00100				CHAPTER XI
00200	 
00300	 
00400	 
00500	          TONAL DISSOLUTION:  CONCLUSION
00600	 
00700	 
00800		Musical %2meaning%1 is conveyed by particular uses of musical
00900	conventions which are either known in advance and apply to a large body
01000	of works, or are learned in the course of an individual work itself.
01100	Evolution seems to be able to push forward the "known" conventions only
01200	to a certain point -- then a revolution is necessary to make the final
01300	break into an area where fresh nuances of expression are possible.
01400	Try as they may, however, revolutionaries are never able to make a
01500	complete break with their past.  Their most important accomplishment
01600	is that they bring to the fore a reassessment of older values.  The
01700	radical shift of emphasis seems to the casual observer like a complete
01800	rejection of the status quo.  Indeed, at %2the%1 moment$$The length of
01900	this "moment" depends on many factors -- especially the talents of the
02000	individuals directly involved.$ of revolution a certain amount of chaos
02100	seems to exist.  In this brief time it is common to find experimental
02200	probes in every direction that seem to have little relation to each
02300	other beyond the fact that they, in some striking fashion, are all
02400	%2unlike%1 the immediate past.  This is an especially difficult time
02500	for the most gifted composers, because their audience cannot yet be
02600	expected to have assimilated the significant elements of the musical
02700	re-evaluation which these composers are guiding.  However, it is
02800	inevitable (just so long as the new music %2is%1 actually performed)
02900	that a "revolutionary" composer's audience will gradually become aware
03000	of the salient features of the new style.  This is true because the
03100	individual members of the audience are, after all, a part of the same
03200	general musical culture as is the composer.  The %2bases%1 of his
03300	musical thought, no matter what his creativity might add, are common 
03400	to all the sophisticated members of his society.
03500	
03600		Many musicians have felt that the seeds of tonal dissolution
03700	were present in the basic premises of functional harmony.  Once such
03800	a form of tonality came into general use, the inherent possibilities
03900	of significant relationships between tonalities were brought to the
04000	fore.  The only convincing means of moving from tonic to tonic is
04100	through the introduction of functional chromaticism.  But this process
04200	is both constructive and destructive.  It establishes or emphasizes
04300	new tonal centers and, in so doing, naturally undermines old ones.
04400	Most often in tonal music the chromaticism is so applied as to throw
04500	the balance strongly in the constructive direction.  That is, the new
04600	tonics are supplementary in nature (even when the result of modulation)
04700	and serve as massive elaboration of one basic tonic.  Already in the
04800	middle of the 19th century, however, the midpoint of this balance was
04900	being approached.  Without a great deal of motivic unity and the frequent
05000	use of harmonic sequences, some of the music of that time might truly
05100	have been as chaotic as a few o the contemporary critics believed it
05200	to be.  As more and more dramatic harmonic relationships were sought,
05300	the more apparent it was that tonality, as the all-important unifying
05400	force, was becoming inadequate.  The tonal center shifted so soon
05500	and so often that it no longer provided a useful point of departure;
05600	or (and even more important) the linear elements began to be combined
05700	in such a manner as to create constant doubt concerning a specific
05800	harmonic function at any given point.  As motivic values increased in
05900	importance, the distinctions between functional versus non-functional
06000	chromaticism and chord versus non-chord notes became arbitrary.  The
06100	%2implications%1 of tonality replaced the %2reality%1 of tonality.
06200	If new music was to retain its vitality, nothing was left at this point
06300	but to call upon a new basic unifying concept.  The word "contextuality"
06350	seems best to describe this concept as it exists in music that
06400	is truly of the 20th century.
06500	
06600		To greatly over-simplify the case, it might be said that the
06700	early composers of this new music generally embarked on one of two
06800	main routes.  These might be characterized by the terms "diatonicism"
06900	and "chromaticism".$$By the middle of the 20th century, the distinctions
07000	between these two types of composers were well on the way toward
07100	vanishing.$  The "diatonic" composers (often of the "French" school)
07200	tended to use unaltered tonal scales and chords built on thirds as 
07300	their materials.  Chromaticism existed mainly in terms of juxtapositions
07400	or combinations of diatonic units (polytonality), and although there
07500	were many %2references%1 to functional harmony, the %2particular uses%1
07600	of the overall material were clearly the most important bases of unity.
