EDITING AND PRINTING MUSIC BY COMPUTER

		    Leland Smith
		    Department of Music
		    Stanford University



	The computerized production of  printed  music  presents  two
main  problems  which  must  be  treated.   These have to do with the
preparation and editing of the text and the actual  creation  of  the
master  copies which will be used as the basis for conventional photo
off-set printing.  This last step in the computer process,  which  is
most dependant upon particular hardware, will be touched on first.

	The  earliest  music  printing  was  done  at  the end of the
fifteenth century.   Since  then  many  processes  have  been  tried.
Woodblocks,   movable   type,  engraved  plates  and,  lately,  music
typewriters have been used.  Although movable type schemes  persisted
into  the  nineteenth  century and various forms of music typewriters
are widely used today, the engraving process remains dominant because
of  its flexibility in dealing with the need for a wide range of both
fixed and variable shapes in musical code.

	The vast majority of musical symbols are fixed  as  to  shape
and  size,  however  a certain number of these items require complete
flexibility in  positioning  as  well  as  the  appearance  of  their
overlapping  other items.  The problem of overprinting notes on staff
lines with consistent accuracy proved  a  major  stumbling  block  to
movable  type  schemes.  The idea of breaking up the staff lines into
small segments which included the desired notes never  produced  fine
copy.   Skillful  use  of a music typewriter can usually overcome the
problems connected with the items of fixed shape and size.

	The question of how to  deal  with  the  variable  items  has
remained  a  major  problem.  In many scores composed during the past
twenty years practically  everything  is  variable.   Some  of  these
scores are  admittedly  closer  to  free  hand  drawing  than musical
notation.  The older methods of music printing have  been  unable  to
cope with these works.

	In what I will call conventional notation, the major variable
items are the ligatures, or ties and slurs, the lengths of note stems
and  the  lengths  and angles of the connecting beams for the quicker
rhythmic values.  Several other items  may  in  fact  be  treated  as
variable but usually only a few variants of each are ever used.

	In the system of computerized music printing now operating at
the Artificial Intelligence Project of Stanford University the master
copy of each page is drawn by a Calcomp 563 plotter using a felt pen.
When this plotter draws diagonals minutely jagged lines result.  Also
all curves must be broken down into a finite number of straight  line
segments.  For these reasons the master copy is made at about 15O% of
the  size  of  the  desired  final  format.        This   master   is
photographically  reduced  when  the  off-set  plate is made, thereby
minimizing the shortcomings of the plotter.

	Most  of  the  fixed  shapes for this printing system are put
into the computer program in terms of data lists of x-y  coordinates.
Because of this it is not at all difficult to change details of these
shapes to suit  individual  tastes.   In  the  first  few  months  of
operation  of  this  program  there  has been a continuous process of
refining the shapes so that  they  more  closely  resemble  those  in
engraved  music.  The treble clef used in the first music printed was
made up of thirty-one straight lines.   The appearance of  this  item
has  been  improved  by  increasing  the  number of lines to over one
hundred.

	Many musical symbols have traditionally required  a  changing
line  width  and  several  require filled in black areas.  (The ball-
point pen has been of limited use to music copyists!)  Thus  a  heavy
vertical  bar  drawn  by the plotter uses seven lines, a single cross
beam uses five lines, etc.  Using the plotter in this  way  has  both
advantages  and  disadvantages.   By  producing an oversize master, a
great variety of line widths may be created, but  since  the  plotter
moves  at a fixed rate, the time required to draw a page of music can
become considerable when there are many solid areas to be filled in.

	It would seem that a combination plotter-line printer  device
of  high  accuracy  would  be  the  ideal solution to the problem. Or
perhaps some sort of device involving  the  projection  of  microfilm
could  be  successfully  adapted  to  this  task.  The development of
special hardware of adequate capability will  surely  come  when  its
commercial  potential  is  realized.  In any case, the Stanford music
printing program, being written in standard FORTRAN IV, can easily be
used in connection with any normal computer interface.

	The  music  printing program, which is called MSS, includes a
switch whereby the output can be directed to either the  plotter,  as
is  the  case  when  the final copy is made, or to a cathode ray tube
display, where further editing may take place.  This switch is  quite
simple  since  exactly the same type of instructions are used to draw
vectors on both the plotter and the CRT.

