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01300	.COMPACT
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33700	
33800		The form of this work is defined mainly by a group of
33900	cadential formulas.  The strength of the points of definition is 
34000	greatly enhanced by the fact that each cadence offers us a new tonal
34100	center.  However, due to the exclusive use of a single set of motives
34200	and the brevity of the piece, modulation (as it is known in the main
34300	body of tonal music) does not occur.  The larger harmonic movement
34400	of this piece is certainly heard as a series of tonics, whose relations
34500	to the main, beginning tonic are at least as strong as their
34600	relations to one another.  Thus, even though ↓_a_↓ appears first as iii of
34700	↓_F_↓, it is finally established as an equal of ↓_F_↓ (in relation to ↓_d_↓)
34800	by the occurrence of the well-prepared cadence at bar 38.  Please note, however, 
34900	that ↓_a_↓'s role as something more than a transient tonic of the ↓_F_↓
35000	scale is not too definite until the point of cadence.  To emphasize these
35100	varying levels of relationships among the tonics, we must start at the
35200	beginning of our diagram with %2two%1 levels in the middle ground, so 
35300	that when a temporary tonic is somehow given greater status and 
35400	becomes what may be called a %2control tonic%1, this change will
35500	appear in a consistent form.  In the above analysis note that on the 
35600	highest level of tonicization the progress from i to III to v coincides
35700	exactly with the full cadences.  However, ↓_F_↓ and ↓_a_↓ are first tonicized
35800	well before the cadences (this shows on the second level of
35900	tonicization).  The numerals of the control tonics will be
36000	underlined.
36100	
36200	
36300		The use of strong cadences is not the only method which can
36400	give a temporary tonic the status of a control tonic.  Another favorite
36500	method is the clear presentation, in some new tonic, of
36600	material (either old or new) of relatively great importance; e.g., in
36700	the Bach Invention, the return to the original ↓_d_↓ as the control tonic
36800	is defined by the 
36900	return of the opening statement (bar 44), rather than by a full cadence.  The
37000	presentation should be long enough so that the new tonic may be heard
37100	as independent beyond the extent of simple tonicization.  The 
37200	functions under a control tonic established in this manner need not
37300	include a strong cadence.  The music might then progress smoothly to
37400	yet another control tonic.  If the important factors of the music seem
37500	to warrant its independence, a new control tonic might even appear as
37600	a lower level of tonicization, below an old control tonic (see next
37700	chapter, Schubert example).
37800	
37900	
38000		Much music can best be analyzed in terms of series of control 
38100	tonics, the term "modulation" being reserved for a shift of the
38200	basic tonic.  No set rule can be given as to when it is advisable to
38300	use an extra, higher level of indications in the middle area of the
38400	analytical diagram.  Any variant of the basic diagram is acceptable
38500	just so long as it contributes to the understanding of the music under
38600	consideration.
38700	
38800	.SKIP 1
38900	.CENTER		        
39000	_______________
39100	.FILL
39200	.adjust
39300	.SKIP 1
39400		It is very evident that as the complexity of harmony increases
39500	there is usually a corresponding increase in the ambiguity of individual
39600	harmonic functions as they relate to the whole.  This is, of course,
39700	the reason for the particular effect of late "Romantic" and "Impressionistic"
39800	harmony, and also the source of the ultimate breakdown of functional
39900	tonality as a meaningful system.  When every harmonic function becomes
40000	ambiguous, then something other than a tonal center (as defined by
40100	harmonic functions) must take over as the prime cohesive force (see last
40200	chapter).  It is significant that in music of the Classical era the 
40300	more complex harmonic progressions are most often relegated to
40400	developmental passages -- passages that depend greatly on motivic
40500	continuity.  In such instances, it is common to hear a series of tonics
40600	which seem to relate only to their immediate surroundings.  (It is
40700	possible for even the original tonic of a developmental section to
40800	reappear for a considerable time without its having any direct
40900	functional relationship with its earlier presentation.)  The
41000	analysis of an extended developmental passage will show continually
41100	added levels in the middle ground, the return to a single level being
41200	conditioned by the reappearance of familiar, stable material in its
41300	proper key.  This traditionally happens at the point of recapitulation
41400	in the sonata form.$$Among the numerous exceptions to the above statements are the
41500	first movement recapitulations of Mozart's %2Sonatas in D%1, K.284c(311)
41600	and %2in C%1, K.545.  In the first of these, the recapitulation begins with
41700	the material of the second key area, but now heard in ↓_D_↓ instead of
41800	↓_A_↓.  The recapitulation of the ↓_C_↓ sonata offers the original
41900	opening material, but in the subdominant, ↓_F_↓.$
42000	.CENTER		        
42100	_______________
42200	.FILL
42300	.adjust
42400	.begin verbatim
42500	
42600	
42700	Exercises for Chapter V
42800	
42900	
43000	Analyze the following works:
43100	
43200	From the 371 Chorales of Bach:
43300	
43400		1.  Chorale 21
43500		2.  Chorale 92
43600		3.  Chorale 200
43700		4.  Chorale 231
43800		5.  Chorale 279
43900	
44000	From the Two-Part Inventions of Bach:
44100	
44200		6.  Invention 11, in g
44300		7.  Invention 12, in A
44400		8.  Invention 13, in a
44500	
44600	From the Well-Tempered Clavier, First Book, Bach:
44700	
44800	        9.  Fugue I, in C
44900	       10.  Fugue X, in e
45000	
45100	From the Preludes, Op.28, of Chopin:
45200	
45300	       11.  Prelude  5, in D
45400	       12.  Prelude 22, in g
45500	.end