07700	$$For very good examples of this style, see the piano pieces, %2Saudades
07800	do Brasil%2, written by Darius Milhaud in the early 1920s.$  The
07900	"chromatic" composers (mainly of the "German" school), on the other
08000	hand, developed the idea of the freely existing %2motive%1.  The lines
08100	containing such motives often resembled late 19th-century lines, but
08200	when put in combination with one another, there was little pretense of
08300	underlying chords built on thirds which might give clear definition to
08400	specific tonic areas.  Any chord structure could be used
08500	just so long as it had motivic value or proved to be no more than the
08600	vertical result of several significant lines.  Here again, the %2use%1
08700	of the material -- the %2context%1 -- was the main basis of organization.
08800	
08900		With the aid of examples from Musorgsky's %2Boris Godounov%1
09000	(1874) and Wagner's %2Parsifal%1 (1882), we shall discuss some of the
09100	problems which must be faced when analyzing the music which made these
09200	early 20th-century "schools" possible.  Then we will conclude with the
09300	discussion of excerpts from music representative of the end of tonal
09400	evolution:  Debussy's %2Preludes for Piano%1 (c.1908) and the
09500	%2Kammersymphonie%1, Op.9, (1906) of Schoenberg.
09600	
09700	←←←←←←←←←←←
09800	
09900		The greatly increased dramatic (in the literary sense) use of
10000	music in the second half of the 19th century was a primary factor in
10100	the rapid demise of functional harmony.  In the following excerpt from
10200	%2Boris%1, Musorgsky creates "dream" music by at first avoiding the
10300	clear "reality" of specific harmonic function.  There is also much
10400	"tone painting" apart from the functional element.  The %2stepwise%1
10500	staccato quarter-notes = a "long ... staircase".  The ascending
10600	triads = "led me to a tower".  The low, rolling notes = "the crowd
10700	(below) ... thronged the square".  The staccato sixteenths = "mocking
10800	laughter".
10900	
11000	Example
11100	
11200	
11300		The staccato scale lines (bars 1-3, 4-5) fit in well with the
11400	pseudo-modal procedures established from the beginning of the opera.
11500	However, there are no direct functional relationships among the chords
11600	which accompany these scales.  Unless one considers the lowering of
11700	the leading tone as non-functional chromaticism (and there is no
11800	particular reason for doing so here), there are no pivot chords.  Thus,
11900	because of the whole step motion down from the root, each of these major
12000	chords after the first one are most easily heard as dominant in function.
12100	Note the tritone relations between the third of each chord and its
12200	following weak-beat quarter-note.  But since the harmony does not return
12300	to the point from whence it came, the resulting third relations lose
12400	significance as elements which can contribute to any particular basic
12500	tonic.  The sequential nature of the passage makes its "form" easy to
12600	grasp in %2spite%1 of the constant moving on to new places which tends
12700	to negate the functional relationships.  In the following analysis of the 
12800	first five bars, a basic tonic on the highest level seems superfluous
12900	and so is omitted.  Control tonics are listed at the end points of the
13000	phrase units, since they stand out in special relief.  At bar 4 we 
13100	return to a #=I=# in the middle ground because we begin again from
13200	an already heard chord.
13300	
13400	Figure
13500	
13600		At bar 6 it might be ventured that the "dream" begins to
13700	become a "reality" for Gregory.  Here the functions are much clearer.
13800	But as Gregory's narration reaches the description of the mocking of
13900	the crowd, "reality" once more disintegrates -- into a chord structure
14000	with a whole-tone potential.  The chord for bars 10 and 11 may be taken
14100	as C-E-G%4S%1, with D and F%4S%1 as appoggiaturas.  One function this
14200	chord can have is Vs of the a minor chord which comes in bar 14.
14300	This notion gets some support from the fact that there are no bass
14400	notes between the low E in bar 12 and the A-E fifth of bar 14.  The
14500	functional connection between the augmented chord and the previous
14600	music is quite weak.  With the enharmonic alteration of all flatted
14700	notes in bar 9 we have chords which, with a charitable outlook, could
14800	be considered as tonicizing the dominant of #=a=#.
