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01400	.COMPACT
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00100	.PAGE←55
00200	.NEXT PAGE
00300	.SKIP 2
00400	.CENTER		
00500	CHAPTER V
00600	.SKIP 2
00700	.CENTER			
00800	EXTENDED TONICIZATION
00900	.SKIP 1
01000	.INDENT 6
01100	.FILL
01200	.ADJUST
01300	.SELECT 1
01400	.BEGIN VERBATIM
01500	
01600	Added Levels of Tonic Function
01700	.END
01800	 
01900		Almost by definition, music of the tonal era depends
02000	on the listener's strong memory of a basic tonic.  The basic tonic is a
02100	cohesive force which sets limits and acts as a reference point for all
02200	types of harmonic movement.  Even %2modulation%1 within a movement never
02300	really destroys this reference point; it merely sets up a foremost
02400	subsidiary point.  When %2tonicization%1 becomes greatly extended, the same
02500	effect is produced on a somewhat smaller scale.  The difference between
02600	extended tonicization and modulation lies in the role the particular
02700	passage is playing in relation to the whole.  There is much music wherein
02800	these two concepts tend to overlap, but in the main, composers of
02900	the music here under consideration have been so intent upon formal
03000	clarity that the dependent character of tonicization, even when
03100	extended, is maintained.
03200	
03300	 
03400		This important facet of tonal music may be represented by
03500	%2added levels of tonicization%1 in the middle area of the analytical
03600	diagram.  These added levels occur when, %2within%1 a %2temporary%1 tonic
03700	area, again a new tonic is approached.  A simple example of this
03800	follows.  The basic key of ↓_C_↓ is understood to be well established
03900	both before and after the example.
04000	 
04100	.begin verbatim
04200	
04300	Example 59
04400	.end
04500	.CENTER
04600	%6⊂⊗⊃L[α%0.00,α%-1.42]:N59X.PLT[C5,LCS]⊂⊗⊃%1
04700	.NEXT PAGE
04800	.begin verbatim
04900	
05000	Figure 59a
05100	.end
05200	.CENTER
05300	%6⊂⊗⊃L[α%0.06,α%-1.20]:N59A.PLT[C5,LCS]⊂⊗⊃%1
05400	.skip 5
05500	.FILL
05600	.INDENT 6
05700	 
05800		The ↓_D_↓ area at (xx) appears in direct relationship only with
05900	the ↓_G_↓ (or tonicized V) area.  Even though every numeral that
06000	appears in the middle area of an analysis is %2understood%1 to be a tonic
06100	(i.e., working as a "I"), a new I is placed under the first
06200	presentation of V as a tonic in order that the interval of the subsequent
06300	movement to ↓_D_↓ (i.e., the dominant relation to ↓_G_↓), is readily apparent.
06400	Similarly, another I appears when the progression returns
06500	to ↓_G_↓ as the tonic.  In the previous example it will be noted that the
06600	tonicized ↓_D_↓ was specifically major.  This new I contains
06700	F%4S%1 -- not a functional probability in terms of the original ↓_C_↓, but
06800	completely compatible with the ↓_G_↓ scale.
06900	
07000	 
07100		This may be made even more clear if we set up what will be
07200	called %2tonic guide tones%1.  These represent, in musical notation,
07300	the elements that appear in the middle area of the analysis.
07400	 
07500	.begin verbatim
07600	
07700	Figure 59b
07800	
07900	.END
08000	.CENTER
08100	%6⊂⊗⊃L[α%0.00,α%-1.60]:N59B.PLT[C5,LCS]⊂⊗⊃%1
08200	
08300	.NEXT PAGE
08400	.FILL
08500	.INDENT 6
08600		The tonics which are most closely related (see table on page 46)
08700	are connected by horizontal bars.  The black notes may be added to show
08800	the mode of each tonic.  When dealing with very complex progressions,
08900	it may often prove quite helpful to sketch out the tonic guide
09000	tones previous to making any final decisions concerning the particular
09100	relationships of the temporary tonics.
09200	 
09300	
09400		If some of the notes of Example 59 are altered so that we
09500	arrive at ↓_d_↓ minor, instead of major, its role as the tonicized V of
09600	↓_G_↓ is greatly weakened.  Voice leading is important in establishing
09700	the ↓_d_↓ area.  The B and C%4S%1, 6th and 7th scale degrees, appear in
09800	ascending lines, the B%4F%1 and C%4N%1 in descending lines.
