00100		$THE $I$I$I AS A SUBSTITUTE CONTINUATION OF $I IS SOMETIMES FOUND
00200	IN THE $I-$I$I$I-$IV PROGRESSION.
00300	
00400	
00500	$EXAMPLES 18A, 18B
00600	
00700	
00800	
00900	
01000	
01100	
01200	
01300	
01400	
01500	
01600	
01700		$IN $EXAMPLES 18A AND 18B THE FUNCTIONS INVOLVED ARE CLEARLY
01800	SIMILAR, SINCE THE $B SOUNDS AS A PASSING NOTE, EN ROUTE TO $A, IN BOTH
01900	CASES.  $HOWEVER, WITH THE SAME UPPER PARTS AND A NEW BASS LINE
02000	($EXAMPLES 19A AND 19B) THE SUBSTITUTE CHARACTER OF THE $I$I$I TENDS
02100	TO DISAPPEAR.  $NOW, DUE TO THE STRENGTH OF THE 5TH DESCENT IN THE
02200	BASS, THREE FUNCTIONS MIGHT BE HEARD INSTEAD OF TWO.  $THE  TIED-OVER $C
02300	CAN BE HEARD AS A SUSPENSION WITH THE FOLLOWING $B AS ITS RESOLUTION.
02400	
02500	
02600	$EXAMPLES 19A, 19B
02700	
02800	
02900	
03000	
03100	
03200	
03300	
03400	
03500	
03600	
03700	
03800	
03900	
04000		$THE VERY SPECIAL EFFECT OF THE ASCENDING 3RD PROGRESSION
04100	MAY BE SEEN AS OCCASIONAL CHARACTERISTIC OF $BRAHMS' WORK.
04200	
04300	
04400	$EXAMPLE 20.  $BRAHMS, $ROMANCE, $OP.118,#5
04500	
04600	
04700	
04800	
04900	
05000	
05100	
05200	
05300	
05400	
05500	
05600		$ANY TWO-NOTE  CHORD  (OR  EVEN  A  SINGLE  NOTE)  CAN  BE  A
05700	SUBSTITUTE FUNCTION WHOSE NUMERAL DESIGNATION DEPENDS ENTIRELY ON THE
05800	CONTEXT.  $IN TWO-PART TONAL COUNTERPOINT THE CLEARLY  IMPLIED  ROOTS
05900	OF  CHORDS  ARE  VERY  OFTEN OMITTED.  $WHEN DOUBT DOES ARISE IN SUCH
06000	MUSIC,  USUALLY  THE  ANALYSIS  WHICH  SHOWS   THE   SIMPLEST,   MOST
06100	CONVENTIONAL  PROGRESSION,  OR  ONE  WHICH  IS PART OF AN ESTABLISHED
06200	PATTERN OR SEQUENCE, IS THE RIGHT ONE.
06300	
06400	
06500	$EXAMPLE 21
06600	
06700	
06800	
06900	
07000	
07100	
07200	
07300		$QUITE SUBTLE IS THE RELATIONSHIP BETWEEN $I$I, ESPECIALLY
07400	$I$I 6-5, AND $I$V.  $IT IS CLEAR THAT WHEN THE $I$I IN ROOT
07500	POSITION MOVES TO $V ITS FUNCTION WILL NOT BE CONFUSED WITH THAT
07600	OF $I$V.  $HOWEVER, IN CADENTIAL FORMULAS THE SENSE OF $I$I 6-5 OR $I$I 6
07700	IS CERTAINLY HEARD AS SUBDOMINANT -- WITH THE ROOT OF $I$I BEING HEARD
07800	USUALLY AS AN ANTICIPATION OR ADDED 6TH OR PASSING TONE.
07900	
08000	
08100	$EXAMPLE 22
08200	
08300	
08400	
08500	
08600	
08700	
08800	
08900	
09000	
09100	
09200	
09300	
09400		$IN CASES AS ABOVE, WHERE THE BASS (AND OFTEN THE SOPRANO TOO)
