CHAPTER III
 
	SIMPLE SECONDARY FUNCTIONS
 
 
Functional and Non-Functional Chromaticism
 
	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.
 
Example 27
 
 
 
	Occasionally the fifth of a chord will 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.*
 
Example 28.  Mozart, Sonata in F, K.533
 
 
 
	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.
 
             --------------------
 
	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 single 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.
 
Example 29
 
 
 
	In the next example the feeling of the dominant of F
is clear until the last second.
 
Example 30.  Mozart, Sonata in a, K.300d(310)
 
 
 
	The first F#, as the lower neighbor to G is non-functionallly
altered; but when F# appears as part of a descending scale, then Fn loses
its tonic potential and the enharmonic spelling of the C7 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 modulation 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
tonicization 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.
 
 
Example 31.  Haydn, Sonata in E, (Edition Peters, #40)
 
 
 
	Here the A# in the bass is chromatic passing tone between
the 4th and 5th detrees of E.  The conflict with the An above it
intensifies the non-functional role of the alteration.  Situations
such as this occur frequently in Haydn, and especailly in C. P. E.
Bach.
 
Example 32.  Mozart, Sonata in Eb, K.189g(282)
 
 
 
 
	In the last two measures above, the bass line certainly
tonicizes F (note the melodic and harmonic tritone, Bb-E).  However,
the conflict with the auxiliary Eb of the upper part minimizes the
functional role of the bass.  Then, too, the direct movement of En
to F might be taken as an appoggiatura from a weak to a strong
beat.  The earlier En, 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.
 
Example 33
 
 
 
Tonicization and Pivot Chords
 
	Tonicized functions will be indicated in the following manner:
 
Example 34.  Bach, Chorale 106
 
 
 
 
 
Figure 33a
 
 
 
 
	The highest level in Figure 33a will not be dealt with for the
present, since it will show only modulation; 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.
 
 
Pivot Chords
 
	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 34, the chord on the first
beat of bar 2 functions both as I of I and IV of V.  This may be
represented:
 
Figure 34b
 
 
 
	The horizontal bracket and the "equals" sign (=) indicate
that both sets of numerals represent to the same chord.  It is possible
that a whle 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).
 
	Often a tonicization will be started by an altered passing tone
(as in the Mozart example, page zzz).  In such cases, either the
preceding harmony or the one under the passing tone may form the
pivot chord.
 
Example 35.  Bach, Chorale 50 (second phrase)
 
 
 
 
 
Figure 35
 
 
 
 
	The first analysis is preferred, since it offers more common
progressions in both of the middle ground tonics.
 
	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 Ib7* may be indicated as Is, so as to show
that the chord is substituting for a true tonic effect.
 
Example 36.  Bach, Chorale 6
 
 
 
 
Figure 36a
 
 
 
 
	Ib7 is usually a pivot to a tonic on IV, hence Is=V7 of IV.
Since VIIb7 is often a substitute for V7, then it follows that a
diminished chord can, under some circumstances, serve as Is even though
the tonic note itself is not present.   The next example shows how a simple
V-I-Iv progression might be transformed so that and diminished chord
takes on the role of a substitute tonic.
 
Example 37
 
***************************⊂ new example ***********************
 
 
 
 
	Also, in the next example, the Db of the bass might have been replaced
by C without altering the basic functions of the harmonies.
 
Example 38
 
 
 
 
Figure 38
 
 
 
	Tonicization may occur without the presence of a pivot chord.
A direct chromatic relationship, such as the A to A# of the following
example, usually rules out any pivotal function.
 
Example 39.  Bach, Chorale 85
 
 
 
 
 
 
Figure 39
						The vertical wavy
						line ( ) will indicate
						the absence of a
						pivot chord.
 
 
 
	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.
 
	In the following example, the ideas of tonicization and mere
non-functional alteration of primary function tend to merge.
 
Example 40
 
 
 
 
	The Bb and F# 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:
 
Figure 40a
 
 
 
 
	The second point of view gives:
 
Figure 40b
 
 
 
 
	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:
 
Figure 40c
 
 
 
 
 
	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.
 
             ---------------------------
 
 
Exercises for Chapter III
 
	Analyze the following works in the manner demonstrated
	by Figures zzz-zzz.
 
	From the 371 Chorales of Bach:
 
	1.  Chorale 18
	2.  Chorale 29
	3.  Chorale 131
	4.  Chorale 181
 
	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.
	7.  Bach, Two-Part Invention #14, in Bb, first 7 bars.
		and last 9 bars.
	8.  Chopin, Prelude in G, Op.28 #3, complete work.