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.SKIP 2
.CENTER		
CHAPTER V
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EXTENDED TONICIZATION
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.INDENT 6
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.BEGIN VERBATIM

Added Levels of Tonic Function
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	Almost by definition, music of the tonal era depends
on the listener's strong memory of a basic tonic.  The basic tonic is a
cohesive force which sets limits and acts as a reference point for all
types of harmonic movement.  Even %2modulation%1 within a movement never
really destroys this reference point; it merely sets up a foremost
subsidiary point.  When %2tonicization%1 becomes greatly extended, the same
effect is produced on a somewhat smaller scale.  The difference between
extended tonicization and modulation lies in the role the particular
passage is playing in relation to the whole.  There is much music wherein
these two concepts tend to overlap, but in the main, composers of
the music here under consideration have been so intent upon formal
clarity that the dependent character of tonicization, even when
extended, is maintained.

 
	This important facet of tonal music may be represented by
%2added levels of tonicization%1 in the middle area of the analytical
diagram.  These added levels occur when, %2within%1 a %2temporary%1 tonic
area, again a new tonic is approached.  A simple example of this
follows.  The basic key of ↓_C_↓ is understood to be well established
both before and after the example.
 
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Example 56
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.begin verbatim

Figure 56a
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.skip 6
 
 
	The ↓_D_↓ area at (xx) appears in direct relationship only with
the ↓_G_↓ (or tonicized V) area.  Even though every numeral that
appears in the middle area of an analysis is %2understood%1 to be a tonic
(i.e., working as a "I"), a new I is placed under the first
presentation of V as a tonic in order that the interval of the subsequent
movement to ↓_D_↓ (i.e., the dominant relation to ↓_G_↓), is readily apparent.
Similarly, another I appears when the progression returns
to ↓_G_↓ as the tonic.  In the previous example it will be noted that the
tonicized ↓_D_↓ was specifically major.  This new I contains
F%4S%1 -- not a functional probability in terms of the original ↓_C_↓, but
completely compatible with the ↓_G_↓ scale.

 
	This may be made even more clear if we set up what will be
called %2tonic guide tones%1.  These represent, in musical notation,
the elements that appear in the middle area of the analysis.
 
.begin verbatim

Figure 56b

 
   Tonic Guide Tones


 
 
 
 
 
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	The tonics which are most closely related (see table on page 46)
are connected by horizontal bars.  The small notes may be added to show
the mode of each tonic.  When dealing with very complex progressions,
it may often prove quite helpful to sketch out the tonic guide
tones previous to making any final decisions concerning the particular
relationships of the temporary tonics.
 

	If some of the notes of Example 56 are altered so that we
arrive at ↓_d_↓ minor, instead of major, its role as the tonicized V of
↓_G_↓ is greatly weakened.  Voice leading is important in establishing
the ↓_d_↓ area.  The B and C%4S%1, 6th and 7th scale degrees, appear in
ascending lines, the B%4F%1 and C%4N%1 in descending lines.
 
.begin verbatim

Example 57
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.skip 8
 
 
	Now, since the I chord of ↓_d_↓ does not disturb the material
of the original scale, it is heard in direct relation to ↓_C_↓.
 
.begin verbatim

Figure 57


   Tonic Guide Tones
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.next page
 
	Very often there will be no clearcut procedure that may be
followed when analyzing situations similar to the next example.  At
(*), the change of mode on the G root makes varying interpretations
of the function of the ↓_d_↓ tonic possible.
 
.begin verbatim

Example 58
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.skip 6
.begin verbatim

Figure 58a

   Tonic Guide Tones

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Figure 58b

   Tonic Guide Tones

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	* When a tonic changes mode for more than the duration of
	an occasional chord, the change may appear superimposed on
	the continuous line running from the original occurrence
	of the tonic.
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Figure 58c

   Tonic Guide Tones


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.ONCE NO FILL INDENT 0 
	* Here the ↓_g_↓ tonic is shown as subsidiary to ↓_d_↓.  This
.ONCE NO FILL INDENT 0 
	interpretation might be preferred if the duration of 
.ONCE NO FILL INDENT 0 
	the ↓_g_↓ tonic area were quite short in relation to the 
.ONCE NO FILL INDENT 0 
        following ↓_d_↓ area (see Example zzz).
.FILL indent 6
 

	Notice that the above examples were, for the purposes of
illustration, presented without varied rhythm.  As always, in more
complex situations, the relations between harmony, melody, and
rhythm will combine to offer a basis for a more specific analytical
interpretation.  However, it must be emphasized that the main
profit to the serious musician is found in the process of wrestling
with such problematical decisions.  The final decision need not be
considered the %2only%1 right one, but rather as the most clarifying of
the actual effect of the music on the individual.