09900	 
10000	.begin verbatim
10100	
10200	Example 60
10300	.end
10400	.CENTER
10500	%6⊂⊗⊃L[α%0.00,α%-1.38]:N60X.PLT[C5,LCS]⊂⊗⊃%1
10600	.skip 7
10700	.FILL
10800	.INDENT 6
10900		Now, since the I chord of ↓_d_↓ does not disturb the material
11000	of the original scale, it is heard in direct relation to ↓_C_↓.
11100	 
11200	.begin verbatim
11300	
11400	Figure 60
11500	
11600	.END
11700	.CENTER
11800	%6⊂⊗⊃L[α%0.00,α%-1.52]:N60F.PLT[C5,LCS]⊂⊗⊃%1
11900	
12000	.NEXT PAGE
12100	.FILL  INDENT 6
12200		Very often there will be no clearcut procedure that may be
12300	followed when analyzing situations similar to the next example.  At
12400	(*), the change of mode on the G root makes varying interpretations
12500	of the function of the ↓_d_↓ tonic possible.
12600	 
12700	.begin verbatim
12800	
12900	Example 61
13000	.end
13100	.CENTER
13200	%6⊂⊗⊃L[α%0.00,α%-1.32]:N61X.PLT[C5,LCS]⊂⊗⊃%1
13300	.skip 6
13400	.begin verbatim
13500	
13600	Figure 61a
13700	
13800	.END
13900	.CENTER
14000	%6⊂⊗⊃L[α%0.02,α%-1.24]:N61A.PLT[C5,LCS]⊂⊗⊃%1
14100	.skip 5
14200	.begin verbatim
14300	
14400	
14500	Figure 61b
14600	
14700	.END
14800	.CENTER
14900	%6⊂⊗⊃L[α%0.02,α%-1.38]:N61B.PLT[C5,LCS]⊂⊗⊃%1
15000	
15100	.skip 5
15200	.begin verbatim
15300	
15400		* When a tonic changes mode for more than the duration of
15500		an occasional chord, the change may appear superimposed on
15600		the continuous line running from the original occurrence
15700		of the tonic.
15800	.end
15900	.NEXT PAGE
16000	.begin verbatim
16100	Figure 61c
16200	
16300	.end
16400	.CENTER
16500	%6⊂⊗⊃L[α%0.00,α%-1.47]:N61C.PLT[C5,LCS]⊂⊗⊃%1
16600	.skip 5
16700	 
16800	 
16900	 
17000	.ONCE NO FILL INDENT 0 
17100		     * Here the ↓_g_↓ tonic is shown as subsidiary to ↓_d_↓.  This
17200	.ONCE NO FILL INDENT 0 
17300		     interpretation might be preferred if the duration of 
17400	.ONCE NO FILL INDENT 0 
17500		     the ↓_g_↓ tonic area were quite short in relation to the 
17600	.ONCE NO FILL INDENT 0 
17700		     following ↓_d_↓ area (see Example 64).
17800	.FILL indent 6
17900	 
18000	
18100		Notice that the above examples were, for the purposes of
18200	illustration, presented without varied rhythm.  As always, in more
18300	complex situations, the relations between harmony, melody, and
18400	rhythm will combine to offer a basis for a more specific analytical
18500	interpretation.  However, it must be emphasized that the main
18600	profit to the serious musician is found in the process of wrestling
18700	with such problematical decisions.  The final decision need not be
18800	considered the %2only%1 right one, but rather as the most clarifying of
18900	the actual effect of the music on the individual.
19000	
19100	 
19200		An extreme example of added levels of tonicization (and it is
19300	often heard) is the progression through the "circle of fifths".
