MUSIC FROM COMPUTERS		
                   Leland Smith, Stanford University


[Example 1 -- Sine Wave Prelude (3 different envelopes, pure sine tones.)]
  
When we listen  to music  produced by  a piano or  a trumpet,  or even  an
 
electric guitar, we do not often stop to ask what is the scientific  basis
 
for the sounds being produced.  But when we hear about a computer  playing
 
music it is usually quite a different thing.  In the past we have  thought
 
of computers as giant adding machines which consumed thousands of  punched
 
cards and then produced  thousands more, in the  form of telephone  bills,
 
paychecks or scientific data.   It is probably better  if we can think  of
 
the computer as a device for manipulating patterns or relationships and  a
 
device which can follow long and detailed lists of instructions.   Perhaps
 
the greatest difference between a computer  and an adding machine is  that
 
the computer has a vast "memory" where information and instructions can be
 
stored.  It will be seen that the production of music can require the full
 
capability of the computer.

 
We have learned that all static  physical things can be measured and  thus
 
described by numbers.   However when something  is constantly changing  we
 
must use algebraic  equations to express  the relationships involved.   In
 
this way we can find the numbers which will describe the particular  state
 
of the changing thing at any frozen moment in time.
 
  
Sound is produced by rapid changes of air pressure in the ear.  When these
 
changes are very great we say the sound is loud.  When they are  irregular
 
we say the sound is noise.  When  the changes are very smooth and  regular
 
we say the sound is musical.  There are simple formulas which can  express
 
the pattern of change in air pressure for a musical sound.  By using  such
 
formulas the computer can  produce a long string  of numbers which give  a
 
close approximation of the changing air pressure of a musical note.
 

 
Once these numbers are computed and stored away they could be used to draw
 
a picture  of the  sound wave  on  a computer  controled device  called  a
 
plotter.  In this  case thousands of  tiny straight lines  would be  drawn
 
which would seem to form smooth curves.
  
 
To produce real sound  these same numbers would  be transmitted at a  very
 
rapid rate to a device called a digital-to-analog converter, or DAC.  Each
 
number read from the  computer's memory is transformed  by the DAC into  a
 
specific voltage level of electricity.   These minute voltage changes  are
 
then sent over wires to an  ordinary amplifier where they are treated  the
 
same way as  voltage changes  produced by  a microphone  or the  vibrating
 
needle of a phonograph.
  
 
Because we need  at least  10,000 numbers to  produce one  second of  good
 
sound it can be understood that the main problem in computer music is  the
 
management of  vast  quantities of  data.   (With our  four-channel  music
 
system at least 6,000,000 numbers are needed for each minute of sound!)
  
 
To better  understand the  process of  computer generated  sound we  might
 
compare it to the process of making moving pictures.  With movies we  know
 
that we are  watching thousands of  still photos which  have captured  the
 
successive positions of  moving objects  at rates  such as  24 times  each
 
second.  Because our visual mechanism can perceive separate images only at
 
rates less  than 16  per second,  the  series of  still images  fuse  into
 
apparent continuous motion.  In a sense the ear is much more sensitive  to
 
abrupt changes than is  the eye.  In order  to produce acceptable  musical
 
sounds in a manner analogous to the  cinema process we must hear at  least
 
10,000 separate sound impulses per second.  A graph of the voltage changes
 
in a microphone  produced by a  flute tone would  look quite smooth.   The
 
computer would simulate this by a  series of short, precise steps.   After
 
the jagged edge is removed from this tone by an ordinary electronic filter
 
it becomes virtually identical to a flute tone.
  
 
A typewriter keyboard is the basic means of communication with a computer.
 
The keyboard may produce punched cards which will be fed into the computer
 
or magnetic  images of  the cards  may be  written onto  some mass  memory
 
system, such  as  a computer  disk.   If you  are  to communicate  with  a
 
computer you must  use a language  it has been  programmed to  understand.
 
The simplest kind of computer language  might consist of a single  letter.
 
