00100			CHAPTER III
00200	 
00300		SIMPLE SECONDARY FUNCTIONS
00400	 
00500	 
00600	Functional and Non-Functional Chromaticism
00700	 
00800		Chromaticism in tonal music generally falls into two
00900	categories which may be labeled functional and non-functional.  Under
01000	the first of these headings come all those alterations which
01100	contribute to even brief movement to a new tonal center.  Non-functional
01200	chromaticism occurs mainly as the conventional flattings of the minor mode,
01300	or as the sharping of decorative lower neighboring notes
01400	or appoggiaturas which usually create or imply at least momentary
01500	dissonance.  Sometimes it may be difficult to recognize non-functional
01600	sharping when it occurs in a scale line that parallels some
01700	conventional tonal scale.  But almost always the context of the scale
01800	will clearly show the role of the chromatic note.
01900	 
02000	Example 30
02100	 
02200	 
02300	 
02400		Occasionally the fifth of a chord will raised, producing
02500	an augmented triad.  This chromaticism is usually non-functional unless
02600	the following music makes the augmented triad work as a substitute dominant
02700	to some new tonic.  Most often the sharped note of an augmented triad
02800	appears as a kind of "frozen" chromatic passing or neighboring note.*
02900	 
03000	Example 31.  Mozart, Sonata in F, K.533
03100	 
03200	 
03300	 
03400		The non-functional alterations do not influence either the tonality
03500	or the harmonic functions within the tonality.  But in the sense that
03600	entire chords can sometimes have primarily contrapuntal (or decorative)
03700	significance, as discussed earlier, the two categories of chromaticism
03800	overlap to a certain extent.
03900	 
04000	             --------------------
04100	 
04200		Functional chromaticism may occur on either chord or non-chord
04300	tones and necessarily defines a new tonal area.  Examples of functional
04400	chromaticism appearing as non-chord tones follow.
04500	 
04600		A single chord may sometimes be caused to sound like a new
04700	tonic (or other function within a new tonic) by means of the scalar
04800	use of functional chromaticism.  There need not be any "progression" in
04900	the new tonic whatsoever.
05000	 
05100	Example 32
05200	 
05300	 
05400	 
05500		In the next example the feeling of the dominant of F
05600	is clear until the last second.
05700	 
05800	Example 33.  Mozart, Sonata in a, K.300d(310)
05900	 
06000	 
06100	 
06200		The first F#, as the lower neighbor to G is non-functionallly
06300	altered; but when F# appears as part of a descending scale, then Fn loses
06400	its tonic potential and the enharmonic spelling of the C7 chord becomes
06500	justified even before the B chord is heard.  By altering this scale note,
06600	Mozart causes V of F to take on new meaning as an augmented sixth
06700	chord in e.  The dominant function of the final B is clear.
06800	 
06900		No matter how brief the occurrence of functional chromaticism,
07000	the implication is that a new tonic is being approached.  When this
07100	occurs on a much larger scale, establishing one of the important
07200	sections of a piece, we say that modulation has taken place; but
07300	when this kind of chromaticism leads only to a temporary tonic,
07400	serving to strengthen it in relation to the main tonic, we say that
07500	tonicization has taken place.  Tonicization covers a very wide
07600	range of situations.  It is by this process that great harmonic variety
07700	within general tonal unity is possible.  It must be emphasized, however,
07800	that no distinctions concerning tonicization (since the problem of harmony
07900	versus counterpoint is often involved) can ever be taken as strict rules.
08000	In the following examples the frequent conflict between functional and
08100	non-functional chromaticism is presented.  In these cases the end result is to
08200	strengthen the dominant and yet maintain its supporting role in
08300	relation to the tonic.  The same process may also appear with regard
08400	to the chords on other scale degrees.
08500	 
08600	 
08700	Example 34.  Haydn, Sonata in E, (Edition Peters, #40)
08800	 
08900	 
09000	 
09100		Here the A# in the bass is chromatic passing tone between
09200	the 4th and 5th detrees of E.  The conflict with the An above it
09300	intensifies the non-functional role of the alteration.  Situations
09400	such as this occur frequently in Haydn, and especailly in C. P. E.
09500	Bach.
09600	 
09700	Example 35.  Mozart, Sonata in Eb, K.189g(282)
09800	 
09900	 
10000	 
10100	 
10200		In the last two measures above, the bass line certainly
10300	tonicizes F (note the melodic and harmonic tritone, Bb-E).  However,
10400	the conflict with the auxiliary Eb of the upper part minimizes the
10500	functional role of the bass.  Then, too, the direct movement of En
10600	to F might be taken as an appoggiatura from a weak to a strong
10700	beat.  The earlier En, even though appearing in a chromatic passing
10800	movement, also has an appreciable tonicizing function because of the
10900	implied diminished 7th chord (Vs of F) at that point.  In this kind
11000	of example the specific analytical conclusions will depend on the degree of
11100	the individual's concern with detail  and with the rhythmic and melodic
11200	factors which are beyond the scope of this book.
11300	 
11400		The simplest form of tonicization occurs when a single note
11500	of a chord or line is altered so as to play the part of either the
11600	leading tone or 4th degree of a new key.  It is possible, however, to
11700	tonicize a tone without any chromatic alteration whatever; but usually
11800	this is not very definitive unless considerable repetition of a
11900	motif takes place and the implication of chromatic change is felt.
12000	 
12100	Example 36
12200	 
12300	 
12400	 
12500	Tonicization and Pivot Chords
12600	 
12700		Tonicized functions will be indicated in the following manner:
12800	 
12900	Example 37.  Bach, Chorale 106
13000	 
13100	 
13200	 
13300	 
13400	 
13500	Figure 37a
13600	 
13700	 
13800	 
13900	 
14000		The highest level in Figure 37a will not be dealt with for the
14100	present, since it will show only modulation; i.e., the largest
14200	relationships of basic tonics.  The enclosed, middle level shows the
14300	relationships of the temporary tonics, and the lowest level the
14400	specific function of each chord.