19400	.begin verbatim
19500	
19600	Example 62
19700	.end
19800	.CENTER
19900	%6⊂⊗⊃L[α%0.03,α%-1.32]:N62X.PLT[C5,LCS]⊂⊗⊃%1
20000	.NEXT PAGE
20100	.begin verbatim
20200	Figure 62
20300	.end
20400	.CENTER
20500	%6⊂⊗⊃L[α%0.00,α%-2.80]:N62F.PLT[C5,LCS]⊂⊗⊃%1
20600	.SKIP 13
20700	.begin verbatim
20800	 
20900	Example 63
21000	.end
21100	.CENTER
21200	%6⊂⊗⊃L[α%0.00,α%-1.46]:N63X.PLT[C5,LCS]⊂⊗⊃%1
21300	.skip 6   
21400	.begin verbatim
21500	 
21600	Figure 63
21700	.end
21800	.CENTER
21900	%6⊂⊗⊃L[α%0.00,α%-2.60]:N63F.PLT[C5,LCS]⊂⊗⊃%1
22000	.NEXT PAGE
22100	.FILL INDENT 6
22200		These diagrams may appear somewhat unwieldy, but they have
22300	the advantage of giving precise pictures, in intervallic terms, of the
22400	relationships involved.
22500	 
22600	
22700		Occasionally a very rapid movement through part of the "circle
22800	of fifths", or the successive use of 7th chords, will cause certain
22900	elements of a progression to stand in relief.
23000	.BEGIN VERBATIM
23100	
23200	Example 64
23300	.END
23400	.CENTER
23500	%6⊂⊗⊃L[α%0.00,α%-1.45]:N64X.PLT[C5,LCS]⊂⊗⊃%1
23600	.SKIP 6
23700	.BEGIN VERBATIM
23800	
23900	Figure 64
24000	.END
24100	.CENTER
24200	%6⊂⊗⊃L[α%0.10,α%-2.32]:N64F.PLT[C5,LCS]⊂⊗⊃%1
24300	.SKIP 9
24400	
24500	.FILL INDENT 6
24600		In the above diagram, the abrupt skip down to a third
24700	level of tonics (which resolves to a I on the second level)
24800	accurately parallels the effect of the example.  Notice the problems 
24900	created by the use of a string of diminished chords over a basically
25000	chromatic line.  Such situations may be analyzed as
25100	substitutes for the "circle of fifths" progression, but generally it
25200	is best to consider all but the first and last chords of the string
25300	as parallel-moving passing chords (see Bach, %2Partita #1 in B%4F%1, Gigue;
25400	Mozart, %2Fantasy in C%1, K.394).  However, in 19th-century music,
25500	details of voice leading (especially the melodic skips) often tend
25600	to give functional importance to the inner chords of strings of
25700	diminished chords (see Chopin, %2Etude in E%1, Op.10,#3, measure 38,
25800	etc.; Liszt, %2Transcendental Etude #6, "Mazeppa"%1, beginning).
25900	
26000		Most often the return to the main tonic will not be made by 
26100	the same route as was the departure.  When this happens, a pivotal
26200	tonic may appear in the middle area of the analysis (see below at
26300	the sign *).
26400	.begin verbatim
26500	
26600	Example 65
26700	.end
26800	.CENTER
26900	%6⊂⊗⊃L[α%0.00,α%-1.25]:N65X.PLT[C5,LCS]⊂⊗⊃%1
27000	.skip 6
27100	.begin verbatim
27200	
27300	Figure 65
27400	.end
27500	.CENTER
27600	%6⊂⊗⊃L[α%0.00,α%-2.60]:N65F.PLT[C5,LCS]⊂⊗⊃%1
27700	.NEXT PAGE
27800	.begin verbatim
27900	Example 66. Mozart, Sonata in D, K.576, 2nd movement.
28000	.end
28100	.CENTER
28200	%6⊂⊗⊃L[α%0.00,α%-7.40]:N66X.PLT[C5,LCS]⊂⊗⊃%1
28300	.NEXT PAGE
28400	.FILL INDENT 6
28500		The exact location of the pivotal tonic will usually depend on
28600	the association of the particular %2means%1 of presenting a given harmonic
28700	function with earlier presentation of the same function.  In other words,
28800	the return to the chord of departure, even with the same function on the
28900	lowest level, can be inconclusive until we also return to the same
29000	melodic and rhythmic presentation of that function.  In Example 66 the f%4S%1
29100	chord at (*) has a tonic function, but ↓_f%4S%1_↓ as a tonic of the middle area
29200	is still subsidiary to another tonic (↓_D_↓) until the return of the 
29300	original material.