	A complete page of music is prepared in sections whose  sizes
are  limited  by  the  quality  of  definition  and the storage char-
acteristics of the CRT display terminal.  There is no  limit  to  how
many  sections may be combined to make up a full page on the plotter.
The digital instructions for drawing each of the sections are  stored
on  separate  files in the disk memory.  When the operator calls up a
section to be displayed, each item is  processed  internally  in  the
order in which it was created and then the complete file is displayed
at once.  If there are no time-sharing  delays,  this  process  takes
very  little time.  If the same file is to be drawn by the plotter, a
juggling routine rearranges the order so that items appearing in  the
lower  left hand corner will be drawn first, with the material in the
upper right corner appearing last.  Thus the time required to move to
each succeeding item, with pen raised, will be kept to a minimum.

	In  the  spring  of  1973  a Xerox Graphics Printer (LDX) was
installed  at  the  Artificial  Intelligence  Project.   This  device
produces very good music copy on 8 1/2" width paper at many times the
speed of the plotter.  This copy is completely  adequate  for  casual
use  however  it  cannot  compete  with  the quality of photo-reduced
plotter output.

	The preparation and editing of each unit of music is the most
useful,  and  most  complex,  work  of  MSS.  Basically, each item to
appear must be entered as a specific  list  of  parameters.   However
several  automatic  features  in  the  program enable the operator to
ignore many of the details.  The first parameter, P1, always holds  a
code number for a particular item or group of items. P2 indicates the
left-right position.  A scale  dividing  the  width  of  the  display
screen  into 200 parts can be projected at any level on the CRT.  The
position of most items is figured from the left leading edge.

	The third parameter gives the staff number.  With the present
system  it  is  practical  to display up to eight staves at one time.
(There is no fixed limit on how many staves can be included on a page
drawn  by  the plotter.) A staff in the middle of the screen would be
numbered zero with those above being numbered one to four  and  those
below  minus  one  to  minus  three.   Where applicable, P4 indicates
up-down spacing in terms of note numbers.  The position of  middle  C
in  the  treble clef, one ledger line below the staff, has been given
the number one.  This basis was chosen because of  simplicity  for  a
musician to think in terms of upward-moving diatonic intervals.  Thus
G above middle C is five, the C above is eight,  etc.   This  musical
logic  breaks  down  somewhat  when  descending  below middle C.  The
position for B is zero, A is minus one and so forth as the scale goes
down.   Since  decimal  numbers  may  be  used,  great flexibility in
positioning is available. Up to eight more parameter entries  can  be
given for a single item.

	For  ordinary  notes  the  code  number  in  P1  is one.  The
position of the note is set in P2, P3 and P4.  P5 serves  the  double
purpose  of  controlling  stem  direction  (or  absence  of stem) and
accidental, i.e. whether the note has a flat, sharp or natural  sign.
Usually  this  parameter  will  have two digits.  If the first (left)
digit is zero (or doesn't exist) there will be no stem.  If the first
digit  is  one  the  stem will be up, if it is two, down.  The second
digit will indicate the accidental which is to appear in front of the
note.   Zero  means  no accidental, one is a flat, two is a sharp and
three is a natural.  By adding further digits beyond a decimal  point
it  is  possible to increase the space between the accidental and the
note to any distance desired.  This extra space is often necessary in
complex chord structures where accidentals would otherwise overlap.

	Notes  will  be  filled  in, or "black", unless P6 is given a
negative number, in which case they will be "white", or  open  notes.
P6  also  aids  in  the  automatic  alignment  of  a  note with other
previously set notes to create chords.  If P6 is ten (plus or minus),
the  note  will shift to the correct position on the right side of an
upward note stem.  The number twenty will cause the note to shift  to
the left side of a downward note stem.

	A single digit in  P7  will  show  the  number  of  tails  or
rhythmic  indication  which  will  appear  on  the  note  stem.  If a
sixteenth note (with two tails) is to be printed, P7 will have a two.
When  P7  has two digits the note will be dotted and the second digit
will give the number of tails.  Decimal values can be added to P7  to
move  a  dot  farther  out  from  the  standard  spacing,  this being
necessary in some chords.

	P8 is used for changing the standard length  of  note  stems.
This  is  usually necessary when chords are printed and in some other
cases. The unit for extensions is the vertical distance  between  one
note of the scale and the next.  Since notes can appear on both lines
and spaces of the staff, the number two then would extend a  stem  by
one  complete  space.   The  proper  number  of  ledger  lines appear
automatically for notes above and below the staff.  If for any reason
the ledger lines are not desired the number one in P9 will cause them
to be suppressed.