09500	MOVES STEPWISE, THE PROBLEM OF HARMONY VERSUS COUNTERPOINT PRESENTS ONE
09600	OF ITS MOST PERPLEXING FACETS.  $IN $EXAMPLE 22 IT IS COMPLETELY
09700	POSSIBLE TO CONCEIVE OF THE ENTIRE $I$I 6-5 AS A PASSING CHORD
09800	BETWEEN THE $I6 AND THE $V.  $IT IS ARGUED BY SOME THAT ALL HARMONIES
09900	THAT OCCUR OVER STEPWISE BASS MOVEMENT (EXCEPTING THOSE THAT COME
10000	AT THE HIGH OR LOW POINT OF SUCH MOVEMENT) HAVE NO FUNCTIONAL SIGNIFICANCE.
10100	$IF THIS VIEW IS ACCEPTED, SOME DISTINCTION (THOUGH NOT A HARD AN FAST
10200	ONE) MUST BE MADE BETWEEN THE "STRUCTURAL" AND "CONTRAPUNTAL"
10300	CHORDS OF A PROGRESSION.  $IN SITUATIONS INCLUDING CHROMATIC ALTERATION
10400	THE PROBLEM IS OFTEN SIMPLIFIED, SINCE IN MOST CASES THE ALTERATIONS
10500	SERVE TO LEAD OUR ATTENTION TO THE MAIN CHORDS.
10600	
10700	
10800	                ----------------------
10900	
11000	
11100		$THE FOLLOWING EXAMPLES SERVE TO ILLUSTRATE THAT THE CONTEXT
11200	IS THE CHIEF CONSIDERATION IN DESIGNATING THE RELATIVE IMPORTANCE OF
11300	CHORDS.
11400	
11500	
11600	$EXAMPLE 23.  $MOZART, $SONATA IN $A, $K.300I (331)
11700	
11800	
11900	
12000		$HEARD ALONE, THE ABOVE IS A SIMPLE $D: $I$V-$V-$I PROGRESSION;
12100	BUT HEARD IN ITS CONTINUING CONTEXT ($EXAMPLE 24) THE $I CHORD 
12200	RETROSPECTIVELY BECOMES A PSEUDO 6-4 CHORD.  $BECAUSE OF THE USE OF THE
12300	$A PEDAL AT THE STARRED (*) POINTS AND THE FACT THAT EACH OF THE TWO BAR
12400	GROUPS PRESENTS THE $A CHORD ON THE STRONG BEATS, THE $F# AND $D OF THE
12500	$D CHORD, EVEN WHEN MOVED TO THE BASS, ARE HEARD AS AUXILIARIES TO $E AND
12600	$C# OF THE $A CHORD.
12700	
12800	$EXAMPLE 24.
12900	
13000	
13100	
13200		$DESPITE THE TWO-PART PRESENTATION, THE ESSENTIAL MOVEMENT OF THE
13300	FOLLOWING PASSAGE FROM $BACH'S $PARTITA #5 IS CLEARLY HEARD AS A
13400	DESCENDING SERIES OF CHORDS; $V$I-$V-$I$V-$I$I$I-$I$I.  $NEEDLESS TO
13500	SAY, THE PROGRESSION FOUND IN THE DETAILS ($V$I-$I$I:$V7-$I :$I$V-$V$I$I :
13600	$I$I$I7-$V$I:$I$I) DOES EXIST.  $BUT THE CONTEXT CAUSES US TO HEAR THE
13700	ALTERNATE CHORDS ($I$I,$I,$V$I$I,$V$I) AS SUBSIDIARY TO THE OTHER
13800	CHORDS.  $THE FACT THAT $V$I-$V-$I$V-$I$I$I-$I$I HARDLY CONSTITUTES AN
13900	EXCITING HARMONIC PROGRESSION DOES NOT ALTER OUR HEARING OF THIS
14000	PASSAGE.  $IT MUST BE UNDERSTOOD THAT, IN THE LARGEST SENSE, THIS PASSAGE
14100	GIVES US A MOVEMENT FROM $V$I TO $I$I.  $IN RELATIVE TERMS, THE MAIN
14200	HARMONIES IN BETWEEN ARE PASSING CHORDS, EACH ELABORATED BY CHORDS
14300	AT THE 4TH ABOVE.  $HOWEVER, THE PARTICULAR EFFECT OF THE
14400	EXAMPLE DEPENDS ON THE FUNCTONS OF ALL THE HARMONIC DETAILS -- $V$I-$I$I
14500	$V7-$I -- ETC.
