00100	
00200			CHAPTER I
00300	
00400				INTRODUCTION
00500	
00600	
00700	Except possibly for the works of a few composers overcome by a theoretical
00800	
00900	bent, music has always been written from the point of view that the  proof
01000	
01100	is in the hearing -- the ear  being the final arbiter.  Of course, we  all
01200	
01300	know that the ear is simply the  receptor of sounds and that what we  mean
01400	
01500	when we say a musical passage "sounds wrong" is that it includes  elements
01600	
01700	which our minds are unable to  accept in terms of the musical  conventions
01800	
01900	which we know or can  conceive of.  It is  obvious that any one,  isolated
02000	
02100	note sounds  neither  right  nor  wrong.   For  that  matter,  those  well
02200	
02300	acquainted with  20th-century music  would hesitate  to apply  "right"  or
02400	
02500	"wrong"  to  even  a  fairly  large  number  of  notes,  produced   either
02600	
02700	melodically or harmonically.  "Rightness"  or comprehensibility is  really
02800	
02900	found only in complete musical passages  or phrases.  The phrase, or  even
03000	
03100	the whole piece, will  be insufficient, however, if  the listener has  not
03200	
03300	established at least some  backlog of experience  in hearing music  of the 
03400	
03500	same general style.
03600	
03700	
03800	Because of the tremendous backlog of experience in hearing music based  on
03900	
04000	triadic tonal harmony, almost  everyone who has grown  up during the  last
04100	
04200	fifty to  one  hundred years  in  contact  with western  culture  is  well
04300	
04400	acquainted with the  conventions established  by music  composed from  the
04500	
04600	time of the late  17th century to the  early 20th century.   Comparatively
04700	
04800	abruptly, 17th-century composers established, from the implications of the
04900	
05000	earlier modal  procedures, the  bases for  the tonal  system.  This  tonal
05100	
05200	system proved  to have  possibilities  vast enough  to intrigue  the  best
05300	
05400	musicians for  almost three  hundred  years.  Then,  in turn,  the  latest
05500	
05600	implications of tonality gave rise to the 20th-century tendency away  from
05700	
05800	the necessities of tonal harmony.
05900	
06000	
06100	Although, strictly  speaking, the  term "atonal"  can be  applied to  some
06200	
06300	20-century music, its use should be frowned upon because it seems to imply
06400	
06500	a lack of organization.  Since contemporary music has transcended tonality
06600	
06700	and depends on clear  organization as much or  more than earlier music,  a
06800	
06900	more positive word, "contextual",  is preferred.  The particular  context,
07000	
07100	as established by the consistent use of the basic elements in each  piece,
07200	
07300	seems to have replaced the role of the tonal center.  Thus Stravinsky  can
07400	
07500	use triads and diatonic scales "atonally"  (i.e., in a manner outside  the
07600	
07700	realm of functional tonal harmony) and be found to follow basic procedures
07800	
07900	remarkably similar to those  followed by Schoenberg in  his use of  single
08000	
08100	series of non-diatonic intervals.
08200	
08300	
08400	
08500	Only now, when the procedures of functional harmony have clearly  outlived
08600	
08700	their usefulness as the primary basis for musical organization for serious
08800	
08900	composers, do we seem to be  able to form consistent views concerning  the
09000	
09100	purely musical significance of tonal  harmonic progressions.*  As we might
09200	
09300	expect, beginnings were  made in this  kind of thinking  just at the  time
09400	
09500	when the demise of functional harmony became assured.  In 1906  Schoenberg
09600	
09700	composed his Kammersymphonie, Op.  9, which carried  tonality to what  was
09800	
09900	near its  farthest  extreme,  and  in  the  same  year  Heinrich  Schenker
10000	
10100	published  "Harmony"  (or  "New  Musical Theories  and  Phantasies  by  an
10200	
10300	Artist"), the first of his group of highly influential works that  brought
10400	
10500	to the fore  the realization that  music was  much more than  a series  of
10600	
10700	isolated progressions and modulations.
10800	
10900	
11000	In retrospect, we can now see (or hear) that the era of tonality was, in a
11100	
11200	sense, an era monotonality.  We see that the concept of modulation is best
11300	
11400	considered in relative terms and that virtually all  music was  intuitively
11500	
11600	written with  a view  to  large-scale tonal  unity, the  exceptions  being
11700	
11800	nearly all in  the realm of  operatic or dramatic  music.  Very useful  in
11900	
12000	this regard is Schenker's term "tonicization"; i.e., to create on a  tone,
12100	
12200	other than the original tonic, a temporary tonic function which plays only
12300	
12400	a secondary role with regard to the basic tonic.  Thus modulation might be
12500	
12600	said to to be tonicization on the largest scale.  However, Roger  Sessions
12700	
12800	has pointed out* that a reasonable basis for differentiating between these
12900	
13000	two terms lies in the examination of the structure of a piece of music and
13100	
13200	the comparison of the larger harmonic movements with the harmonic details.