	To display F sharp above middle C as a dotted sixteenth  note
on the middle of the screen the following parameters would be given.




			   P1  P2  P3  P4  P5  P6  P7  P8  P9
        ex. 1		   1   100  0   4  12   0  12   0   0




Note that P5 and P7 serve  double  duty.    The  first  digit  in  P5
indicates that the stem goes up and the two calls a sharp.  The first
digit in P7 causes the dot to appear and the two calls for two tails.

	Used  in  this  way this parameter system could become rather
cumbersome.  The multiple use of  some  parameters  was  arranged  in
order  to  save  storage  space in the program at a time when program
size was a factor in speed under a time-sharing system.  However,  as
shall  be  seen  later,  most of the more complicated aspects of this
system, as applied to setting up individual  notes,  seldom  need  be
considered  by  the  operator.   The  important  thing is that if any
particular detail  requires  changing,  the  right  numbers  for  the
situation are not too hard to find.

	The  choice  of the specific code numbers to be used in P1 to
designate the various item groups was  completely  arbitrary.   Words
might have been used instead of numbers but there are many situations
where, after a little practice, an all number system  can  be  easier
and faster to operate.

	The  item  put  on  the  screen  first is usually a five-line
staff. For this the code number in P1  is  ten.   P2  will  give  the
horizontal  position  for  the left end of the staff, P3 the vertical
position number (from  minus  three  to  three),  P4  the  horizontal
position for the right end of the staff and a number in P5 will cause
any desired vertical displacement.  From this point on any item  that
is to appear in relation to this staff will use the same value for P3
(vertical position number).  If P5 has displaced  the  staff  by  any
amount,  automatic adjustment will be made for all items appearing on
that staff.  P6 can be used to alter the vertical size of the  staff.
The  dimensions  of  all  items  thereafter put on that staff will be
controlled by the number put in P6.  In music engraving  only  a  few
basic  sizes are ordinarily available.  With this computer system the
flexibility is complete.

	Because of their variable lengths and slopes the heavy  cross
beams  which  connect  the notes of smaller rhythmic values present a
number of problems.  The code number for beams is nine.  P2  has  the
position  of  the  left side of the beam or beams.  Since it would be
time  consuming  to ascertain the precise position of any  note  stem
this  number  need be only approximate.  Before the beam is drawn the
exact position is found by the  program  and  the  number  in  P2  is
properly  adjusted.   As usual, P3 holds the staff number.  P4 and P5
are the vertical levels of the first and last notes to  be  connected
by the beam.  The approximate horizontal position of the last note is
put  into  P6.   As  with  P2,  the   precise   position   is   found
automatically.  The  proper  slope  for the beam is determined by the
program's  consideration  of P2, P4, P5 and  P6.   Of  course  it  is
necessary  to  tell  whether the stems are to go up or down.  A first
digit of one (up) or two (down) in P7 conveys this information.   The
second digit in P7 will tell how many beams are to be drawn.

	Partial  beams  are  sometimes  needed.   If P8 has a ten the
partial beam will be attached to the first note stem; a  twenty  puts
it  on the last stem of the group.  The end point of the partial beam
is put in P9.  P10 is used to displace the beam from the outer  limit
of  the  stems  toward the note heads (necessary with partial beams).
After all the beams are in place a special feature may be used  which
automatically  adjusts  to  the proper length every note stem falling
within the span of each beam.  An example of beam drawing  parameters
is given.





			ex. 2






   P1  P2  P3  P4  P5  P6  P7  P8  P9  P10 

   9   51  0   3   2   83  12  0   0   0   (sets the two upper beams)

   9   51  0   3   2   83  11  10 54.5 2   (sets right partial beam)

   9   51  0   3   1   83  11  20  68  2   (sets left partial beam)

	The  upper  two  beams  are  described  within  one  set   of
parameters since they have the same characteristics.  The two partial
beams must be described separately.  It must  again  be  pointed  out
that  the  operator  need  be  concerned with these details only when
making changes after the original input stage.  In  the  first  input
the rhythms must be given and then it is only necessary to state that
the group of notes from 1 to 7 are to be  beamed;  then  the  program
creates  the three parameter lists shown above. The "homing" features
used in  beam  drawing  are  also  used  to  facilitate  the  precise
placement of various markings such as accents and staccato dots.

