just us but for an entire generation or two of composers, we came in late--we get the
short end of the stick; we get the few crumbs on the table that might remain; over and
over we are humiliated by finding out that this or that brilliant inspiration has already
been used in Garstig von Esel's Symphony No. 3, or maybe Gromkoshumoff's Fourth
Rhapsody. How could it be otherwise in our lifetimes after thousands of composers have
done millions of hours at pianos and writing-desks and violins and horns? We are
punished for being born after the first decade or two of the 19th century and in the USA
instead of Europe.

So back before I was even born, at the last gasp of the 1900's, Wagnerian chromaticism
had piled complication on lushness and the orchestra had hypertrophied to huge
mammoth proportions, and the major and minor scales had been contradicted with hordes
of accidentals and modulations had run riot. Several people thought of abolishing tonality
and the seeds of serialism were planted. The popular music world lagged behind, but
eventually has caught up. Now with computers and other high-tech means, it might pass
it by. I have heard some of these possibilities, and also the way that they sound too much
like one another.

In passing, there is now an affair called new Age Music, which often is not new but
reminiscent of the 19th Century Romantics or sometimes of Debussy and the
Impressionists. Or it may be like the so-called Minimalists--rather monotonous and long-
drawn-out....maybe of a background nature. However, there is hope for it--if it can be (or
rather its composers can be) persuaded to use new scales, it could be part of the March of
Musical Progress. If it is to belong to a real New Age, it has to develop a new idiom and
manner, so why don't we offer the New Agers our new Scales and New Resources?

No, don't jump on me--I did not say that the New Agers or many of the experimental
composers were going to turn to 13-tone. Merely, some people will use it when they need
its peculiar mood or its melodic possibilties attract them.

I mentioned 13-tone first because of the CONTRAST it offers with 12. Because it is
UNTWELVE, NEW MOOD, not harmonic in the ordinary sense, a definite break, a new
experience, something to break up the hackneyed symmetrical patterns of the highly
divisible number 12--2,3,4 and 6 divide 12 evenly, creating symmetrical patterns called
the whole-tone scale, the diminished seventh chord, the augmented triad, and the tritone;
and also creating a repetition of sounds in spite of the different notations and names
given those sounds in run-of-the-mill standard ordinary twelve-tone-tempered music.

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13 is a prime number and cannot be divided evenly, so the 13-tone scale has non-
repeating patterns and unexpected turns of phrase and asymmetric combinations. This is
also true of some other scales such as 17, 19, and 31, while 23 and 29 which are other
prime numbers, may not be as important for the composer--but they are there if that is
your cup of tea.

Don't knock it till you've tried it--that means hearing actual pieces of music in 13, 14, 15,
and so on as far as convenient. In other publications I have suggested several places to
start, depending on your ambitions, resources, goals, and facilities.

Some people have scolded me because they thought I was maligning just intonation, but
that just is not true: I use it where it is the way to go. How can anybody look at my
Megalyra Family of Instruments with colored fret-lines in in just intonation, and listen to
my just intonation tapes and keep on making this false accusation?

Two-part counterpoint can be used as effectively for introducing new people to just
intonation as it can be used for getting used to a rich palette of new temperaments, equal
and unequal. Two kinds of compositions are NOT under consideration here as they way
to start using two-part counterpoint. If they were I could just refer you to them and save
paper and ink! Neither the antiquarian scholar's 16th-Century Counterpoint in its Species
and the textbook Examples nor the time-honored and esteemed Two-Part Inventions of
Johann Sebastian Bach are under consideration here. Whatever I may be, I am not the
reincarnation of Ebenezer Prout and now that the world is jam-full of those lovely
marvelous computers and sequencers and eager-beaver programmers to get Bach
performed perfectly so that you don't have to be tortured by amateur bashings of these
difficult pieces, I can go in for Progress instead of Nostalgia and Necrolatry and
Reminiscence.