 
	An extreme example of added levels of tonicization (and it is
often heard) is the progression through the "circle of fifths".
.begin verbatim

Example 59
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.skip 7
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.begin verbatim
Figure 59






                                                                        * When many levels
                                                                        of tonics appear, the
                                                                        letter names of the
                                                                        various keys should
                                                                        be added to avoid
                                                                        confusion.

 
 
 
.end
.begin verbatim
 
Example 60
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.skip 7   
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Figure 60
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	These diagrams may appear somewhat unwieldy, but they have
the advantage of giving clear pictures, in intervallic terms, of the
relationships involved.
 

	Occasionally a very rapid movement through part of the circle
of fifths, or the successive use of 7th chords, will cause certain
elements of a progression to stand in relief.
.BEGIN VERBATIM

Example 61
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.BEGIN VERBATIM

Figure 61
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.SKIP 11

	In the above diagram, the abrupt skip down to a third
level of tonics (which resolves to a I on the second level)
accurately parallels the effect of the example.  Notice the problems 
created by the use of a string of diminished chords over a basically
chromatic line.  Such situations may be analyzed as
substitutes for the "circle of fifths" progression, but generally it
is best to consider all but the first and last chords of the string
as parallel-moving passing chords (see Bach, %2Partita #1 in B%4F%1, Gigue;
Mozart, %2Fantasy in C%1, K.394).  However, in 19th-century music,
details of voice leading (especially the melodic skips) often tend
to give functional importance to the inner chords of strings of
diminished chords (see Chopin, %2Etude in E%1, Op.10,#3, measure 38,
etc.; Liszt, %2Transcendental Etude #6, "Mazeppa"%1, beginning).


	Most often the return to the main tonic will not be made by 
the same route as was the departure.  When this happens, a pivotal
tonic may appear in the middle area of the analysis (see below at
the sign *).
.begin verbatim

Example 62
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.begin verbatim

Figure 62
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.begin verbatim
Example 63. Mozart, Sonata in D, K.576, 2nd movement.
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	The exact location of the pivotal tonic will usually depend on
the association of the particular means of presenting a given harmonic
function with earlier presentation of the same function.  In other words,
the return to the chord of departure, even with the same function on the
lowest level, can be inconclusive until we also return to the same
melodic and rhythmic presentation of that function.  In Example 63 the f%4S%1
chord at (*) has a tonic function, but f%4S%1 as a tonic of the middle area
is still subsidiary to another tonic (↓_D_↓) until the return of the 
original material.
.begin verbatim

Figure 63
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.SKIP 15
	The middle area of the first analysis is preferred at (+),
because the tonic chord of f%4S%1 is completely consistent with the scale
of ↓_D_↓, and there are no other factors that might deter one from
hearing the passage as a stepwise progression of tonics (I, ii, iii).
If, for any reason, it seems undesirable to show a pivot in cases where
two or more levels of tonics are involved, the wavy vertical line ( )
might be used to show the lack of continuity along any given level
(see Figure 68).  However, it rarely happens that a logical connection
between tonics cannot be made.

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Control Tonics
.end
	An extension of the previous line of thought will serve well
when considering the following analysis of music typical of the work
of Bach.
.BEGIN VERBATIM

Example 64.  Bach, Invention No.4 in d.
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.BEGIN VERBATIM






Figure 64a.  Bach, Invention No.4 in d (bars 7-45).