	There are some code numbers which are used to produce  groups
of items which can later be edited separately if desired.  The number
sixteen allows the writing of any letters or numbers into the  score.
It  is  possible  to  place  the  beginning  of a line of text at any
position and the size of the letters is flexible.  Bold face printing
is simulated by duplicating each letter with a  slight  displacement.
The  elegance  of the letter shapes has not yet been considered since
it is planned to have a wide variety of  type  faces  when  different
hardware for the creation of the master pages is developed.  The code
number eighteen causes key signatures of  any  number  of  sharps  or
flats  to  be  written  when only the clef name and the major key are
entered.   The accidentals will automatically be positioned in  their
proper places for the given clef.


	The  most  useful item-grouping in MSS is available under the
code number fourteen.  With this number extended  strings  of  notes,
along  with  most  of  their  accompanying details, can be entered at
once.  The program prompts the operator  for  the  various  kinds  of
information  required.   The  first  prompt  asks for the notes to be
typed.  All notes are typed by letter names with a octave number  and
a  letter  (F,  S  or N) for the accidental if needed.*1. So that the
notes will appear at the proper levels, the clef must be given at the
beginning of the line and each time a change of clef occurs.  A colon
following a note indicates that the note  will  appear  in  the  same
rhythmic  position as the previous note so as to produce a chord.  In
some close-knit chords the notes must appear on  alternate  sides  of
the  stem  and  accidentals  must be spaced out.  This section of MSS
takes care of these  things  automatically.   The  following  example
shows some results of this chord-spacing procedure.






			ex. 3







	The second prompt asks for position  one  and  position  two.
These  numbers  will  set  the horizontal limits within which all the
given notes will fall.  At this point the notes will  appear  on  the
CRT  as  equally spaced quarter note values.  Next, the operator will
be asked to "TYPE RHYTHM".  The denominators of conventional  musical
fractions are used.  Thus four equals a quarter note, eight an eighth
note, etc.  Dots added to these numbers will  produce  musical  dots.
Now  the  music  on  the  screen will be repositioned relative to the
given rhythmic values. All the proper rhythmic tails will appear  and
the half notes and whole notes will change to "white" notes.

	Next the  operator  will be asked, "ADD BEAMS?"  If these are
needed, pairs of numbers, indicating the first and last note of  each
beamed  group,  must  be  entered.   If  a group is to have its stems
turned downward, the second number of  the  pair  must  be  negative.
Most  combinations  of  partial  and  complete  beams will be created
automatically according to the rhythmic values previously  given  for
the  notes in the group. After the beams appear all unnecessary tails
will disappear and the stem lengths will be normalized.  After  this,
similar  procedures  are  followed  to add accents and staccato dots,
etc. to the passage and  then  slurs  and  ties.   Following  is  the
operator's input to create the music of Example 5:


    TR/K2S/4 4/D5//E/R/M/F///B4/E5/G/M/G/F/E/D/E/F/M/F/E/D/E/F/M/*

    4./8/4//4./8 X 6/4/8///4/8/16//4/2*

    7 9/ 16 18*

    7 9 2/ 10 11 1/ 15 16 1/ 15 18 2*

	In the first line TR stands for treble clef.  K2S indicates a
key signature of two sharps.   4 4 is the meter.  The note  D  is  to
appear  in the fifth octave of the piano keyboard.  R is a rest and M
is a measure line. The second line gives the denominators of all  the
rhythmic  values.   The third line tells which notes are to be beamed
together.  The line for  accents,  etc. is  omitted.   The  last line
gives the location of the ligatures.   The third number of each group
indicates the curvature desired.

	The horizontal spacing of printed music is usually related to
the rhythm in only a  general way.  Following the directions outlined
above,  the  sections  with  quicker  values  will be closely bunched
together  while  the  slow values will occupy rather large areas.  By
using the editing techniques available  in  MSS  a  special  line  of
rhythms may be set up at the top of the screen which will control the
spacing of everything put below.  What this  does  in  effect  is  to
change  internally the values of the horizontal spacing numbers.  For
example, if a whole note is made to occupy the  same  space  on  this
highest  line  as  a  following  quarter  note, then the program will
consider the space under the whole note as being four times as  great
as  that  under  the quarter when the automatic "equal" spacing takes
place.  In this way the practical, readable spacing of the  music  is
easily managed.

