00100			$C$H$A$P$T$E$R $I$I$I
00200	
00300		$S$I$M$P$L$E $S$E$C$O$N$D$A$R$Y $F$U$N$C$T$I$O$N$S
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 27
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 28.  $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 29
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 30.  $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 31.  $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 32.  $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 33
12200	
12300	
12400	
12500	$TONICIZATION AND $PIVOT $CHORDS
12600	
12700		$TONICIZED FUNCTIONS WILL BE INDICATED IN THE FOLLOWING MANNER:
12800	
12900	$EXAMPLE 34.  $BACH, $CHORALE 106
13000	
13100	
13200	
13300	
13400	
13500	$FIGURE 33A
13600	
13700	
13800	
13900	
14000		$THE HIGHEST LEVEL IN $FIGURE 33A 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	
14550	
14600	$PIVOT $CHORDS
14700	
14800		$IN MOST CASES OF TONICIZATION ONE OR MORE PIVOT CHORDS WILL BE
14900	PRESENT.  $A PIVOT CHORD WILL FUNCTION SIMULTANEOUSLY IN BOTH THE
15000	OLD AND NEW TONICS.  $IN $EXAMPLE 34, THE CHORD ON THE FIRST
15100	BEAT OF BAR 2 FUNCTIONS BOTH AS $I OF $I AND $I$V OF $V.  $THIS MAY BE
15200	REPRESENTED:
15300	
15400	$FIGURE 34B
15500	
15600	
15700	
15800		$THE HORIZONTAL BRACKET AND THE "EQUALS" SIGN (=) INDICATE
15900	THAT BOTH SETS OF NUMERALS REPRESENT TO THE SAME CHORD.  $IT IS POSSIBLE
16000	THAT A WHLE GROUP OF CHORDS MAY FUNCTION, RETROSPECTIVELY, IN TWO
16100	DIFFERENT KEYS.  $HOWEVER, GENERALLY IT IS MOST PRACTICAL TO BE 
16200	CONCERNED ONLY WITH THE LAST CHORD BEFORE THE INTRODUCTION OF
16300	FUNCTIONAL CHROMATICISM (SEE PAGE ZZZ ALSO).
16400	
16500		$OFTEN A TONICIZATION WILL BE STARTED BY AN ALTERED PASSING TONE
16600	(AS IN THE $MOZART EXAMPLE, PAGE ZZZ).  $IN SUCH CASES, EITHER THE 
16700	PRECEDING HARMONY OR THE ONE UNDER THE PASSING TONE MAY FORM THE
16800	PIVOT CHORD.
16900	
17000	$EXAMPLE 35.  $BACH, $CHORALE 50 (SECOND PHRASE)
17100	
17200	
17300	
17400	
17500	
17600	$FIGURE 35
17700	
17800	
17900	
18000	
18100		$THE FIRST ANALYSIS IS PREFERRED, SINCE IT OFFERS MORE COMMON
18200	PROGRESSIONS IN BOTH OF THE MIDDLE GROUND TONICS.
18300	
18400		$FREQUENTLY A FLATTED 7TH WILL APPEAR WITH A TONIC THAT HAS
18500	JUST BEEN PRECEDED BY ITS DOMINANT.  $EVEN THOUGH THE NEW SCALE NOTE
18600	IS PRESENT IN THE TONIC ITSELF, THAT CHORD WILL BE THE PIVOT CHORD
18700	BECAUSE IT IS AT ONCE A NEW DOMINANT AND THE CLEAR GOAL OF THE 
18800	PRECEDING DOMINANT.  $THE $IB7* MAY BE INDICATED AS $IS, SO AS TO SHOW
18900	THAT THE CHORD IS SUBSTITUTING FOR A TRUE TONIC EFFECT.
19000	
19100	$EXAMPLE 36.  $BACH, $CHORALE 6
19200	
19300	
19400	
19500	
19600	$FIGURE 36A
19700	
19800	
19900	
20000	
20100		$IB7 IS USUALLY A PIVOT TO A TONIC ON $I$V, HENCE $IS=$V7 OF $I$V.
20200	$SINCE $V$I$IB7 IS OFTEN A SUBSTITUTE FOR $V7, THEN IT FOLLOWS THAT A
20300	DIMINISHED CHORD CAN, UNDER SOME CIRCUMSTANCES, SERVE AS $IS EVEN THOUGH
20400	THE TONIC NOTE ITSELF IS NOT PRESENT.   $THE NEXT EXAMPLE SHOWS HOW A SIMPLE
20500	$V-$I-$IV PROGRESSION MIGHT BE TRANSFORMED SO THAT AND DIMINISHED CHORD
20600	TAKES ON THE ROLE OF A SUBSTITUTE TONIC.
20700	
20800	$EXAMPLE 37
20900	
21000	***************************⊂ NEW EXAMPLE ***********************
21100	
21200	
21300	
21400	
21500		$ALSO, IN THE NEXT EXAMPLE, THE $DB OF THE BASS MIGHT HAVE BEEN REPLACED
21600	BY $C WITHOUT ALTERING THE BASIC FUNCTIONS OF THE HARMONIES.
21700	
21800	$EXAMPLE 38
21900	
22000	
22100	
22200	
22300	$FIGURE 38
22400	
22500	
22600	
22700		$TONICIZATION MAY OCCUR WITHOUT THE PRESENCE OF A PIVOT CHORD.