  Tonic Guide Tones
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	The location of the pivot (at +) is arbitrary, because the
following twelve bars are based on the descending form of the ↓_d_↓
scale -- which is identical with the ↓_F_↓ scale.  If it seems necessary
to specify the dual function of such progressions, the following method
is suggested.  The %2retrospective%1 functions in ↓_F_↓ are circled to
keep them distinct from the earlier perceived ↓_d_↓ functions.
.begin verbatim

Figure 64b
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	The form of this work is defined mainly by a group of
cadential formulas.  The strength of the points of definition is 
greatly enhanced by the fact that each cadence offers us a new tonal
center.  However, due to the exclusive use of a single set of motives
and the brevity of the piece, modulation (as it is known in the main
body of tonal music) does not occur.  The larger harmonic movement
of this piece is certainly heard as a series of tonics, whose relations
to the main, beginning tonic are at least as strong as their
relations to one another.  Thus, even though ↓_a_↓ appears first as iii of
↓_F_↓, it is finally established as an equal of ↓_F_↓ (in relation to ↓_d_↓)
by the occurrence of the well-prepared cadence at bar 38.  Please note, however, 
that ↓_a_↓'s role as something more than a transient tonic of the ↓_F_↓
scale is not too definite until the point of cadence.  To emphasize these
varying levels of relationships among the tonics, we must start at the
beginning of our diagram with %2two%1 levels in the middle ground, so 
that when a temporary tonic is somehow given greater status and 
becomes what may be called a %2control tonic%1, this change will
appear in a consistent form.  In the above analysis note that on the 
highest level of tonicization the progress from i to III to v coincides
exactly with the full cadences.  However, ↓_F_↓ and ↓_a_↓ are first tonicized
well before the cadences (this shows on the second level of
tonicization).  The numerals of the control tonics will be
underlined.


	The use of strong cadences is not the only method which can
give a temporary tonic the status of a control tonic.  Another favorite
method is the clear presentation, in some new tonic, of
material (either old or new) of relatively great importance; e.g., in
the Bach Invention, the return to the original ↓_d_↓ as the control tonic
is defined by the 
return of the opening statement (bar 44), rather than by a full cadence.  The
presentation should be long enough so that the new tonic may be heard
as independent beyond the extent of simple tonicization.  The 
functions under a control tonic established in this manner need not
include a strong cadence.  The music might then progress smoothly to
yet another control tonic.  If the important factors of the music seem
to warrant its independence, a new control tonic might even appear as
a lower level of tonicization, below an old control tonic (see next
chapter, Schubert example).


	Much music can best be analyzed in terms of series of control 
tonics, the term "modulation" being reserved for a shift of the
basic tonic.  No set rule can be given as to when it is advisable to
use an extra, higher level of indications in the middle area of the
analytical diagram.  Any variant of the basic diagram is acceptable
just so long as it contributes to the understanding of the music under
consideration.

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	It is very evident that as the complexity of harmony increases
there is usually a similar increase in the ambiguity of individual
harmonic functions as they relate to the whole.  This is, of course,
the reason for the particular effect of late "Romantic" and "Impressionistic"
harmony, and also the source of the ultimate breakdown of functional
tonality as a meaningful system.  When every harmonic function becomes
ambiguous, then something other than a tonal center (as defined by
harmonic functions) must take over as the prime cohesive force (see last
chapter).  It is significant that in music of the Classical era the 
more complex harmonic progressions are most often relegated to
developmental passages -- passages that depend greatly on motivic
continuity.  In such instances, it is common to hear a series of tonics
which seem to relate only to their immediate surroundings.  (It is
possible for even the original tonic of a developmental section to
reappear for a considerable time without its having any direct
functional relationship with its earlier presentation.)  The
analysis of an extended developmental passage will show continually
added levels in the middle ground, the return to a single level being
conditioned by the reappearance of familiar, stable material in its
proper key.  This traditionally happens at the point of recapitulation
in the sonata form.$$Among the numerous exceptions to the above statements are the
first movement recapitulations of Mozart's %2Sonatas in D%1, K.284c(311)
and %2in C%1, K.545.  In the first of these, the recapitulation begins with
the material of the second key area, but now heard in ↓_D_↓ instead of
↓_A_↓.  The recapitulation of the ↓_C_↓ sonata offers the original
opening material, but in the subdominant, ↓_F_↓.$
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.begin verbatim


Exercises for Chapter V


Analyze the following works:

From the 371 Chorales of Bach:

	1.  Chorale 21
	2.  Chorale 92
	3.  Chorale 200
	4.  Chorale 231
	5.  Chorale 279

From the Two-Part Inventions of Bach:

	6.  Invention 11, in g
	7.  Invention 12, in A
	8.  Invention 13, in a

From the Well-Tempered Clavier, First Book, Bach:

        9.  Fugue I, in C
       10.  Fugue X, in e

From the Preludes, Op.28, of Chopin:

       11.  Prelude  5, in D
       13.  Prelude 22, in g
.end