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.SKIP 2
.CENTER		
CHAPTER III
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.CENTER			
SIMPLE SECONDARY FUNCTIONS
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.INDENT 6
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.BEGIN VERBATIM

Functional and Non-Functional Chromaticism
.END
 
 
	Chromaticism in tonal music generally falls into two
categories which may be labeled functional and non-functional.  Under
the first of these headings come all those alterations which
contribute to even brief movement to a new tonal center.  Non-functional
chromaticism occurs mainly as the conventional flattings of the minor mode,
or as the sharping of decorative lower neighboring notes
or appoggiaturas which usually create or imply at least momentary
dissonance.  Sometimes it may be difficult to recognize non-functional
sharping when it occurs in a scale line that parallels some
conventional tonal scale.  But almost always the context of the scale
will clearly show the role of the chromatic note.
.BEGIN VERBATIM
 
Example 30
.END
.SKIP 10
 
	Occasionally the fifth of a chord will be raised, producing
an augmented triad.  This chromaticism is usually non-functional unless
the following music makes the augmented triad work as a substitute dominant
to some new tonic.  Most often the sharped note of an augmented triad
appears as a kind of "frozen" chromatic passing or neighboring 
note.$$See last bar of Example zzz and also page zzz.  Related to this
is the problem of the augmented sixth chord (see page zzz).$
.BEGIN VERBATIM
 
Example 31.  Mozart, Sonata in F, K.533
.END
.SKIP 7
 
	The non-functional alterations do not influence either the tonality
or the harmonic functions within the tonality.  But in the sense that
entire chords can sometimes have primarily contrapuntal (or decorative)
significance, as discussed earlier, the two categories of chromaticism
overlap to a certain extent.
 
.CENTER		        
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.FILL
 
	Functional chromaticism may occur on either chord or non-chord
tones and necessarily defines a new tonal area.  Examples of functional
chromaticism appearing as non-chord tones follow.
 
	A %2single%1 chord may sometimes be caused to sound like a new
tonic (or other function within a new tonic) by means of the scalar
use of functional chromaticism.  There need not be any "progression" in
the new tonic whatsoever.
 
.BEGIN VERBATIM
 
Example 32
.END
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	In the next example the feeling of the dominant of F
is clear until the last second.
 
.BEGIN VERBATIM
 
Example 33.  Mozart, Sonata in a, K.300d(310)
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	The first F%4S%1, as the lower neighbor to G is non-functionally
altered; but when F%4S%1 appears as part of a descending scale, then F%4N%1 loses
its tonic potential and the enharmonic spelling of the C%47%1 chord becomes
justified even before the B chord is heard.  By altering this scale note,
Mozart causes V of ↓_F_↓ to take on new meaning as an augmented sixth
chord in ↓_e_↓.  The dominant function of the final B is clear.

 
	No matter how brief the occurrence of functional chromaticism,
the implication is that a new tonic is being approached.  When this
occurs on a much larger scale, establishing one of the important
sections of a piece, we say that %2modulation%1 has taken place; but
when this kind of chromaticism leads only to a temporary tonic,
serving to strengthen it in relation to the main tonic, we say that
%2tonicization%1 has taken place.  Tonicization covers a very wide
range of situations.  It is by this process that great harmonic variety
within general tonal unity is possible.  It must be emphasized, however,
that no distinctions concerning tonicization (since the problem of harmony
versus counterpoint is often involved) can ever be taken as strict rules.
In the following examples the frequent conflict between functional and
non-functional chromaticism is presented.  In these cases the end result is to
strengthen the dominant and yet maintain its supporting role in
relation to the tonic.  The same process may also appear with regard
to the chords on other scale degrees.
 
 
.BEGIN VERBATIM
 
Example 34.  Haydn, Sonata in E, (Edition Peters, #40)
.END
.SKIP 7
 
	Here the A%4S%1 in the bass is a chromatic passing tone between
the 4th and 5th degrees of ↓_E_↓.  The conflict with the A%4N%1 above it
intensifies the non-functional role of the alteration.  Situations
such as this occur frequently in Haydn, and especially in C. P. E.
Bach.
 
.BEGIN VERBATIM
 
.END
.ONCE NO FILL INDENT 0 
Example 35.  Mozart, Sonata in E%4F%1, K.189g(282)
.SKIP 7
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	In the last two measures above, the bass line certainly
tonicizes F (note the melodic and harmonic tritone, B%4F%1-E).  However,
the conflict with the auxiliary E%4F%1 of the upper part minimizes the
functional role of the bass.  Then, too, the direct movement of E%4N%1
to F might be taken as an appoggiatura from a weak to a strong
beat.  The earlier E%4N%1, even though appearing in a chromatic passing
movement, also has an appreciable tonicizing function because of the
implied diminished 7th chord (Vs of ↓_F_↓) at that point.  In this kind
of example the specific analytical conclusions will depend on the degree of
the individual's concern with detail  and with the rhythmic and melodic
factors which are beyond the scope of this book.

 
	The simplest form of tonicization occurs when a single note
of a chord or line is altered so as to play the part of either the
leading tone or 4th degree of a new key.  It is possible, however, to
tonicize a tone without any chromatic alteration whatever; but usually
this is not very definitive unless considerable repetition of a
motif takes place and the implication of chromatic change is felt.
 