If you typed "P" (for  play) the computer might  play some folk tune.   If
 
this could be  called a language  at all it  would be a  very limited  and
 
special purpose  one;  and it  must  be understood  that  a good  deal  of
 
programming in other languages would necessary before we got to the  point
 
where the letter "P" became  the symbol for the  sound of any tune.   Even
 
the best known computer languages, FORTRAN and BASIC, are programmed  into
 
each different machine by means of other special languages.

 
I have attempted  to develop a  music language for  computers.  Once  this
 
language, which is called  SCORE, is learned it  is possible to cause  the
 
computer to play  virtually any  piece of music  by merely  typing in  the
 
score, that is, the notes, rhythms, and other pertinent musical data.  The
 
main principle of the SCORE language  is that the progress of each  aspect
 
of the sound is  treated separately.  Each  note in a  piece of music  has
 
many aspects -- or  parameters.  The parameters for  any given note  might
 
include pitch, begin time, duration, loudness, timbre, stereo position and
 
many others.  By treating the various parameters separately SCORE  enables
 
the musician  to create  performances with  nuances and  expression  which
 
approach the sound of live players.  However the greater the  flexibility,
 
the greater the mass of detail that must be considered.  To alleviate this
 
problem  SCORE  includes  many  features  which  automatically  deal  with
 
continuous processes of change.   SCORE also has  several ways of  dealing
 
with the redundancies which abound in most music.  Any string of events in
 
a parameter may be given an  identifying symbol.  Whenever this string  is
 
to appear again only the symbol need be typed.
  
 
Insofar  as  possible  I  have  tried  to  make  the  SCORE  language  use
 
terminology that all  musicians already  understand.  If the  music to  be
 
played uses the  tempered scale, the  ordinary letter names  of notes  are
 
used.  Of  course the  particular  octave range  must also  be  specified.
 
Sharps and flats are indicated by the letters "S" and "F". However,  SCORE
 
also allows easy use of microtones, that is, the pitches in between  those
 
found in our usual musical scales.  Letter names cannot be used for  these
 
sounds so they are expressed either  in Hertz numbers (cycles per  second)
 
or as steps in tempered scales of any number of divisions of the octave.
  
[Example 2 -- 13-tone scale from middle C. (2 times, no leader between)]
 
[Example 3 -- 13 over 12; 14/12; 15/12; 18/12; 24/12.  Stereo, no reverb.]
  
 
Musical rhythm is usually expressed in fractions, the lower number in  the
 
fraction simply indicating how many equal parts are to be found in a whole
 
note.  In the SCORE language only this lower number need be typed.  8 = an
 
eighth note, 4 = quarter note, etc.   SCORE is by no means limited to  the
 
usual rhythms.  5ths, 7ths, 11ths, etc. can be combined in any way.  It is
 
very difficult for human musicians to play rhythms such as 13 against  12.
 
For  the  computer  this  is  quite  easy  because  SCORE  can  understand
 
thirteenth and twelfth notes as easily as quarter notes.
 
[Example 4 -- Woodblock (xylo) rhythms.  
       8th note bass, Eb-G.  Upper, C, F#, etc.
       8ths;  triplets(12th);  16th;  quintuplets(20);  sextuplets(24);
       septuplets(28);   nonuplets(36);   13:2(26ths).]
 
We must remember that musical  rhythmic notation is purely relative.   The
 
real time value of each note is  determined by the tempo which is  usually
 
indicated by the number of beats to  be played in one minute.  With  SCORE
 
it is possible to set the tempo as often as desired.  Also it is  possible
 
to create accelerations or retards from one tempo to another over any time
 
span.  Internally the SCORE program processes the rhythmic values and  the
 
tempo factors so as to produce the exact real time values for each note in
 
a piece.

[Example 5 -- Same as above but 2 times with accel. and rit.
						  mm=60→180,  180→32.]
 