14600	
14700	$EXAMPLE 25.  $BACH, $PARTITA #5, $PRAEAMBULUM
14800	
14900	
15000		$UNDOUBTEDLY THE INTERNAL STRUCTURE OF THIS PASSAGE MAY BE
15100	HEARD ON MANY DIFFERENT LEVELS.  $THE NUMBER OF LEVELS MAY VARY BUT,
15200	GENERALLY, THE USE OF THREE IN AN ANALYSIS WILL SUFFICE TO GIVE A CLEAR 
15300	PICTURE OF THE WAY IN WHICH A PIECE CAN BE HEARD.  $THE PRIMARY LEVEL OF THIS
15400	SORT OF ANALYSIS WILL INDICATE THE KEY OF THE PARTICULAR AREA OF THE
15500	PIECE UNDER CONSIDERATION.  $THE SECONDARY LEVEL WILL SHOW THE
15600	LARGER HARMONIC MOTIONS WITHIN THE AREA, AND THE TERTIARY LEVEL WILL GIVE 
15700	VIRTUALLY ALL THE HARMONIC DETAILS.  $THE MIDDLE LEVEL WILL OFFER THE 
15800	GREATEST PROBLEMS, SINCE IT IS LISTENING AT THIS LEVEL (I.E., NOT
15900	CONCENTRATING ON EVERY DETAIL AND, AT THE SAME TIME, MAINTAINING
16000	A HARMONIC AWARENESS OF MORE THAN JUST THE END POINTS) THAT THE MOST
16100	VARIETY OCCURS.  $IN RETURNING TO THE EXAMPLE FROM THE $PARTITA WE SEE THAT
16200	THE FIRST LEVEL MAY CONSIDERED FOR NOW AS $C: $I.  $BECAUSE OF THE CLEAR
16300	STEPWISE DESCENT OF THE BASS FROM FIRST BEAT TO FIRST BEAT OF EACH BAR, 
16400	WHICH IS CONCLUDED ONLY ON THE LOW $D, WE CAN SAY THAT THE MOVEMENT ON
16500	THE SECOND LEVEL IS SIMPLY $V$I-$I$I (OR ALTERNATIVELY, BECAUSE OF THE
16600	PATTERNS OF THE UPPER PART, THE PASSAGE MAY BE HEARD IN TWO-BAR GROUPS
16700	 -- $V$I-$I, $I$V-$V$I, $I$I).  $THE THIRD LEVEL OFFERS -- WITHOUT
16800	GOING INTO THE DETAILS OF MINUTE CHORD INVERSIONS -- THE ANALYSIS GIVEN
16900	UNDER THE EXAMPLE.  $PUTTING THE THREE LEVELS TOGETHER WE HAVE:
17000	
17100	$FIGURE 25
17200	
17300	
17400	
17500		1.  $THE KEY IS ESTABLISHED (ALTHOUGH THE $I CHORD OCCUPIES NO
17600	PROMINENT POSITION).
17700		2.  $THE MAIN MOVEMENT WITH THE KEY IS FROM $V$I TO $I$I (OR THE
17800	ALTERNATIVE MENTIONED ABOVE).
17900		3.  $THE DETAILS OF HARMONIC ELABORATION ARE GIVEN.
18000	
18100	             --------------
18200	
18300		$FOR A SOMEWHAT MORE COMPLICATED EXAMPLE WE TURN TO A PASSAGE FROM
18400	$SCHUBERT'S $PIANO $SONATA IN $BB (FOURTH MOVEMENT, MEASURE 86).
18500	
18600	$EXAMPLE 26
18700	
18800	
18900		$HERE THE FIRST LEVEL GIVES US $F: $I.  $IN CASES WHERE THE 
19000	SECOND LEVEL BECOMES QUITE SUBTLE, IT IS OFTEN ADVISABLE TO BYPASS IT
19100	AND RETURN LATER FROM THE THIRD LEVEL.  $THE THIRD LEVEL OFFERS NO MORE
19200	PROBLEMS THAN DID THE $BACH EXAMPLE.  $HERE THE PROGRESSION IS:
19300	
19400	$FIGURE 26A
19500	
19600	
19700		$ALTHOUGH THIS PASSAGE CERTAINLY DOES NOT SOUND "WEAK", ALL
19800	THE DIRECT PROGRESSIONS IN THE FIRST FOUR BARS ARE BY 2NDS AND 3RDS.  $IF
19900	WEE APPLY THE CONCEPT OF SUBSTITUTE FUNCTIONS TO THE 3RD RELATIONS,
20000	THE SITUATION BECOMES MORE CLEAR.  $THUS $I$I$I MAY SERVE FOR $I AND $V$I
20100	MAY SERVE FOR $I$V.  $THE $I$I 6-4 IS NON-FUNCTIONAL, SINCE ITS UPPER
20200	TWO NOTES RESOLVE STEPWISE TO THE FINAL $V$I.  $THIS MAY BE INDICATED:
20300	
20400	$FIGURE 26B
