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.SKIP 2
.CENTER		
CHAPTER VIII
.SKIP 2
.CENTER			
SUMMARY OF PROCEDURES
.SKIP 1
.INDENT 6
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.SELECT 1
 
 
	The analytical procedures exhibited in the earlier chapters
should prove sufficient for dealing with the harmonic implications of
any truly tonal music.  There is no reason why the details of
diagramming should not be changed to fit any particular situation.
What is of the utmost importance is that the diagram symbolically
represents the listener's view of the significant harmonic events
of a piece of music.  The diagram has two essential facets which
cannot exist without one another; horizontally it shows, in intervallic
terms, the %2movement%1 of each harmonic function to the next,
and vertically it shows the
%2tonal basis%1 for the relationship of these functions.  The underlying factors
of tonal harmony are so stereotyped that musical intuition (based, of
course, on perceptive experience) and knowledge of the technology of
harmony are all that are necessary as prerequisites for the harmonic
analysis of tonal music.

	To catalogue the functions of all possible two-chord progressions
would constitute a needless waste of space.  A few general rules will
give the musician ample means for adequately grasping the various
functional relationships in tonal music.

	↓_First_↓, the distinction between chord and non-chord tones must
be made. The bases for this distinction can usually be found in the
music itself.  Care should be taken to avoid the opposite pitfalls of
"discovering" too few or too many chordal changes.  If there is doubt
about the precise definition of a chord, the possible alternatives
should appear in the analysis, even if some verbal explanation is
necessary. (However, footnotes, etc. should kept at a minimum, since
the main point of such a graphic analysis is that it can express the
functions of a harmonic progression much more clearly than can words.)

	↓_Second_↓, after each chord is clearly defined, it must be
ascertained whether it is working as its specific relation to the key
which contains it would indicate, or whether the context causes it to
serve as a substitute for another function in that or another key.
When dealing with interpretation of context, the only reliable aid
for making decisions is a large backlog of listening experience in 
music of the style under consideration.

	↓_Third_↓, every chromatic alteration of the particular scale in 
use at any given time must be understood as functional or non-functional.
If an altered note is non-chordal, does the context allow that this
note be heard as part of a scale with a new tonic (functional
chromaticism), or is it apparent that the alteration does not influence
the scale but merely decorates a single note (non-functional 
chromaticism)?  Do not forget that the flattings (of either chord or
non-chord notes) which produce minor scales are non-functional unless
they are used as the 1st, 4th, or 5th of a new tonic.  When any chord
tone is sharped, does this constitute a "correction" of an alteration
of the minor mode, or does the chromaticism effect the 1st, 4th, or
5th of the tonic?  If the former is the case, does the context cause
the resulting chord to be heard as some function of a new tonic?

	One must always be on the lookout for the conventional
alterations that form the augmented sixth chords.  In these special
cases, the raised 4th of the scale is admissible without the 
introduction of a new tonic.  The augmented sixth often appears
enharmonically as a minor 7th, so frequently a composer's notation
is not to be trusted.  Most difficult to deal with in this realm are
alternating progressions.  If the chromaticism involved in a passage
cannot be resolved into a single key for more than one chord at a
time, then it is likely that some goal is being approached from
more than one harmonic direction.

	↓_Fourth_↓, as new tonics are established, it is necessary to 
decide what relationship the various temporary tonics bear to each
other.  As we get further away from the foreground of tonal experience
(those specific functions appearing on the bottom line of the 
analytical diagram), the more important becomes the larger context
of the music in giving us clues for satisfactory decisions.  In a 
large section of music, if the various %2tonic%1 triads involved 
(middle ground) all include only notes of the section's %2original%1, unaltered
scale, be it major or minor, most often the tonics will be heard in
direct relation with one another.  If, however, the new tonic triads
include notes which are altered (%4F%1 or %4S%1) from the original scale,
then the possibility of the tonics being only secondarily related
becomes much greater. If the root of any new tonic triad represents
an alteration of the 1st, 4th, or 5th of the original scale (excepting
enharmonic change), then the relationship of the tonics is surely 
indirect.  When the situation becomes complex, confusion may be avoided
by setting up Tonic Guide Tones for the passage in question (see pages 46
and 57).

	↓_Fifth_↓, once the relationships of the various temporary tonics
are established, then it must be decided which among them emerge as
%2control tonics%1 or even become %2new basic tonics%1 on a par with the
original tonic (modulation).  For a great many pieces there will be
no need to show control tonics, since they will coincide at all times
with the basic tonics which appear on the highest level.  When they
add to the clarity of an analysis, new control tonics will usually
appear at the beginnings of phrases (because specific material is
presented in a new tonic) or at the endings of phrases (because some
kind of strong cadence defines a harmonic goal).  If used properly, 
the concept of control tonics should give the musician the means to
outline clearly large harmonic movement (goals and points of departure)
within larger basic tonic areas.

	↓_Sixth_↓, the largest possible harmonic movements, modulations,
usually depend strongly on melodic and rhythmic factors for their
definition.  However, the most important harmonic factor involved in
modulation is that the original basic tonic no longer is a direct
influence on the middle ground movements of control tonics or simple
temporary tonics.  If the original tonic no longer appears in any
important way as a temporary tonic and the musical material is not
that associated with the original tonic, then modulation most likely
has occurred.  It often happens that the musical material associated
with the original tonic will be used again after modulation (see
especially the sonata form movements of Haydn).  When this happens,
the harmonic factors usually are so clear as to leave no doubt about
the modulation.

.CENTER		        
_______________
.fill indent 6

	The analytical procedures just summarized should not
necessarily be applied in the order given above, which leads one
from the details of a piece to the whole.  Most musicians can readily
deal with the first three of these general procedures on an intuitive
level.  Actually, it is probably best to use an approach which begins
with the largest relationships in a piece and works by steps to the
details -- and then to retrace these steps, to make sure that the
analysis of the details really does support the interpretation of
the larger movements.  This way, harmonic %2goals%1 on each level are dealt
with first and then the means of achieving these goals are defined.
As the %2means%1 are defined, the goals and their relations to one
another take on added significance.  The writing out of an analysis
is probably best done in a somewhat haphazard manner.  The elements
which seem most certain should go down first, regardless of their
chronological order in the music -- but even these first decisions
must be left open to constant revision.  As the details expand the
diagram, the earlier perceptions will either be enhanced or weakened.
Never be afraid to show alternative interpretations.  It is only by
maintaining an open mind (even when the situation is only mildly
problematical) that the vital force of the music in the mind of the
individual may be sustained.

	In the following chapters, two relatively large pieces will
be analyzed -- the slow movement of Mozart's %2Piano Sonata in F%1, K.533,
and (inevitably) the %2Prelude%1 to %2Tristan und Isolde%1 of Wagner.  It is
hoped that by this means the broad and perhaps unsystematic use of
these analytical procedures will be made clear.