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CHAPTER I
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.CENTER			
INTRODUCTION
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.INDENT 6
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	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
20th-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 %2particular context%1,
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.$$ This is not
to imply that music based on functional tonal harmony, written in the tonal
era, has lost, or ever will lose its vitality.$ 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 %2Kammersymphonie%1, Op.9, which carried  tonality to what  was
nearly its  farthest  extreme,  and  in  the  same  year  Heinrich  Schenker
published  %2Harmony (or New  Musical Theories  and  Phantasies  by  an
Artist)%1, 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 of 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$$ Roger Sessions, Harmonic Practice, Harcourt Brace, New York, 
1951.$ 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 %2to%1 a  new musical area;  tonicization is movement
%2within%1 a single musical area.

.CENTER		        
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	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 %2are%1 present,  but their  significance  seems
subtly different  in kind  from those  found %2within%1 the various  unified
sections of a long work.  (An extreme example:  %2Parsifal%1 begins in A%4F%1 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 %2retrospective%1 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 %2functions%1 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 %2fully%1 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 %2note%1, %2tone%1 and %2pitch%1 will be used interchangeably.  %2Key%1
and %2tonality%1 will serve as synonyms; however, the word %2tonic%1 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., ↓_B%4F%1_↓, 
↓_D_↓, ↓_f%4S%1_↓, ↓_g_↓).  The word %2function%1 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 %2Sonata in C,%1 Op.2, #3.)  In a certain
sense, some chords (particularly!! 64; 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.
.SKIP 1
.CENTER		
___________________
.SKIP 1
.FILL
	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
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