20500	
20600	
20700		$HOWEVER, THE DESCENDING FIGURE OF TWO NOTES IN THE SOPRANO IN
20800	EACH OF THE LAST FOUR BARS DRAWS ONE'S ATTENTION TO THE LAST NOTE
20900	AND CHORD IN EACH BAR.  $THE FIRST BEAT IN EACH OF THESE BARS MAY BE
21000	CONSIDERED A KIND OF HARMONIZED APPOGGIATURA, EVEN THOUGH THE BASS DOES
21100	NOT ALWAYS MOVE IN A STEPWISE MANNER.  $NOW:
21200	
21300	$FIGURE 26C
21400	
21500	
21600	BECOMES OUR SECOND LEVEL.  $THE THREE LEVELS TOGETHER FORM:
21700	
21800	$FIGURE 26D
21900	
22000	
22100		$IN THE FOREGOING DISCUSSION, THE WORD "LEVELS" IS USED IN
22200	FULL REALIZATION THAT ITS USE IN THIS CONNECTION COULD BECOME CONFUSED WITH
22300	ITS USE IN THE OVERLAPPING AND SOMEWHAT SIMILAR REALM OF PURE HARMONIC 
22400	FUNCTIONS.  $DECISIONS CONCERNING THE BROADER STRUCTURAL LEVELS
22500	HEARD IN A PIECE WILL GENERALLY BE MUCH LESS SPECIFIC THAN THOSE
22600	CONCERNING THE LEVELS OF HARMONIC FUNCTION.  $IN THE FORMER
22700	CATEGORY, THE TOTALITY OF A PIECE MUST BE DEALT WITH; IN THE LATTER,
22800	ONE MUST DEAL PRIMARILY WITH AN ABSTRACTION OF THE RELATIONS BETWEEN
22900	THE VERTICAL OCCURRENCES OF A PIECE -- I.E., HARMONY.  $IT IS
23000	BELIEVED THAT THE DEVELOPMENT OF CONSISTENT TERMINOLOGY FOR THE DISCUSSION
23100	OF HARMONIC FUNCTIONS MUST SUPECREDE THE TOTAL ANALYSIS OF
23200	MUSIC.  $IN THE FOLLOWING CHAPTERS, "LEVELS" WILL BE
23300	USED WITH REGARD TO HARMONIC FUNCTIONS.
23400	
23500	
23600	                 -----------------
23700	
23800	
23900	$EXERCISES FOR $CHAPTER $I$I
24000	
24100	$I.	$WRITE OUT THE FOLLOWING PASSAGES.  $SHOW EACH TRITONE
24200		RELATIONSHIP AND INDICATE THE HALF OR WHOLE STEPS ON EITHER
24300		SIDE OF THE TRITONE.  $FROM THIS, ASCERTAIN THE VARIOUS
24400		TEMPORARY TONICS INVOLVED.  $FOLLOW THE FORM USED IN
24500		$EXAMPLE ZZZ ON PAGE ZZZ.
24600	
24700		$FROM THE $MOZART $SONATAS:
24800	
24900		1.  $SONATA IN $BB, $K.189F(281), FIRST MOVEMENT, BAR 48 TO
25000				FIRST NOTE OF BAR 54 (BOTH HANDS).
25100	
25200		2.  $SONATA IN A, $K.300D(310), LAST MOVEMENT, BARS 52-59
25300			(RIGHT HAND ONLY).
25400	
25500		3.  $PHANTASIE (NR.4) IN C, $K.475, SIX BARS, STARTING
25600			FROM 12 BEFORE $ANDANTINO (BOTH HANDS).
25700	
25800		4.  $SONATA IN $C, $K.545, BARS 29-42 (RIGHT HAND ONLY).
25900	
26100	$I$I.	$ANALYZE THE FOLLOWING DIATONIC PASSAGES.  $SHOW ALL SUBSTITUTE
26200		FUNCTIONS AND "PASSING" OR "CONTRAPUNTAL" CHORDS.
26300	
26400		$FROM THE 371 $CHORALES OF $BACH:
26500	
26600		1.  $CHORALE 1, FIRST 10 BARS
26700		2.  $CHORALE 5, FIRST 6 BARS
26800		3.  $CHORALE 14, FIRST 6 BARS
26900		4.  $CHORALE 125, FIRST 4 BARS
27000		5.  $CHORALE 209, LAST 5 BARS
27100	
27200		$FROM THE $MOZART $SONATAS:
27300	
27400		6.  $SONATA IN $G, $K.189H(283), FIRST MOVEMENT, BARS 1-10
27500		7.  $SONATA IN $G, $K.189H(283) SECOND MOVEMENT, BARS 1-4
27600		8.  $SONATA IN $C, $K545, THIRD MOVMENT, LAST 10 BARS
27700		9.  $SONATA IN $D, $K.284C(311), SECOND MOVEMENT, BARS 1-11