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