00100	Figure 86b
00200	
00300	
00400	
00500	
00600	
00700	
00800		The harmony of bars 60-62 is quite similar, but now moving from
00900	d and employing three-note substitutes for the seventh chords.
01000	
01100	Figure 86c
01200	
01300	
01400	
01500	
01600	
01700	
01800	
01900		Taking only the primary chords of the next bars, we find the
02000	same progression, now in c:
02100	
02200	Figure 86d
02300	
02400	
02500	
02600	
02700	
02800		Next, the progression is expanded to three seventh chords in
02900	a row.  Following the previous analyses, we can only assume that
03000	this represents an overlapping of an implied tonicization of f and
03100	a real one of g.
03200	
03300	Figure 86e
03400	
03500	
03600	
03700	
03800	
03900		There is no doubt that the material thus far presented on
04000	this passage gives a fair picture of the essential movement of the
04100	harmony and would make a relatively uncluttered analysis.  Unfortunately,
04200	this degree of simplicity is achieved only by omitting mention of the
04300	subtle changes which occur at the ends of many of the measures.  When
04400	these are taken into account, we find several pivot chords and
04500	justification for showing some more brief tonicizations.
04600	
04700		First, in bars 63 and 64, it might be said that the root 
04800	of each beginning harmony is tonicized by the previous eighth note.
04900	Below the analysis, the earlier simple view is presented.
05000	
05100	Figure 86f
05200	
05300	
05400	
05500	
05600	
05700	
05800	
05900		Because of the slight changes in the presentation of the motive
06000	in bars 65-69, we now find somewhat different harmonic details.  The
06100	harmony of bar 65 is first heard as c: I, the disjunctly approached Ab
06200	at the end changing the function to VI7.  Continuing on this basis,
06300	bar 66 will give c: II acting at same time as f: nVI, which then becomes
06400	f: IV7 at the end of the bar.  (Note that a Bb7 chord rarely can be
06500	truly functional in c.)  Bar 67 then has f: nVII to V7, which works
06600	equally well as g: nVI to IV7.  This leads to g: #VII7 in bar 68 and
06700	then I at the beginning of bar 69.
06800	
06900	Figure 86g
07000	
07100	
07200	
07300	
07400	
07500	
07600	
07700		However, it hardly seems necessary to show these changes of
07800	nVI to IV7, etc. in bars 66-68, the root of each seventh chord being
07900	delayed until the last eighth note.  But if the same reasoning is
08000	applied to the slightly different structures of bars 65 and 69, what
08100	is first heard clearly as I then is "completed" as IV7 of a major key.
08200	
08300	Figure 86h
08400	
08500	
08600	
08700	
08800	
08900	
09000	
09100	
09200	
09300	
09400		The difficulty in analyzing this last half of the development
09500	section stems mainly from the ambiguity of function in the long string
09600	of ascending seventh chords.  Even though a satisfactory analysis of the
09700	tonal bases can be worked out here, it is obvious that our comprehension
09800	of such passages depends greatly on the much less problematical element
09900	of motivic continuity.  It will be seen later how the functional 
10000	ambiguity of late 19th-century music led to a situation wherein the
10100	motivic or, more broadly speaking, contextual element took over the
10200	primary organizational role from tonal harmony.
10300	
10400		The recapitulation of this Mozart movement offers no new
10500	complications.  The few new tonics can easily be identified.
10600	
10700		It will be noticed that most of the work on the role of the
10800	piece's more complex chromaticism has been assumed during the
10900	preceding discussion.  This can hardly be otherwise, even when
11000	approaching a work from the largest view first.  The more complicated
11100	the details are, the more difficult it usually becomes to form an
11200	immediate view of the larger tonal movements.  The same will often
11300	prove true concerning the other of the first three analytical 
11400	procedures outlined in Chapter VIII.  What questions that may be
11500	left in this area will probably be covered in the discussion which
11600	follows the complete analysis of the movement.
11700	
11800	Figure 87.  Mozart, Sonata in F, K.533, second movement (Andante).
11900	
12000	
12100	
12200		Space does not permit discussion of all the problematical
12300	details, but a few things should be pointed out.  Many more chords
12400	of weak structural nature might be enclosed by parentheses (see bar 1),
12500	but to do this aspect full justice a complete rhythmical analysis
12600	would be necessary.  The linear element, especially in the bass, is
12700	another factor which has been largely neglected but which certainly
12800	contributes to the relative value of the function of the chords.  (Note
12900	the bass ascent from bar 3; F-G-A-Bb-C-D-Eb-F, etc.)  
12950		At bars 24 and 25 there is no question of a 6-4 chord, since 
13050	the bass is melodic.  At bar 29 its melodic role is much weaker.  From 
13150	bar 33 to bar 38 we have a prolonged F cadence with "contrapuntal" 
13250	decorating functions.  The functions listed on the third beats of
13350	bars 37 and 38 are formed by the implications of the lines.  Notice
13400	especially the details of the line in bar 37; it is almost the same 
13500	in bars 50 and 52.  In these latter cases, however, some ambiguity
13600	results, since it is a little difficult to specify all the chord
13700	tones.  The thrice repeated cambiata figure first gives the impression
13800	of defining chord tones at intervals of the fourth.  However, the primary
13900	note of the last cambiata in each case is itself an emphasized 
14000	appoggiatura to the next to last note of the bar.  Thus these two
14100	measures present the F7 chord unless they are viewed as inverted
14200	positions of the dominant ninth chord.
14300	
14400		Naturally, if the repeat of the second section is considered,
14500	there would be a small change on the highest line of the middle
14600	ground.  The d control tonic at bar 47 might read iii (of the basic
14700	tonic Bb) the second time through.  Everything below that line would
14800	remain the same.
14900	
15000		Many more harmonic relationships lie in the piece than are
15100	expressed in our large diagram, but this process of creating an
15200	analysis may be adapted to whatever scale of detail might be desired.
15300	It is hoped that this process will instill the individual with a 
15400	heightened awareness of the music, thereby clearing the way for the
15500	comprehension of the work's full intellectual and emotional potential.
15600	
15700	
15800	                     -----------------------------
15900	
16000	
16100	Exercises for Chapter IX
16200	
16300		Analyze the following movements from the Sonatas of Mozart:
16400	
16500	  1.  Sonata in Bb, K.189f(281), last movement (Rondo).
16600	  2.    "    in a, K.300d(310), first movement.
16700	  3.    "    in F, K.300k(332), last movement.
16800	  4.    "    in c, K.457, second movement.
16900	  5.    "    in D, K.576, first movement.