I have said nothing yet about the  parameter of timbre.  This is a  rather
 
complicated subject and one which requires a knowledge of acoustics beyond
 
that of most musicians.  At its  simplest, timbre, or tone color,  depends
 
upon particular mixtures of  several harmonics, which  alone are pure,  or
 
"colorless" tones.  With the Stanford computer music system it is possible
 
to create almost any  combination of harmonics.   However we have  learned
 
that our perception of timbre  is dependent upon several changing  factors
 
in each  note.  My  colleague at  Stanford, Professor  John Chowning,  has
 
found a  method utilizing  the principles  of frequency  modulation  which
 
provides a means  of simplifying  the production of  the most  complicated
 
sounds.  This  work has  progressed for  a few  years now  and the  Yamaha
 
Company of Japan is currently incorporating Chowning's FM system in  their
 
newest digital electric organs.
 
[Example 6 -- FM: Small bells, then trumpets.  
			 (Chowning's father-in-law's carol.)]
  
 
Another important factor that influences  our perception of tone color  is
 
the "envelope" of a note.  The envelope can be described by a graph  which
 
shows the detailed amplitude, or loudness changes throughout the  duration
 
of note.  Ordinary instruments produce very complex envelopes.  In fact it
 
turns out that many instruments  produce independent envelopes on each  of
 
upwards of 32 harmonics.  This is one reason why it is rather difficult to
 
successfully create the effect of a "live" instrument.

 
The dull sound of a simple sinusoid  wave can become a pleasant bell  when
 
an envelope of an exponential shape  is applied.  The sine wave becomes  a
 
flute when a slight emphasis is added  to the first part of the  envelope.
 
The same basic wave  can take on the  characteristic of a tuned  woodblock
 
when the full volume is  restricted to just a  few complete cycles of  the
 
wave.

[Example 7 -- Repeat of Sine Wave Prelude  (3 different envelopes, 
		pure sine tones, "flute", "small bells", "xylo".)]
 
 
Some of you may  have heard tales of  computers actually composing  music.
 
To a certain extent  this really can  be done.  In  order to discuss  this
 
properly I would  have to investigate  thoroughly the human  compositional
 
process.  It will have to suffice  to point out that all composers  follow
 
rules, whether they  know it  or not.   Usually even  the simpler  musical
 
styles involve rules with  vast possibilities.  With computer  composition
 
as  many  rules  as  possible  are  written  into  a  program  as  logical
 
statements.  These programs  usually include subprograms  known as  random
 
number generators.  The notes and rhythms may be picked at random but  the
 
given rules may often  reject certain choices,  causing the random  number
 
generator to try again until it picks something suitable.  Some years  ago
 
I made some first  steps at teaching the  computer the principles of  jazz
 
improvisation.  The  bass  line  picks  only notes  which  fit  the  chord
 
progression of the "blues".  The solo line, however, can pick from as many
 
as ten notes at any given time,  even though there are only three or  four
 
notes in the various  chords.  The program was  so constructed as to  make
 
any "non-chord" note that happened to be picked conform to the traditional
 
rules of harmony.  The result is  hardly inspired jazz.  Rather it  sounds
 
like the  first attempts  of an  earnest, but  not very  talented  student
 
trying his hand at improvisation.
  
[Example 8 -- Jazz improvisation.  (3 choruses, Blues in C)]

 
The next few examples were created in order to test the ease of using  the
 
SCORE language with conventional music.  I  chose works by Bach because  I
 
feel quite sure that the computer  manipulation of themes would have  been
 
of great interest  to this composer  of canons and  fugues.  The first  of
 
this set, (which  I call  "Binary Bach") is  the "riddle  canon" from  the
 
Musical Offering.  This little  piece, which has the  title, "seek and  ye
 
shall find", is written as single line of music.  But it is really a  duet
 
where the lower voice  is to play backwards  from the music turned  upside
 
down.  It was necessary to type in only the notes of the main voice to the
 
SCORE program.  By  designating the main  voice "Z", the  second voice  is
 
created to Bach's specifications by  typing "$Z-10".  The "$" inverts  the
 
voice and the "-10" transposes it down 10 half steps to create the  proper
 
harmonic combinations.
 
