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		CHAPTER I

			INTRODUCTION


Except possibly for the works of a few composers overcome by a theoretical

bent, music has always been written from the point of view that the  proof

is in the hearing -- the ear  being the final arbiter.  Of course, we  all

know that the ear is simply the  receptor of sounds and that what we  mean

when we say a musical passage "sounds wrong" is that it includes  elements

which our minds are unable to  accept in terms of the musical  conventions

which we know or can  conceive of.  It is  obvious that any one,  isolated

note sounds  neither  right  nor  wrong.   For  that  matter,  those  well

acquainted with  20th-century music  would hesitate  to apply  "right"  or

"wrong"  to  even  a  fairly  large  number  of  notes,  produced   either

melodically or harmonically.  "Rightness"  or comprehensibility is  really

found only in complete musical passages  or phrases.  The phrase, or  even

the whole piece, will  be insufficient, however, if  the listener has  not

established at least some  backlog of experience  in hearing music  of the 

same general style.


Because of the tremendous backlog of experience in hearing music based  on

triadic tonal harmony, almost  everyone who has grown  up during the  last

fifty to  one  hundred years  in  contact  with western  culture  is  well

acquainted with the  conventions established  by music  composed from  the

time of the late  17th century to the  early 20th century.   Comparatively

abruptly, 17th-century composers established, from the implications of the

earlier modal  procedures, the  bases for  the tonal  system.  This  tonal

system proved  to have  possibilities  vast enough  to intrigue  the  best

musicians for  almost three  hundred  years.  Then,  in turn,  the  latest

implications of tonality gave rise to the 20th-century tendency away  from

the necessities of tonal harmony.


Although, strictly  speaking, the  term "atonal"  can be  applied to  some

20-century music, its use should be frowned upon because it seems to imply

a lack of organization.  Since contemporary music has transcended tonality

and depends on clear  organization as much or  more than earlier music,  a

more positive word, "contextual",  is preferred.  The particular  context,

as established by the consistent use of the basic elements in each  piece,

seems to have replaced the role of the tonal center.  Thus Stravinsky  can

use triads and diatonic scales "atonally"  (i.e., in a manner outside  the

realm of functional tonal harmony) and be found to follow basic procedures

remarkably similar to those  followed by Schoenberg in  his use of  single

series of non-diatonic intervals.



Only now, when the procedures of functional harmony have clearly  outlived

their usefulness as the primary basis for musical organization for serious

composers, do we seem to be  able to form consistent views concerning  the

purely musical significance of tonal  harmonic progressions.*  As we might

expect, beginnings were  made in this  kind of thinking  just at the  time

when the demise of functional harmony became assured.  In 1906  Schoenberg

composed his Kammersymphonie, Op.  9, which carried  tonality to what  was

near its  farthest  extreme,  and  in  the  same  year  Heinrich  Schenker

published  "Harmony"  (or  "New  Musical Theories  and  Phantasies  by  an

Artist"), the first of his group of highly influential works that  brought

to the fore  the realization that  music was  much more than  a series  of

isolated progressions and modulations.


In retrospect, we can now see (or hear) that the era of tonality was, in a

sense, an era monotonality.  We see that the concept of modulation is best

considered in relative terms and that virtually all  music was  intuitively

written with  a view  to  large-scale tonal  unity, the  exceptions  being

nearly all in  the realm of  operatic or dramatic  music.  Very useful  in

this regard is Schenker's term "tonicization"; i.e., to create on a  tone,

other than the original tonic, a temporary tonic function which plays only

a secondary role with regard to the basic tonic.  Thus modulation might be

said to to be tonicization on the largest scale.  However, Roger  Sessions

has pointed out* that a reasonable basis for differentiating between these

two terms lies in the examination of the structure of a piece of music and

the comparison of the larger harmonic movements with the harmonic details.

Modulation is movement  to a  new musical area;  tonicization is  movement

within a single musical area.


			------------


While form and the larger aspects of harmony will also be dealt with,  the

main body of this handbook will  treat problems that arise within  unified

areas of  pieces.  The  relationships  within a  single tonal  area,  even

though quite complex,  can usually  be grasped --  up to  the point  where

tonality is destroyed.  However,  when the large-scale harmonic  movements

of a long work  are highly complicated, it  becomes nearly impossible  for

even the best musicians  to follow all  the functional relationships.   It

seems doubtful that composers have  ever expected their audience to  grasp

some of the largest relationships in  anything more than the most  general

terms.  These  relationships are  present,  but their  significance  seems

subtly different  in kind  from thoses  found within  the various  unified

sections of a long work.  (An extreme example:  Parsifal begins in Ab  and

ends, hours later, in the same key.)


We have been conditioned  to expect rather specific  things in a piece  of

music  once  we  are  presented   with  any  small  group  of   recognized

relationships.  When an expected pattern is broken, we have learned to  be

especially wary for  the ultimate,  even if  long delayed,  return to  the

pattern.  Or, if  a piece begins  with elements that  are juxtaposed in  a

manner new to us, we seek  a retrospective justification for the  opening.

