perm filename CH6A[HHA,LCS] blob sn#412597 filedate 1979-01-24 generic text, type T, neo UTF8
00100				CHAPTER VI
00200	 
00300	 
00400	 
00500	    ALTERNATING PROGRESSIONS AND INDIRECT RELATIONSHIPS
00600	 
00700	 
00800		The simplest form of alternating progression is that in which
00900	a particular chord is approached from two points of view with regard 
01000	to its harmonic function.  In most cases there is not the slightest
01100	doubt as to the primary function (usually dominant) of the final chord.
01200	
01300	Example 61
01400	
01500	
01600	
01700	
01800	
01900	
02000	
02100	Figure 61
02200	
02300	
02400	
02500	
02600	
02700	
02800		Here the delayed resolution of the D7th chord to its tonic, G,
02900	may be shown as above.  The primarily dominant function of the G chord 
03000	is ensured by the immediately preceding subdominant (II4-3-1b)
03100	function.  Thus the G major chord is tonicized by the second chord and
03200	"dominantized" by the third chord, the last relationship in the
03300	series being the most influential.  Here, once more, the voice-leading
03400	or contrapuntal element becomes relevant and, from a broad point of
03500	view, the bass notes F#, Ab, and G form a kind of cambiata figure
03600	which minimizes the effect of the D7th chord as a dominant.  In detail,
03700	however, the above example does offer us the musical effect
03800	indicated by the analysis.
03900	*********** insert re. idea of II#3 chord - why its a bad idea****
04000	
04100		Similar progressions occur in the Mazurka No.38, Op.59,#3,
04200	of Chopin (measures 16-24):
04300	
04400	Example 62a
04500	
04600	
04700	
04800	
04900	
05000	
05100	
05200	
05300		As the progressions under study become more complex, the
05400	following method for clarifying the relationships may be used.  The
05500	horizontal bars connecting various parts of the Chordal Reduction
05600	serve the purpose of showing which of the harmonies may be directly
05700	related to one another.  On any given level, the horizontal bar
05800	connects  chords which all serve the same temporary tonic.  It
05900	should be noted that sometimes a chord of substitute function will
06000	be found on a given tonic's bar even though the chord is at the same
06100	time more clearly related to another tonic.  These Chordal Reductions
06200	are not to be confused with the diagrams outlining Tonic Guide Tones.
06300	Tonic Guide Tones will be used solely as a means of clarifying
06400	relationships among the tonics involved in any progression.  (See page zzz.)
06500	
06600	Figure 62
06700	
06800	Chordal Reduction
06900	
07000	
07100	
07200	
07300	
07400	
07500		Here the control tonic of III (A) has been established.  The
07600	section in A is far too brief to warrant the use of the term
07700	"modulation".  In measure 17 the G and the clearly implied C# form
07800	a tritone which is most readily heard as dominant to D.  However,
07900	measure 18 first offers us a 7th chord on B -- this heard as dominant
08000	to E.  Then follows a d minor chord, the logical result of measure 17.
08100	In measure 19 is heard an E7th chord (over a tonic A pedal) which is
08200	a substitute for the simple tonic expected after the B7th chord.  At
08300	measure 21 things become a little more complex.  The last chord contains
08400	an A#, which could be interpreted merely as a chromatic passing note,
08500	but which certainly does tend to tonicize the following B (as the
08600	sixth degree, normally a minor tonic, of D), which then functions as it
08700	did earlier.  At the end of measure 22, the tonic expected after the
08800	A7th chord of four beats back is replaced by the II4-3-n1 of A.
08900	
09000		Since the successive functions in such music sometimes bear
09100	only a secondary relation to each other, very skillful voice leading,
09200	as in the Chopin example, is necessary in order that the progression
09300	remains clear.  From one point of view, there is no doubt at all that
09400	this passage can be interpreted as a chromatic "working out" of the
09500	A chord.
09600	
09700	Example 62b.  (Reduction of Example 62a.  The doubling of the
09800			highest part at the octave below is omitted.)
09900	
10000	
10100	
10200	
10300	
10400	
10500		However, the particular form the chromaticism takes in this
10600	Mazurka also gives the unmistakable impression of a series of varied
10700	harmonic functions.
10800	
10900		For more examples of chords which have both contrapuntal and
11000	harmonic significance we will turn to the opening of Schubert's
11100	Quintet in C, Op.163.
11200	
11300	Example 63.  Schubert, String Quintet in C, Op.163
11400			(Reduction of measures 1-26.)
11500	
11600	
11700	
11800	
11900	
12000		Complete diminished 7th chords (at [4] and [13]) are often
12100	used non-functionally, as multiple neighboring notes.  Taking this
12200	point of view, Figure 63a treats most of the altered chords as
12300	purely contrapuntal.  Thus the harmonic movement remains quite
12400	simple and without any new tonicization until the end of the excerpt.