Frankly, I am not enthusiastic about Serialsm, especially the only kind anybody ever
does, twelve-tone-equal-temperament played-on-the-piano serialism. Its rules are so strict
and since they can now be translated into sound via computer without much human
intervention, why should I use up the little valuable composing time that I might have
remaining at age 72, trying to do better than the computer and all the good programs that
will generate 12-tone serialism in huge quantities? Why should you?

I heard a random 12-tone-pitch selector turn out at great speed a never-ending stream of
atonal themes--a simple addition to a program could make these legitimate 12-tone rows
and now doubt that is being done all over the country, nay, the world. I heard it back
about 1977, and now anybody could do better. Sure I know: there are theoretically
Factorial-12, i.e., 479,001,600 possible 12-tone rows so there ought to be that many and
more possible different compositions made out of them, but they sound too much alike.

I am quite willing to use Atonality when it is appropriate, or I wouldn't be advocating
two-part counterpoint in such scales as 13, 16, 17, 18, and many others which can do
atonality supremely well. Serialism may have required human thinking and human action
when it was first invented or elaborated from Schoenberg's and others' atonality and still
others' work that followed the decline of the key-system and traditional harmony. But
serialism today is largely if not entirely capable of total automation. Oh, sure: some
college composer will deny that and object, but does any composition of theirs in that

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style sound different enough from what the computers now can do so well that it would
be worth the human composer's time?

Let's face it: the Notation Tail is wagging the Sound Dog! Many people I have met
during the last four decades or so value a written score far far far above any realization of
that score in audible sounds. So much is done with the mathematical and permutational
side of Serialism and strict 12-tone atonality that is visible on the page, but not audible to
the concert audience or the tape listeners. Much of what is taught in how to compose with
serial 12-tone methods will not help in systems which are not symmetrical as 12-equal is
because 12 is so divisible.

Back to the 13 tone scale: first Metachromatic scale beyond 12. It works for atonality,
and might work for serialism (my friends agree on that). 13 being prim,e the structure is
asymmetrical. Since most chords in it of 3 or more tones are dissonant, this is a good
reason to start using 13 by composing 2-part counterpoint. As with the other non-12s,
start with a drone against a one-voice melody; then move the drone around, then go to
two movable parts. As much to make it easier for your listeners as for yourself. After you
are comfortable with two-part counterpoint, first improvise trying out three- and more-
part chords and take it from there.

The old rules of 12-tone harmony do not hold for 13, so don't annoy yourself or others
with them. Now we come to an extremely important matter which by itself would be
justification for this article: timbre determines harmony--dissonant intervals in "normal"
qualities of tone can be tamed or even made agreeable by changing the timbre. With
modern resources of additive and subtractve synthesis and filtering and evvelope control,
it becomes easy to make 13 quite acceptable: marimbas, vibraphones, ocarinas, song
whistles, kalimbas, etc. Special synthesized timbres. For 13, don't use reedy tones and
penetrating string-tones at first. Get into those later on. Tones with special inharmonic
partials are quite possible now. Try that if you have the equipment.

Compensate for the reduction of ordinary harmony by increasing the rhythmic element--
more catchy rhythmic figures, enough rests in each part, whatever. After all,
contemporary listeners are used to drummers playing something which has no scale at
all! This makes all those arguments about 13-tone and some other scales being
inharmonic, extremely silly. The public listens to the unpitched percussionists anyhow,
so these new scales aren't going to stop them either.

Now for the promised remarks about writing 13-tone and other new scales down. Julian
Carrillo, the Mexican innovator, invented one way out: get rid of note-heads. Write the
half-notes with BENT STEMS. Use numbers instead of note-heads, and reduce the staff
to one line. That system is neutral as to what scale it is for, while traditional notation is in
favor of certain systems (12, 17, 19, 31) and very awkward for others (22, 23, 13, 10).
Another way will be various typewritten codes compatible with computer keyboards and
the ASCII system.

Graph paper is suitable for certain notations already in use by some composers, so again
this is a system-neutral way of writing something in a new strange scale. But for the
purposes of relatively simple melodies and spontaneous spur-of-the-moment
improvisations, we really don't need notation with all the recording equipment now

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