29400	.begin verbatim
29500	
29600	Figure 66
29700	.end
29800	.CENTER
29900	%6⊂⊗⊃L[α%-.05,α%-3.30]:N66F.PLT[C5,LCS]⊂⊗⊃%1
30000	.SKIP 14
30100	.FILL INDENT 6
30200		The middle area of the first analysis is preferred at (+),
30300	because the tonic chord of f%4S%1 is completely consistent with the scale
30400	of ↓_D_↓, and there are no other factors that might deter one from
30500	hearing the passage as a stepwise progression of tonics (I, ii, iii).
30600	If, for any reason, it seems undesirable to show a pivot in cases where
30700	two or more levels of tonics are involved, the wavy vertical line (%4W%1)
30800	might be used to show the lack of continuity along any given level
30900	(see Figure 71).  However, it rarely happens that a logical connection
31000	between tonics cannot be made.
31100	.NEXT PAGE
31200	.begin verbatim
31300	Control Tonics
31400	.end
31500	.FILL INDENT 6
31600		An extension of the previous line of thought will serve well
31700	when considering the following analysis of music typical of the work
31800	of Bach.
31900	.BEGIN VERBATIM
32000	
32100	Example 67.  Bach, Invention No.4 in d.
32200	.END
32300	.CENTER
32400	%5⊂⊗⊃L[α0,α%-6.7]:N67XA.PLT[C5,LCS]⊂⊗⊃%1
32500	.NEXT PAGE
32600	.CENTER
32700	%5⊂⊗⊃L[0,α%-.75]:N67XB.PLT[C5,LCS]⊂⊗⊃%1
32800	.SKIP 4
32900	.BEGIN VERBATIM
33000	Figure 67a.  Bach, Invention No.4 in d (bars 7-45).
33100	
33200	.END
33300	.CENTER
33400	%5⊂⊗⊃L[α%-.05,α%-3.2]:N67FA.PLT[C5,LCS]⊂⊗⊃%1
33500	.SKIP 14
33600	.FILL INDENT 6
33700	
33800		The location of the pivot (at +) is arbitrary, because the
33900	following twelve bars are based on the descending form of the ↓_d_↓
34000	scale -- which is identical with the ↓_F_↓ scale.  If it seems necessary
34100	to specify the dual function of such progressions, the following method
34200	is suggested.  The %2retrospective%1 functions in ↓_F_↓ are circled to
34300	keep them distinct from the earlier perceived ↓_d_↓ functions.
34400	.begin verbatim
34500	
34600	Figure 67b
34700	.end
34800	.CENTER
34900	%5⊂⊗⊃L[α%-.2,α%-1.5]:N67FB.PLT[C5,LCS]⊂⊗⊃%1
35000	
35100	.NEXT PAGE
35200	.FILL INDENT 6
35300		The form of this work is defined mainly by a group of
35400	cadential formulas.  The strength of the points of definition is 
35500	greatly enhanced by the fact that each cadence offers us a new tonal
35600	center.  However, due to the exclusive use of a single set of motives
35700	and the brevity of the piece, modulation (as it is known in the main
35800	body of tonal music) does not occur.  The larger harmonic movement
35900	of this piece is certainly heard as a series of tonics, whose relations
36000	to the main, beginning tonic are at least as strong as their
36100	relations to one another.  Thus, even though ↓_a_↓ appears first as iii of
36200	↓_F_↓, it is finally established as an equal of ↓_F_↓ (in relation to ↓_d_↓)
36300	by the occurrence of the well-prepared cadence at bar 38.  Please note, however, 
36400	that ↓_a_↓'s role as something more than a transient tonic of the ↓_F_↓
36500	scale is not too definite until the point of cadence.  To emphasize these
36600	varying levels of relationships among the tonics, we must start at the
36700	beginning of our diagram with %2two%1 levels in the middle ground, so 
36800	that when a temporary tonic is somehow given greater status and 
36900	becomes what may be called a %2control tonic%1, this change will
37000	appear in a consistent form.  In the above analysis note that on the 
37100	highest level of tonicization the progress from i to III to v coincides
37200	exactly with the full cadences.  However, ↓_F_↓ and ↓_a_↓ are first tonicized
37300	well before the cadences (this shows on the second level of
37400	tonicization).  The numerals of the control tonics will be
37500	underlined.
