00100				CHAPTER VIII
00200	 
00300	 
00400	 
00500	                  SUMMARY OF PROCEDURES
00600	 
00700	 
00800		The analytical procedures exhibited in the earlier chapters
00900	should prove sufficient for dealing with the harmonic implications of
01000	any truly tonal music.  There is no reason why the details of
01100	diagramming should not be changed to fit any particular situation.
01200	What is of the utmost importance is that the diagram symbolically
01300	represents the listener's view of the significant harmonic events
01400	of a piece of music.  The diagram has two essential facets which
01500	cannot exist without each other; horizontally it shows, in intervallic
01600	terms, "what" moves to "what", and vertically it shows "what" is the
01700	basis for the relationship of these things.  The underlying factors
01800	of tonal harmony are so stereotyped that musical intuition (based, of
01900	course, on perceptive experience) and knowledge of the technology of
02000	harmony are all that are necessary as prerequisites for the harmonic
02100	analysis of tonal music.
02200	
02300		To catalogue the functions of all possible two-chord progressions
02400	would constitute a needless waste of space.  A few rules of thumb will
02500	give the musician ample means for adequately grasping the various
02600	functional relationships in tonal music.
02700	
02800		First, the distinction between chord and non-chord tones must
02900	be made. The bases for this distinction can usually be found in the
03000	music itself.  Care should be taken to avoid the opposite pitfalls of
03100	"discovering" too few or too many chordal changes.  If there is doubt
03200	about the precise definition of a chord, the possible alternatives
03300	should appear in the analysis, even if some verbal explanation is
03400	necessary. (However, footnotes, etc. should kept at a minimum, since
03500	the main point of such a graphic analysis is that it can express the
03600	functions of a harmonic progression much more clearly than can words.)
03700	
03800		Second, after each chord is clearly defined, it must be
03900	ascertained whether it is working as its specific relation to the key
04000	which contains it would indicate, or whether the context causes it to
04100	serve as a substitute for another function in that or another key.
04200	When dealing with interpretation of context, the only reliable aid
04300	for making decisions is a large backlog of listening experience in 
04400	music of the style under consideration.
04500	
04600		Third, every chromatic alteration of the particular scale in 
04700	use at any given time must be understood as functional or non-functional.
04800	If an altered note is non-chordal, does the context allow that this
04900	note be heard as part of a scale with a new tonic (functional
05000	chromaticism), or is it apparent that the alteration does not influence
05100	the scale but merely decorates a single note (non-functional 
05200	chromaticism)?  Do not forget that the flattings (of either chord or
05300	non-chord notes) which produce minor scales are non-functional unless
05400	they are used as the 1st, 4th, or 5th of a new tonic.  When any chord
05500	tone is sharped, does this constitute a "correction" of an alteration
05600	of the minor mode, or does the chromaticism effect the 1st, 4th, or
05700	5th of the tonic?  If the former is the case, does the context cause
05800	the resulting chord to be heard as some function of a new tonic?
05900	
06000		One must always be on the lookout for the conventional
06100	alterations that form the augmented sixth chords.  In these special
06200	cases, the raised 4th of the scale is admissible without the 
06300	introduction of a new tonic.  The augmented sixth often appears
06400	enharmonically as a minor 7th, so frequently a composer's notation
06500	is not to be trusted.  Most difficult to deal with in this realm are
06600	alternating progressions.  If the chromaticism involved in a passage
06700	cannot be resolved into a single key for more than one chord at a
06800	time, then it is likely that some goal is being approached from
06900	more than one harmonic direction.
07000	
07100		Fourth, as new tonics are established, it is necessary to 
07200	decide what relationship the various temporary tonics bear to each
07300	other.  As we get further away from the foreground of tonal experience
07400	(those specific functions appearing on the bottom line of the 
07500	analytical diagram), the more important becomes the larger context
07600	of the music in giving us clues for satisfactory decisions.  In a 
07700	large section of music, if the various tonic triads involved 
07750	(middle ground) all include only notes of the section's original, unaltered
07900	scale, be it major or minor, most often the tonics will be heard in
08000	direct relation with one another.  If, however, the new tonic triads
08100	include notes which are altered (b or #) from the original scale,
08200	then the possibility of the tonics being only secondarily related
08300	becomes much greater. If the root of any new tonic triad represents
08400	an alteration of the 1st, 4th, or 5th of the original scale (excepting
08500	enharmonic change), then the relationship of the tonics is surely 
08600	indirect.  When the situation becomes complex, confusion may be avoided
08700	by setting up Tonic Guide Tones for the passage in question (see pp.zzz
08800	and zzz).
08900	
09000		Fifth, once the relationships of the various temporary tonics
09100	are established, then it must be decided which among them emerge as
09200	control tonics or even become new basic tonics on a par with the
09300	original tonic (modulation).  For a great many pieces there will be
09400	no need to show control tonics, since they will coincide at all times
09500	with the basic tonics which appear on the highest level.  When they
09600	add to the clarity of an analysis, new control tonics will usually
09700	appear at the beginnings of phrases (because specific material is
09800	presented in a new tonic) or at the endings of phrases (because some
09900	kind of strong cadence defines a harmonic goal).  If used properly, 
10000	the concept of control tonics should give the musician the means to
10100	outline clearly large harmonic movement (goals and points of departure)
10200	within larger basic tonic areas.
10300	
10400		Sixth, the largest possible harmonic movements, modulations,
10500	usually depend strongly on melodic and rhythmic factors for their
10600	definition.  However, the most important harmonic factor involved in
10700	modulation is that the original basic tonic no longer is a direct
10800	influence on the middle ground movements of control tonics or simple
10900	temporary tonics.  If the original tonic no longer appears in any
11000	important way as a temporary tonic and the musical material is not
11100	that associated with the original tonic, then modulation most likely
11200	has occurred.  It often happens that the musical material associated
11300	with the original tonic will be used again after modulation (see
11400	especially the sonata form movements of Haydn).  When this happens,
11500	the harmonic factors usually are so clear as to leave no doubt about
11600	the modulation.
11700	
11800	                 ---------------------
11900	
12000		The analytical procedures just summarized should not
12100	necessarily be applied in the order given above, which leads one
12200	from the details of a piece to the whole.  Most musicians can readily
12300	deal with the first three of these general procedures on an intuitive
12400	level.  Actually, it is probably best to use an approach which begins
12500	with the largest relationships in a piece and works by steps to the
12600	details -- and then to retrace these steps, to make sure that the
12700	analysis of the details really does support the interpretation of
12800	the larger movements.  This way, harmonic goals on each level are dealt
12900	with first and then the means of achieving these goals are defined.
13000	As the means are defined, the goals and their relations to one
13100	another take on added significance.  The writing out of an analysis
13200	is probably best done in a somewhat haphazard manner.  The elements
13300	which seem most certain should go down first, regardless of their
13400	chronological order in the music -- but even these first decisions
13500	must be left open to constant revision.  As the details expand the
13600	diagram, the earlier perceptions will either be enhanced or weakened.
13700	Never be afraid to show alternative interpretations.  It is only by
13800	maintaining an open mind (even when the situation is only mildly
13900	problematical) that the vital force of the music in the mind of the
14000	individual may be sustained.
14100	
14200		In the following chapters, two relatively large pieces will
14300	be analyzed -- the slow movement of Mozart's Piano Sonata in F, K.533,
14400	and (inevitably) the Prelude to Tristan und Isolde of Wagner.  It is
14500	hoped that by this means the broad and perhaps unsystematic use of
14600	these analytical procedures will be made clear.