13300	
13400	Modulation is movement  to a  new musical area;  tonicization is  movement
13500	
13600	within a single musical area.
13700	
13800	
13900				------------
14000	
14100	
14200	While form and the larger aspects of harmony will also be dealt with,  the
14300	
14400	main body of this handbook will  treat problems that arise within  unified
14500	
14600	areas of  pieces.  The  relationships  within a  single tonal  area,  even
14700	
14800	though quite complex,  can usually  be grasped --  up to  the point  where
14900	
15000	tonality is destroyed.  However,  when the large-scale harmonic  movements
15100	
15200	of a long work  are highly complicated, it  becomes nearly impossible  for
15300	
15400	even the best musicians  to follow all  the functional relationships.   It
15500	
15600	seems doubtful that composers have  ever expected their audience to  grasp
15700	
15800	some of the largest relationships in  anything more than the most  general
15900	
16000	terms.  These  relationships are  present,  but their  significance  seems
16100	
16200	subtly different  in kind  from thoses  found within  the various  unified
16300	
16400	sections of a long work.  (An extreme example:  Parsifal begins in Ab  and
16500	
16600	ends, hours later, in the same key.)
16700	
16800	
16900	We have been conditioned  to expect rather specific  things in a piece  of
17000	
17100	music  once  we  are  presented   with  any  small  group  of   recognized
17200	
17300	relationships.  When an expected pattern is broken, we have learned to  be
17400	
17500	especially wary for  the ultimate,  even if  long delayed,  return to  the
17600	
17700	pattern.  Or, if  a piece begins  with elements that  are juxtaposed in  a
17800	
17900	manner new to us, we seek  a retrospective justification for the  opening.
18000	
18100	All comprehension of music  is based on the  listener's ability to  relate
18200	
18300	what has gone before  with what is  momentarily at hand  and with what  he
18400	
18500	expects (or  knows) is  coming.  One  reason we  can understand  on  first
18600	
18700	hearing a tonal  work that is  new to us  is because at  almost any  given
18800	
18900	point we  need  concern  ourselves  with  a  relatively  small  number  of
19000	
19100	alternatives as to what will happen  next.  Since tonal music is based  on
19200	
19300	conventions most of  us have assimilated  in childhood, it  might be  said
19400	
19500	that at this time in our culture  no adult really ever hears such a  piece
19600	
19700	for the first time.
19800	
19900	
20000	However, it is only when a musical phrase is complete that we can hope  to
20100	
20200	grasp the true implications of the various parts of the phrase.  Likewise,
20300	
20400	it is only when a  piece or movement is ended  that we are presented  with
20500	
20600	all the facts and are  then able to receive the  full impact of the  work.
20700	
20800	For these reasons, harmonic functions can  never be studied in a  vertical
20900	
21000	sense.  The chords  themselves are vertical  occurrences but the  harmonic
21100	
21200	functions exist only in the  horizontal presentation of series of  chords.
21300	
21400	When we are attempting to ascertain the function of a particular chord, we
21500	
21600	must look (or listen)  both forward and  backward.  Composers always  have
21700	
21800	particular goals in mind  and only after these  goals are achieved can  we
21900	
22000	detect the specific justifications for  the harmonic means used.  That  it
22100	
22200	is valuable, either as  listener or performer, to  be completely aware  of
22300	
22400	these processes  seems  obvious.  For  a  composer, even  though  he  uses
22500	
22600	nothing of  functional  tonality  in  his work,  high awareness  of  tonal
22700	
22800	processes is even more valuable, in  that it may help him develop  insight
22900	
23000	into the most  basic factors  of the art  -- factors  which transcend  the
23100	
23200	special conventions of tonality.  Perhaps analysis can never teach  anyone
23300	
23400	anything about music  that he  does not  already grasp  in some  intuitive
23500	
23600	manner, but  it can  help  develop a  vocabulary  for the  expression  and
23700	
23800	consideration of these intuitions.