22800	$A DIRECT CHROMATIC RELATIONSHIP, SUCH AS THE $A TO $A# OF THE FOLLOWING
22900	EXAMPLE, USUALLY RULES OUT ANY PIVOTAL FUNCTION.
23000	
23100	$EXAMPLE 39.  $BACH, $CHORALE 85
23200	
23300	
23400	
23500	
23600	
23700	
23800	$FIGURE 39
23900							$THE VERTICAL WAVY
24000							LINE ( ) WILL INDICATE
24100							THE ABSENCE OF A
24200							PIVOT CHORD.
24300	
24400	
24500	
24600		$IN THE ABOVE EXAMPLE AND FIGURE IS A PARTICULARLY CLEAR CASE 
24700	OF A CHORD (IN PARENTHESES) WHICH APPEARS AS THE RESULT OF STEPWISE
24800	MOTION AND HAS ONLY SMALL FUNCTIONAL SIGNIFICANCE.  $THE SKIP IN
24900	THE SOPRANO FROM THE $E UP TO THE $B CAUSES THE ENTIRE MEASURE TO
25000	BE HEARD AS A SINGLE FUNCTION.
25100	
25200		$IN THE FOLLOWING EXAMPLE, THE IDEAS OF TONICIZATION AND MERE
25300	NON-FUNCTIONAL ALTERATION OF PRIMARY FUNCTION TEND TO MERGE.
25400	
25500	$EXAMPLE 40
25600	
25700	
25800	
25900	
26000		$THE $BB AND $F# MAY BE CALLED EITHER CHROMATIC PASSING TONES
26100	OR TONES WHICH CHANGE THE FUNCTIONS OF THE CHORDS IN QUESTION.  $IN THE
26200	FIRST INSTANCE OUR ANALYSIS WOULD GIVE:
26300	
26400	$FIGURE 40A
26500	
26600	
26700	
26800	
26900		$THE SECOND POINT OF VIEW GIVES:
27000	
27100	$FIGURE 40B
27200	
27300	
27400	
27500	
27600		$NEITHER OF THESE RESULTS IS COMPLETELY SATISFACTORY.  $A MIXTURE
27700	OF THE TWO MIGHT BE GIVEN, BECAUSE THE 4TH OF A SCALE SEEMS  A WEAKER
27800	TONIC-DETERMINING FACTOR THAN THE LEADING TONE AND THE LAST
27900	CHORD OF A PHRASE USUALLY TAKES ON MORE IMPORTANCE THAN THE MIDDLE CHORDS.
28000	$THUS:
28100	
28200	$FIGURE 40C
28300	
28400	
28500	
28600	
28700	
28800		$ONE SHOULD NOT BE OVERLY CONCERNED WITH SUCH DETAILS UNLESS
28900	THE MUSIC INDICATES THAT THE COMPOSER WAS INTENT ON DIRECTING THE
29000	LISTENER'S ATTENTION TO THEM.  $IN MOST CASES THE ACTUAL DURATION OF
29100	AN ALTERATION AND ITS POSITION IN THE PHRASE MIGHT BE GOOD BASES
29200	FOR DECISIONS.  $FOR EXAMPLE, IF THE PROPER SCALE DEGREE WERE INVOLVED,
29300	AN ALTERED NOTE OF A CHORD TWICE AS LONG AS ITS PRECEDING UNALTERED
29400	FORM WOULD TEND TO CHANGE THE CHORD'S FUNCTION.
29500	
29600	             ---------------------------
29700	
29800	
29900	$EXERCISES FOR $CHAPTER $I$I$I
30000	
30100		$ANALYZE THE FOLLOWING WORKS IN THE MANNER DEMONSTRATED
30200		BY $FIGURES ZZZ-ZZZ.
30300	
30400		$FROM THE 371 $CHORALES OF $BACH:
30500	
30600		1.  $CHORALE 18
30700		2.  $CHORALE 29
30800		3.  $CHORALE 131
30900		4.  $CHORALE 181
31000	
31100		5.  $BACH, $TWO-$PART $INVENTION #1, IN $C, FIRST 9 BARS
31200			AND FIRST NOTE OF BAR 10.
31300		6.  $BACH, $TWO-$PART $INVENTION #10, IN $G, COMPLETE WORK.
31400		7.  $BACH, $TWO-$PART $INVENTION #14, IN $BB, FIRST 7 BARS.
31500			AND LAST 9 BARS.
31600		8.  $CHOPIN, $PRELUDE IN $G, $OP.28 #3, COMPLETE WORK.