[Example 9 -- Bach, "Musical Offering", 
			Riddle canon (Seek and ye shall find.)]
  
 
Bach wrote the Musical Offering as a tribute to Frederick the Great,  King
 
of Prussia.  The title of the next piece is "the modulation ascends as the
 
glory of the king ascends".  Bach  was a true diplomat because this  music
 
implies that the king's glory is boundless and eternal.  The written music
 
concludes with the first measure repeated  a step higher than it had  been
 
at the beginning.   Bach then  puts a  wavy line  to show  that the  piece
 
should go on this  way, always higher and  higher, never ending.  To  make
 
the work a practical length I have the voices constantly accelerating  and
 
moving by circular paths into the distance, until they finally  disappear.
 
Using SCORE, this required less than one page of typing.
 
[Example 10-- Bach, "Musical Offering",  Endless ascending modulation.
                (The modulation ascends as does the glory of the King.)]
  
 
The next  two  pieces are  also  from  the Musical  Offering.   The  first
 
includes woodblock sounds which are  produced by limiting the duration  of
 
each note to  only ten  cycles of the  sound.  Along  with this  frequency
 
modulation sounds are used in the bass.  The second piece has a constantly
 
changing organ-type bass and woodblock and bell sounds.
 
[Example 11-- Bach, "Musical Offering", 3-part canon with changing FM 
						    and additive sounds.]

[Example 12-- Bach, "Musical Offering", 4-part canon in G minor.]
 
  
By now you can  see that the  computer may be  considered as just  another
 
musical instrument.  But perhaps it is the ultimate musical instrument.  I
 
believe it will be able to play any sounds that a musician can imagine  in
 
his mind.  Beyond this the  computer can, in a  limited way, take part  in
 
the  compositional  process  itself.   In  my  "Rhapsody  for  Flute   and
 
Computer", composed in 1971, perhaps  two-thirds of the notes were  chosen
 
by some sort of  controlled random selection methods.   Some of the  flute
 
part was written first, then the  computer part was produced and then  the
 
flute part was  expanded to its  final form to  take advantage of  certain
 
aspects of the computer choices.
  
 
The last music to be heard is  from the end of "Machines of Loving  Grace"
 
which I composed in 1970.  Only the computer part of this excerpt will  be
 
heard but  the original  of this  work includes  a reading  of a  poem  by
 
Richard Brautigan and  a part  for solo  bassoon.  Two  melodic lines  and
 
three chord structures form  the basis for this  piece.  In the middle  of
 
the excerpt you will hear the melodic  lines in their simple form, but  as
 
they proceed,  the slide  from one  note to  another becomes  greater  and
 
greater until the sound is a kind of wailing.  The lines then evolve  into
 
pinpoints of staccato notes as the final chords of the work emerge.
 
[Example 13-- Excerpt from end of "Machines of Loving Grace".  
                       Gradual glissando, etc. (quote poem too?)]

  
Computer music is  still in its  beginning stages but  there seems  little
 
doubt that this medium of expression will soon occupy a prime position  in
 
our culture.   The means  for  producing computer  music are  still  quite
 
expensive but there is every reason to believe that the cost for  adequate
 
facilities can eventually  become less  than the  price of  three or  four
 
grand pianos.  Meanwhile the number  of computer music centers is  growing
 
to the point where it will not be too long before all the world's  leading
 
composers will have the opportunity to work in this medium.
 
[Example 14--   (extra)
    Brief excerpt from "Preludio a Cristobal Colon" by Julian Carrillo.
                96-tone octave.  Starts with 1/8 tones (i.e. 48/oct), 
                then 1/4s (24/oct),then 1/8s again.  
                Starts on E, fermata on E, E, B, E:B.]

       [Possible added examples: "mirror canon", and no. V.]