23900	
24000	
24100	The approach  to analysis  to be  presented on  the following  pages  will
24200	
24300	consider harmonic  factors almost  exclusively.  Of  course, it  is  never
24400	
24500	possible to fully appreciate the role  of harmony when it is isolated  and
24600	
24700	studied by itself.  In  fact, harmony can  hardly be said  to exist, in  a
24800	
24900	musical sense, apart from the  melodic and rhythmic factors which  project
25000	
25100	it.  While these factors certainly cannot  be ignored, no attempt will  be
25200	
25300	made here to offer any consistent method of analyzing them.  Because music
25400	
25500	is made up of a multiplicity of events that move in time, it is impossible
25600	
25700	to speak  of all  of  the various  elements  simultaneously.  Due  to  the
25800	
25900	limitations of verbal expression, each aspect of music must be dealt  with
26000	
26100	separately, the final  synthesis being  extraverbal and  unique with  each
26200	
26300	individual.  Nor will acoustical  justifications of harmonic functions  be
26400	
26500	treated in any detail.  This latter subject has been discussed in  several
26600	
26700	volumes -- with notable lack of success.
26800	
26900	
27000	
27100	
27200	
27300	
27400	Harmonic functions will be considered as occurring on various
27500	"levels", and maintaining a clear distinction between these levels
27600	will be seen as a highly problematic aspect of analysis.  The use
27700	of the traditional names for the harmonies on the various scale
27800	degrees, other than tonic, subdominant and dominant, will generally
27900	be avoided.  The Roman numerals are preferred as a direct and
28000	immediate indication of the relative positions of harmonies.  The
28100	words 'note', 'tone' and 'pitch' will be used interchangeably.  'Key'
28200	and 'tonality' will serve as synonyms; however, the word 'tonic' will
28300	have many meanings.  We speak of a basic tonic (or main key), a
28400	temporary tonic (or supplementary key), a tonic note (the first
28500	note of a key's scale), etc.  Individual notes will be referred to
28600	by capital letters (e.g., F, A, C); tonalities will appear as
28700	underlined letters, capitals for major and lower case letters
28800	for minor (e.g., Bb, D, f#, g).  The word function is used mainly in the
28900	special sense herein developed; i.e., the function of a chord is
29000	usually dependent upon the interval relation of its root to the
29100	tonic note.  Also, a functional chord is one which plays a truly
29200	harmonic role and has a noticeable influence on the harmonic
29300	movement.  Other uses of this word will be defined as they appear.
29400	
29500	Generally speaking, every note of a piece should be related
29600	in some way to the harmonic functions.  It is essential that each
29700	note be examined with regard to its potentially chordal or auxiliary role.
29800	Related to this is the problem of "contrapuntal chords", 
29900	passing chords without harmonic function.  There are
30000	situations where chords (usually in first inversion) have no
30100	functional role but rather appear as a continuous parallel motion
30200	from one functional chord to finally another.  (See the opening
30300	of the finale of Beethoven's Sonata in C, Op. 2, #3.)  In a certain
30400	sense, some chords (particularly 6-4 chords) that occur in
30500	passages where the outer voices move in a simple stepwise manner
30600	may be considered as passing chords.  However, in most cases the
30700	choice of notes for the details of the inner parts is dictated
30800	primarily by considerations of harmony rather than counterpoint.
30900	The concept of contrapuntal chords must often be taken into account,
31000	but almost always as an extension of the principles
31100	guiding the use of auxiliary notes.
31200	
31300			-------------------
31400	
31500	In developing any "formula" for harmonic analysis, it must always
31600	be remembered that while music exists as a specific series of
31700	events, the listener rarely concentrates to the point of hearing
31800	every note.  More important, the relationships between the notes
31900	are rarely heard in exactly the same way twice.  This is
32000	especially true in so-called "wandering" or "roving" passages.  The
32100	creation of consistent means of accounting for the possible
32200	variations in hearing would call for an exhaustive study of the role
32300	of the levels of harmonic function  in relation to the complex
32400	levels of rhythmic and melodic occurrences.  Clearly an understanding
32500	of the implications of harmonic functions is prerequisite
32600	to the formulation of an approach to the complete piece of music
32700	that gives an undistorted view of the piece and yet remains flexible
32800	enough to admit the possible variants in individual perception.
32900	The graphing of these functional implications will not always
33000	present a simple picture.  It will generally be simple or complex in
33100	relation to the music it is representing.  To strive overly for
33200	simplicity in analysis is to forget that even the simplest four-bar
33300	phrase in Mozart is made up of acoustical and psychological
33400	relationships that, if all were recounted, would stagger the mind.