14500	 
14600	 
14700	Pivot Chords
14800	 
14900		In most cases of tonicization one or more pivot chords will be
15000	present.  A pivot chord will function simultaneously in both the
15100	old and new tonics.  In Example 37, the chord on the first
15200	beat of bar 2 functions both as I of I and IV of V.  This may be
15300	represented:
15400	 
15500	Figure 37b
15600	 
15700	 
15800	 
15900		The horizontal bracket and the "equals" sign (=) indicate
16000	that both sets of numerals represent to the same chord.  It is possible
16100	that a whle group of chords may function, retrospectively, in two
16200	different keys.  However, generally it is most practical to be
16300	concerned only with the last chord before the introduction of
16400	functional chromaticism (see page zzz also).
16500	 
16600		Often a tonicization will be started by an altered passing tone
16700	(as in the Mozart example, page zzz).  In such cases, either the
16800	preceding harmony or the one under the passing tone may form the
16900	pivot chord.
17000	 
17100	Example 38.  Bach, Chorale 50 (second phrase)
17200	 
17300	 
17400	 
17500	 
17600	 
17700	Figure 38
17800	 
17900	 
18000	 
18100	 
18200		The first analysis is preferred, since it offers more common
18300	progressions in both of the middle ground tonics.
18400	 
18500		Frequently a flatted 7th will appear with a tonic that has
18600	just been preceded by its dominant.  Even though the new scale note
18700	is present in the tonic itself, that chord will be the pivot chord
18800	because it is at once a new dominant and the clear goal of the
18900	preceding dominant.  The Ib7* may be indicated as Is, so as to show
19000	that the chord is substituting for a true tonic effect.
19100	 
19200	Example 39.  Bach, Chorale 6
19300	 
19400	 
19500	 
19600	 
19700	Figure 39
19800	 
19900	 
20000	 
20100	 
20200		Ib7 is usually a pivot to a tonic on IV, hence Is=V7 of IV.
20300	Since VIIb7 is often a substitute for V7, then it follows that a
20400	diminished chord can, under some circumstances, serve as Is even though
20500	the tonic note itself is not present.   The next example shows how a simple
20600	V-I-IV progression might be transformed so that and diminished chord
20700	takes on the role of a substitute tonic.
20800	 
20900	Example 40
21000	 
21200	 
21300	 
21400	 
21500	 
21600		Also, in the next example, the Db of the bass might have been replaced
21700	by C without altering the basic functions of the harmonies.
21800	 
21900	Example 41
22000	 
22100	 
22200	 
22300	 
22400	Figure 41
22500	 
22600	 
22700	 
22800		Tonicization may occur without the presence of a pivot chord.
22900	A direct chromatic relationship, such as the A to A# of the following
23000	example, usually rules out any pivotal function.
23100	 
23200	Example 42.  Bach, Chorale 85
23300	 
23400	 
23500	 
23600	 
23700	 
23800	 
23900	Figure 42
24000							The vertical wavy
24100							line ( ) will indicate
24200							the absence of a
24300							pivot chord.
24400	 
24500	 
24600	 
24700		In the above example and figure is a particularly clear case
24800	of a chord (in parentheses) which appears as the result of stepwise
24900	motion and has only small functional significance.  The skip in
25000	the soprano from the E up to the B causes the entire measure to
25100	be heard as a single function.
25200	 
25300		In the following example, the ideas of tonicization and mere
25400	non-functional alteration of primary function tend to merge.
25500	 
25600	Example 43
25700	 
25800	 
25900	 
26000	 
26100		The Bb and F# may be called either chromatic passing tones
26200	or tones which change the functions of the chords in question.  In the
26300	first instance our analysis would give:
26400	 
26500	Figure 43a
26600	 
26700	 
26800	 
26900	 
27000		The second point of view gives:
27100	 
27200	Figure 43b
27300	 
27400	 
27500	 
27600	 
27700		Neither of these results is completely satisfactory.  A mixture
27800	of the two might be given, because the 4th of a scale seems  a weaker
27900	tonic-determining factor than the leading tone and the last
28000	chord of a phrase usually takes on more importance than the middle chords.
28100	Thus:
28200	 
28300	Figure 43c
28400	 
28500	 
28600	 
28700	 
28800	 
28900		One should not be overly concerned with such details unless
29000	the music indicates that the composer was intent on directing the
29100	listener's attention to them.  In most cases the actual duration of
29200	an alteration and its position in the phrase might be good bases
29300	for decisions.  For example, if the proper scale degree were involved,
29400	an altered note of a chord twice as long as its preceding unaltered
29500	form would tend to change the chord's function.
29600	 
29700	             ---------------------------
29800	 
29900	 
30000	Exercises for Chapter III
30100	 
30200		Analyze the following works in the manner demonstrated
30300		by Figures zzz-zzz.
30400	 
30500		From the 371 Chorales of Bach:
30600	 
30700		1.  Chorale 18
30800		2.  Chorale 29
30900		3.  Chorale 131
31000		4.  Chorale 188
31100	 
31200		5.  Bach, Two-Part Invention #1, in C, first 9 bars
31300			and first note of bar 10.
31400		6.  Bach, Two-Part Invention #10, in G, complete work.
31500		7.  Bach, Two-Part Invention #14, in Bb, first 5 bars.
31600			and last 8 bars.
31700		8.  Chopin, Prelude in G, Op.28 #3, complete work.