12500	This is very likely the way the music is heard (and intended to be heard).
12600	
12700		As we come to know the piece rather well, especially as
12800	regards the violoncellos' repetition of the opening theme at bar 33
12900	(see Example 64), we may feel that the various altered chords in the
13000	first part also carry a potential of having functional implications.
13100	Any given listener may not always hear this example in the same, even
13200	if he has memorized it.  While the main purpose of our analyses is to
13300	show how the harmony of a piece is most simply heard, we should also
13400	try to provide for other, less simple possibilities that may be
13500	inherent in the music.
13600	
13700		Figure 63b shows the implications of the various altered chords.
13800	The diminished chord at bar 13 is shown as d: Vs of V (Ab=G#) simply
13900	because of its being in a position analogous to that of the first 
14000	diminished chord, bar 4.  Bar 13 has, of course, at the same time the 
14100	role of Vs of C.  This is demonstrated by the indications below the
14200	second analysis.  Thereby the symmetry of the first and second
14300	phrases is clearly shown.  At (*) three functions are given for the
14400	d minor harmony.  They represent 1) its relation to the previous
14500	function, 2) its present function, as defined by a new statement of
14600	the main motive, and 3) its relation to the following function. Such
14700	triple indications should be used sparingly, since they could easily
14800	obscure the most important elements of a progression.
14900	
15000		Perhaps Schubert wished to prove that these altered chords
15100	could have harmonic functions, since his varied restatement of the
15200	opening gives the following progression.
15300	
15400	Example 64.  Schubert, Quintet in C, Op.163 (Reduction of bars 33-46)
15500	
15600	
15700	
15800	
15900	
16000	Figure 64
16100	
16200	
16300	
16400	
16500		Now, the first diminished chord is certainly working as a
16600	tonicizing agent to G.  The three chords found in measures 40 to 44
16700	give the effect of a deceptive progression in a, the final chord
16800	of the group being also subdominant in terms of what follows.  Note
16900	that no pivotal tonic is used when the control tonic returns to I.
17000	It is felt that the time spent under the control tonic of ii (d) is
17100	of such relatively brief duration that C could scarcely be heard as
17200	a tonicized VII.  However, some other piece with a different
17300	presentation of a similar progression might be analyzed rather
17400	differently.
17500	
17600		In the March to the Scaffold from Berlioz' Fantastic Symphony
17700	occurs a passage that has puzzled many musicians.  Its dramatic effect
17800	is highly dynamic and specific, but its musical justification has been
17900	difficult.  The problem arises from the alternation of the tonic g
18000	minor harmony and the Db chord.  It might seem that the closest link
18100	between these tritone-related minor and major chords would be found at
18200	the fourth above the tonic, or c minor.  Thus the relationship could
18300	be shown:
18400	
18500	Figure 65
18600	
18700	
18800	
18900	
19000	
19100		However, the composer does not seem to take this view of the
19200	relationship (nor does he treat Db in this manner when it appears a
19300	few moments earlier).  The alternation of chords continues until Db
19400	is almost heard as a new and functionally unrelated tonic.  But, as the 
19500	drive of the passage subsides, it progresses to Eb7 and thence to a
19600	tutti chord, at which time the previous happenings may be reassessed.
19700	The analysis following the example represents the result of this
19800	reassessment.  There is inadequate basis for choice until the end
19900	of the passage.
20000	
20100	Example 66.  Berlioz, Fantastic Symphony (Reduced from the fourth movement)
20200	
20300	
20400	
20500	
20600	Figure 66.
20700	
20800	
20900	
21000	
21100	
21200		Below the main body of the analysis is shown the separate
21300	movement of each of the two alternating progressions.  The one in g is 
21400	quite simple; in fact, the whole g chord acts as a pedal until the
21500	augmented sixth chord leads to the dominant.  The progression begun
21600	by the Db chord is listed under an Ab tonic because, in view of the
21700	ultimate hearing of the Eb7 (enharmonic), Ab is the most direct
21800	connecting link, even though its I chord is not used, to g.  The
21900	functions listed in parentheses might be interpreted as chromatic
22000	elaboration of the Db chord (see Example 63).  Thus the overall
22100	progress from the Db chord is likewise simple -- Ab: IV...V,
22200	wherein the V serves doubly as the G6 of g.  Notice that in all this
22300	the possibility of treating the Db chord as a bV or #IV relationship
22400	in g is avoided.  A true direct relation of the tritone between two
22500	tonics tends to destroy both of them.******see Schumann, Carnaval*****
22600	Such a relationship would merely constitute a juxtaposition of keys
22700	whose tonic chords were incompatible except as they both served as
22800	subsidiaries to a third tonic (see page zzz).
22900