37600	
37700	
37800		The use of strong cadences is not the only method which can
37900	give a temporary tonic the status of a control tonic.  Another favorite
38000	method is the clear presentation, in some new tonic, of
38100	material (either old or new) of relatively great importance; e.g., in
38200	the Bach Invention, the return to the original ↓_d_↓ as the control tonic
38300	is defined by the 
38400	return of the opening statement (bar 44), rather than by a full cadence.  The
38500	presentation should be long enough so that the new tonic may be heard
38600	as independent beyond the extent of simple tonicization.  The 
38700	functions under a control tonic established in this manner need not
38800	include a strong cadence.  The music might then progress smoothly to
38900	yet another control tonic.  If the important factors of the music seem
39000	to warrant its independence, a new control tonic might even appear as
39100	a lower level of tonicization, below an old control tonic (see next
39200	chapter, Schubert example).
39300	
39400	
39500		Much music can best be analyzed in terms of series of control 
39600	tonics, the term "modulation" being reserved for a shift of the
39700	basic tonic.  No set rule can be given as to when it is advisable to
39800	use an extra, higher level of indications in the middle area of the
39900	analytical diagram.  Any variant of the basic diagram is acceptable
40000	just so long as it contributes to the understanding of the music under
40100	consideration.
40200	
40300	.SKIP 1
40400	.CENTER		        
40500	_______________
40600	.FILL
40700	.adjust
40800	.SKIP 1
40900		It is very evident that as the complexity of harmony increases
41000	there is usually a corresponding increase in the ambiguity of individual
41100	harmonic functions as they relate to the whole.  This is, of course,
41200	the reason for the particular effect of late "Romantic" and "Impressionistic"
41300	harmony, and also the source of the ultimate breakdown of functional
41400	tonality as a meaningful system.  When every harmonic function becomes
41500	ambiguous, then something other than a tonal center (as defined by
41600	harmonic functions) must take over as the prime cohesive force (see last
41700	chapter).  It is significant that in music of the Classical era the 
41800	more complex harmonic progressions are most often relegated to
41900	developmental passages -- passages that depend greatly on motivic
42000	continuity.  In such instances, it is common to hear a series of tonics
42100	which seem to relate only to their immediate surroundings.  (It is
42200	possible for even the original tonic of a developmental section to
42300	reappear for a considerable time without its having any direct
42400	functional relationship with its earlier presentation.)  The
42500	analysis of an extended developmental passage will show continually
42600	added levels in the middle ground, the return to a single level being
42700	conditioned by the reappearance of familiar, stable material in its
42800	proper key.  This traditionally happens at the point of recapitulation
42900	in the sonata form.$$Among the numerous exceptions to the above statements are the
43000	first movement recapitulations of Mozart's %2Sonatas in D%1, K.284c(311)
43100	and %2in C%1, K.545.  In the first of these, the recapitulation begins with
43200	the material of the second key area, but now heard in ↓_D_↓ instead of
43300	↓_A_↓.  The recapitulation of the ↓_C_↓ sonata offers the original
43400	opening material, but in the subdominant, ↓_F_↓.$
43500	.CENTER		        
43600	_______________
43700	.FILL
43800	.adjust
43900	.begin verbatim
44000	
44100	
44200	Exercises for Chapter V
44300	
44400	
44500	Analyze the following works:
44600	
44700	From the 371 Chorales of Bach:
44800	
44900		1.  Chorale 21
45000		2.  Chorale 92
45100		3.  Chorale 200
45200		4.  Chorale 231
45300		5.  Chorale 279
45400	
45500	From the Two-Part Inventions of Bach:
45600	
45700		6.  Invention 11, in g
45800		7.  Invention 12, in A
45900		8.  Invention 13, in a
46000	
46100	From the Well-Tempered Clavier, First Book, Bach:
46200	
46300	        9.  Fugue I, in C
46400	       10.  Fugue X, in e
46500	
46600	From the Preludes, Op.28, of Chopin:
46700	
46800	       11.  Prelude  5, in D
46900	       12.  Prelude 22, in g
47000	.end