	Example 4a shows an extreme case of what can happen if strict
rhythmic spacing is adhered to.






			ex. 4a








	Example 4b shows how the use of the spacing line can  produce
a readable form of the same input.








			ex. 4b










	The spatial problems of entering the text in vocal music  are
greatly  facilitated  by  a feature which displays order numbers over
the notes of a given line.  The  various  syllables  and  dashes  are
typed in with slashes separating each group of characters requiring a
unique position.  Then a parallel series of numbers are entered which
will designate the precise position for each of the groups.







            ex. 5







    Input to MSS for text:    KY/-/RI/-/E,/KY/-/RI/-/E/  etc.
                              1/1.6/2/2.6/3/4/4.7/5/  etc.





	Most  of  the  conventional  musical symbols are available in
MSS.  Any special shapes may  be  created  by  use  of  a  subsidiary
program  which  allows  you  to  draw on the display screen either by
typed commands or by use of a light pen.  Expanded  outline  drawings
are made and then any areas may be designated for filling in.  One of
the more complicated parts of MSS is the  routine  whereby  the  dark
areas  are  given  exactly the right number of lines to properly fill
them regardless  of  the  overall  size  factors.  Once  a  shape  is
completed  it may be freely edited.  Points may be moved, inserted or
deleted.  When the shape is used in a score it  may  be  inverted  or
reversed  or expanded or contracted by varying the proper parameters.
Scores including  a  combination  of  ordinary  and  non-conventional
graphic notation will be easily produced.










		ex. 6

	Perhaps  the  most  important elements of MSS are its various
editing features.  Once any group of items is set up it is  essential
that  corrections  of all sorts can be made with a minimum of effort.
The program has given each symbol entered an item number  and  it  is
quite  easy to seek out a particular item for editing.  The items may
be searched for by number, by category (i.e. notes,  beams,  letters,
etc.)  or  by  position.   A  box  appears  around each item as it is
brought up for editing.  Once the correct  item  is  found,  all  its
current  parameters  are  listed  on  the  bottom of the screen.  New
values may be given for any or all of the parameters.    The old form
of  the  symbol  remains on the screen while the newly edited form is
created.  When the edit mode is left it is possible to delete or save
the  old  form of the symbol.  In this way it is possible to copy any
single  item  from  one place to  another  by  typing  only  the  new
position  parameters.   There  are  also ways to copy whole groups of
items from one position to another. MSS allows for the  expansion  or
contraction  of the horizontal spacing on any staff, or on all staves
at once.  This is usually used as a last step to arrange the  various
parts of completed lines into a visually pleasing and readable whole.
By typing J, an entire brace of music, including several staves,  can
be  properly  justified  at  once.    Space will be "stolen" from the
slower rhythmic values and from notes without accidentals in order to
provide the minimum space requirements for each type of item.













		ex. 7

	All work done with  MSS  can  be  stored  on  various  memory
devices  for  further  use.  When a particular unit of work is called
back into the program it may be combined with other units  or  edited
some  more  or  sent  to the plotter for the production of hard copy.
When a section is plotted, the overall dimensions may be adjusted  to
any size desired.

	With  older  music printing methods, the parts for individual
players of an ensemble piece had to be created separately.  With MSS,
the  extraction  of parts from a full score can be done automatically
using a small subsidiary program.   Some  spacings  may  have  to  be
changed and full measures of rests combined, but little other editing
should be necessary.

	While MSS has been  conceived  for  use  on  a  time-sharing,
display  oriented computer system, a practical variant of the program
could be developed for the archaic punched  card  systems.   In  this
case  a  considerable  amount  of advance planning of layout would be
advisable  so that not too many plotter  runs  for  proofs  would  be
needed.

	It  is  reasonable  to  predict that some computerized system
such as the one described will eventually be utilized for most  music
publication.   The time required to set up a page with this system is
already competitive with good hand copy work. This time is much  less
than  that  needed  for engraving or music typewriting. None of these
older methods can match the ease of editing and entering  corrections
of all sorts that a computer program can offer.  As computer time and
equipment become less and less expensive it seems  likely  that  this
method  for  printing  music will prove to be economically attractive
and, as a result, present day composers will  gain  much  more  ready
access to quality publication.




Notes

1.  The conventions for musical input in  MSS  are  very  similar  to
those  used  in  an  extensive  program  written  by  this author for
translating  musical  terminology  to  input  for  a  computer  sound
generation  system.  A description of this is found in, Leland Smith,
"SCORE- A Musician's Approach to  Computer  Music,"  Journal  of  the
Audio  Engineering  Society,  Jan./Feb.  1972,  vol.  20,  number  1.
Especially useful in  SCORE  are  the  several  ways  of  efficiently
dealing with the various kinds of repetition found in most music.