All comprehension of music  is based on the  listener's ability to  relate

what has gone before  with what is  momentarily at hand  and with what  he

expects (or  knows) is  coming.  One  reason we  can understand  on  first

hearing a tonal  work that is  new to us  is because at  almost any  given

point we  need  concern  ourselves  with  a  relatively  small  number  of

alternatives as to what will happen  next.  Since tonal music is based  on

conventions most of  us have assimilated  in childhood, it  might be  said

that at this time in our culture  no adult really ever hears such a  piece

for the first time.


However, it is only when a musical phrase is complete that we can hope  to

grasp the true implications of the various parts of the phrase.  Likewise,

it is only when a  piece or movement is ended  that we are presented  with

all the facts and are  then able to receive the  full impact of the  work.

For these reasons, harmonic functions can  never be studied in a  vertical

sense.  The chords  themselves are vertical  occurrences but the  harmonic

functions exist only in the  horizontal presentation of series of  chords.

When we are attempting to ascertain the function of a particular chord, we

must look (or listen)  both forward and  backward.  Composers always  have

particular goals in mind  and only after these  goals are achieved can  we

detect the specific justifications for  the harmonic means used.  That  it

is valuable, either as  listener or performer, to  be completely aware  of

these processes  seems  obvious.  For  a  composer, even  though  he  uses

nothing of  functional  tonality  in  his work,  high awareness  of  tonal

processes is even more valuable, in  that it may help him develop  insight

into the most  basic factors  of the art  -- factors  which transcend  the

special conventions of tonality.  Perhaps analysis can never teach  anyone

anything about music  that he  does not  already grasp  in some  intuitive

manner, but  it can  help  develop a  vocabulary  for the  expression  and

consideration of these intuitions.


The approach  to analysis  to be  presented on  the following  pages  will

consider harmonic  factors almost  exclusively.  Of  course, it  is  never

possible to fully appreciate the role  of harmony when it is isolated  and

studied by itself.  In  fact, harmony can  hardly be said  to exist, in  a

musical sense, apart from the  melodic and rhythmic factors which  project

it.  While these factors certainly cannot  be ignored, no attempt will  be

made here to offer any consistent method of analyzing them.  Because music

is made up of a multiplicity of events that move in time, it is impossible

to speak  of all  of  the various  elements  simultaneously.  Due  to  the

limitations of verbal expression, each aspect of music must be dealt  with

separately, the final  synthesis being  extraverbal and  unique with  each

individual.  Nor will acoustical  justifications of harmonic functions  be

treated in any detail.  This latter subject has been discussed in  several

volumes -- with notable lack of success.






Harmonic functions will be considered as occurring on various
"levels", and maintaining a clear distinction between these levels
will be seen as a highly problematic aspect of analysis.  The use
of the traditional names for the harmonies on the various scale
degrees, other than tonic, subdominant and dominant, will generally
be avoided.  The Roman numerals are preferred as a direct and
immediate indication of the relative positions of harmonies.  The
words 'note', 'tone' and 'pitch' will be used interchangeably.  'Key'
and 'tonality' will serve as synonyms; however, the word 'tonic' will
have many meanings.  We speak of a basic tonic (or main key), a
temporary tonic (or supplementary key), a tonic note (the first
note of a key's scale), etc.  Individual notes will be referred to
by capital letters (e.g., F, A, C); tonalities will appear as
underlined letters, capitals for major and lower case letters
for minor (e.g., Bb, D, f#, g).  The word function is used mainly in the
special sense herein developed; i.e., the function of a chord is
usually dependent upon the interval relation of its root to the
tonic note.  Also, a functional chord is one which plays a truly
harmonic role and has a noticeable influence on the harmonic
movement.  Other uses of this word will be defined as they appear.

Generally speaking, every note of a piece should be related
in some way to the harmonic functions.  It is essential that each
note be examined with regard to its potentially chordal or auxiliary role.
Related to this is the problem of "contrapuntal chords", 
passing chords without harmonic function.  There are
situations where chords (usually in first inversion) have no
functional role but rather appear as a continuous parallel motion
from one functional chord to finally another.  (See the opening
of the finale of Beethoven's Sonata in C, Op. 2, #3.)  In a certain
sense, some chords (particularly 6-4 chords) that occur in
passages where the outer voices move in a simple stepwise manner
may be considered as passing chords.  However, in most cases the
choice of notes for the details of the inner parts is dictated
primarily by considerations of harmony rather than counterpoint.
The concept of contrapuntal chords must often be taken into account,
but almost always as an extension of the principles
guiding the use of auxiliary notes.

		-------------------

In developing any "formula" for harmonic analysis, it must always
be remembered that while music exists as a specific series of
events, the listener rarely concentrates to the point of hearing
every note.  More important, the relationships between the notes
are rarely heard in exactly the same way twice.  This is
especially true in so-called "wandering" or "roving" passages.  The
creation of consistent means of accounting for the possible
variations in hearing would call for an exhaustive study of the role
of the levels of harmonic function  in relation to the complex
levels of rhythmic and melodic occurrences.  Clearly an understanding
of the implications of harmonic functions is prerequisite
to the formulation of an approach to the complete piece of music
that gives an undistorted view of the piece and yet remains flexible
enough to admit the possible variants in individual perception.
The graphing of these functional implications will not always
present a simple picture.  It will generally be simple or complex in
relation to the music it is representing.  To strive overly for
simplicity in analysis is to forget that even the simplest four-bar
phrase in Mozart is made up of acoustical and psychological
relationships that, if all were recounted, would stagger the mind.