.BEGIN VERBATIM
 
Example 36
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.CENTER		        
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.BEGIN VERBATIM

 
Tonicization and Pivot Chords
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	Tonicized functions will be indicated in the following manner:
 
.BEGIN VERBATIM
 
Example 37.  Bach, Chorale 106
.END
.SKIP 8
 
 
 
.BEGIN VERBATIM
 
Figure 37a
.END
.SKIP 5
 
 
	The highest level in Figure 37a will not be dealt with for the
present, since it will show only modulations; i.e., the largest
relationships of basic tonics.  The enclosed, middle level shows the
relationships of the temporary tonics, and the lowest level the
specific function of each chord.
 
 
.BEGIN VERBATIM

 
Pivot Chords
.END
	In most cases of tonicization one or more pivot chords will be
present.  A pivot chord will function simultaneously in both the
old and new tonics.  In Example 37, the chord on the first
beat of bar 2 functions both as I of I and IV of V.  This may be
represented:
 
.BEGIN VERBATIM
 
Figure 37b
.END
.SKIP 6
 
	The horizontal bracket and the "equals" sign (=) indicate
that both sets of numerals represent the same chord.  It is possible
that a whole group of chords may function, retrospectively, in two
different keys.  However, generally it is most practical to be
concerned only with the last chord before the introduction of
functional chromaticism (see page zzz also).

.NEXT PAGE
	Often a tonicization will be started by an altered passing tone
(as in the Mozart example, page 31).  In such cases, either the
preceding harmony or the one under the passing tone may form the
pivot chord.
 
.BEGIN VERBATIM
 
Example 38.  Bach, Chorale 50 (second phrase)
.END
.SKIP 10
 
.BEGIN VERBATIM
 
Figure 38
.END
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	The first analysis is preferred, since it offers more common
progressions in both of the middle ground tonics.
.INDENT 6
.FILL
.ADJUST
 
	Frequently a flatted 7th will appear with a tonic that has
just been preceded by its dominant.  Even though the new scale note
is present in the tonic itself, that chord will be the pivot chord
because it is at once a new dominant and the clear goal of the
preceding dominant.  The I%4F7%1$$For brevity, most functions
will be listed in root position rather than in terms of any
specific inversions.$  may be indicated as Is, so as to show
that the chord is substituting for a %2true%1 tonic effect.
 
.NEXT PAGE      
 
.BEGIN VERBATIM
Example 39.  Bach, Chorale 6
.END
.SKIP 9
 
.BEGIN VERBATIM
 
Figure 39
.END
.SKIP 7

 
	I%4F7%1 is usually a pivot to a tonic on IV, hence Is=V%47%1 of IV.
Since VII%4F7%1 is often a substitute for V%47%1, then it follows that a
diminished chord can, under some circumstances, serve as Is even though
the tonic note itself is not present.   In the next example, the D%4F%1 
of the bass might have been replaced by C without altering the basic
functions of the harmonies.
 
.BEGIN VERBATIM
 
Example 40
.END
.next page
.begin verbatim
Figure 40
.END
.skip 7
 
 
	Tonicization may occur without the presence of a pivot chord.
A direct chromatic relationship, such as the A to A%4S%1 of the following
example, usually rules out any pivotal function.
 
.BEGIN VERBATIM
 
Example 41.  Bach, Chorale 85
.end
.skip 9
 
 
 
.begin verbatim
Figure 41
 

                                                                          The vertical wavy
                                                                          line (  ) will indicate
                                                                          the absence of a
                                                                          pivot chord.
 

.end
 
	In the above example and figure is a particularly clear case
of a chord (in parentheses) which appears as the result of stepwise
motion and has only small functional significance.  The skip in
the soprano from the E up to the B causes the entire measure to
be heard as a single function.
 
.INDENT 6
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	In the following example, the ideas of tonicization and mere
non-functional alteration of primary function tend to merge.
.begin verbatim
 
Example 42
.end 
.skip 7
 
 
	The B%4F%1 and F%4S%1 may be called either chromatic passing tones
or tones which change the functions of the chords in question.  In the
first instance our analysis would give:
.begin verbatim

Figure 42a
.end
.skip 6
 
 
	The second point of view gives:
.begin verbatim
 
Figure 42b
.end
.skip 6
 
 
	Neither of these results is completely satisfactory.  A mixture
of the two might be given, because the 4th of a scale seems  a weaker
tonic-determining factor than the leading tone and the last
chord of a phrase usually takes on more importance than the middle chords.
Thus:
 
.begin verbatim
 
Figure 42c
.end
.skip 6
 
	One should not be overly concerned with such details unless
the music indicates that the composer was intent on directing the
listener's attention to them.  In most cases the actual duration of
an alteration and its position in the phrase might be good bases
for decisions.  For example, if the proper scale degree were involved,
an altered note of a chord twice as long as its preceding unaltered
form would tend to change the chord's function.
 
.CENTER		        
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.FILL
.begin verbatim

 
Exercises for Chapter III
 
	Analyze the following works in the manner demonstrated
	by Figures 38-41.
 
	From the 371 Chorales of Bach:
	1.  Chorale 18
	2.  Chorale 29
	3.  Chorale 131
	4.  Chorale 188
 
	5.  Bach, Two-Part Invention #1, in C, first 9 bars
						and first note of bar 10.
	6.  Bach, Two-Part Invention #10, in G, complete work.
.end
.ONCE NO FILL INDENT 0 
	7.  Bach, Two-Part Invention #14, in B%4F%1, first 5 bars
.begin verbatim
						and last 8 bars.
	8.  Chopin, Prelude in G, Op.28 #3, complete work.
.end