14900	
15000	Figure
15100	
15200		On the other hand, it is more reasonable to take the F%4F%1 of
15300	bar 9 as a chromatic passing note in an area which has strong
15400	orientation toward #=b=#%4F%1.  Then if we reverse our position on bar 10
15500	and take E-G%4S%1 as neighboring notes to D-F%4S%1, the chord for 
15600	that bar may be read enharmonically A%4F%1-C-E%4FF%1-G%4F%1, or the
15700	altered dominant of #=D=#%4F%1.  This is useful, since #=D=#%4F%1 is
15800	the control tonic which appeared at the end of Figure zzz.  The
15900	elements of the possible #=a=# control tonic appear directly below
16000	the analysis of the #=D=#%4F%1 functions.  #=C=# becomes a new
16100	and independent control tonic at the end of the excerpt.
16200	
16300	Figure
16400	
16500		The ambiguity of many of the progressions in this excerpt
16600	makes possible the derivation of many other dubious functions.  It
16700	should be clear that the primary basis of organization in this
16800	passage is hardly any longer functional harmony.  In the first five bars
16900	the %2pattern of third relations%1 seems ascendent.  The particular
17000	temporary tonics and their relationship to any basic tonic are
17100	important only in that they continually lead %2away%1 from the
17200	possibility of a simple functional return to the point of departure.
17300	In bars 6 to 15 the %2interval of the third%1 is handled in a
17400	broader fashion.  The bass at first descends by thirds, the fourth
17500	leap being reserved for the phrase ending.  The highest part spans
17600	the third A%4F%1-C twice, the C persisting as a pedal point from
17700	bar 8 through to its tonic role at the end.  However, the fact that
17800	chords such as those of the excerpt %2usually%1 do have functional
17900	significance (and Musorgsky's audience certainly assumed this
18000	intuitively) contributes greatly to the effect of the passage.
18100	
18200	-------------------
18300	
18400		In %2Parsifal%1, Wagner has extended the technique of functional
18500	ambiguity which we have studied in connection with %2Tristan und Isolde%1.
18600	In our coming example from the opening of the Third Act of %2Parsifal%1,
18700	we are placed in almost continual doubt as to the specific role of each
18800	note.  It is the rule rather than the exception that notes may be heard
18900	as both chord and non-chord tones at once.  Especially noticeable are
19000	the long suspensions whose relative consonance often forms
19100	independent chords with distant functions.  The very slow tempo leaves us
19200	lingering on these "non-chord" chords, so that it is quite possible to
19300	lose entirely the sense of harmonic direction.  And when we come to
19400	know the music well enough to maintain our harmonic orientation, we
19500	realize that the specific functions are hardly important and that
19600	ultimately our sense of direction is preserved rather by our
19700	understanding of the particular means of handling the functional 
19800	ambiguity.  The first analyses given below (Figure zzz) is based on the
19900	slowest possible harmonic rhythm that may be heard in this music.
20000	The functions given are those of the chords at the various points of
20100	resolution.  It is only by studying the whole example carefully that
20200	we can feel sure about just where the points of resolution really 
20300	fall.  We are reasonably safe in assuming that all of Wagner's
20400	functional chords will be based on thirds.  In addition, we must
20500	realize that our diatonic-based system of notation is outmoded for
20600	music like this and that enharmonic equivalence must always be taken
20700	into consideration.  Proceeding with these things in mind, we see that,
20800	from the broad point of view, the essential harmony changes no more
20900	quickly than the time of a half-note -- and sometimes even more slowly
21000	than that.  In the second measure, the leap in the bass makes both
21100	parts of the tritone stand out as chord notes, the preceding G%4F%1(=F%4S%1)
21200	being an upward-resolving suspension.  The soprano's E-F-B%4F%1 work
21300	the same way, the pattern of half-note harmony with quarter-note
21400	overall movement thereby being well established.
21450		  In two spots, the
21500	traditions regarding leaps away from non-chord tones are stretched
21600	somewhat.  At bars 5 and 8 the diminished octave skip in the bass
21700	almost leads one to hear both notes of the interval as chord tones.
21800	Then the chord formed by the suspensions above the low half-notes
21900	would seem to have functional significance (see second analysis, 
22000	Figure zzz).  However, when the upper three notes resolve, it becomes
22100	clear that, in the largest sense, the diminished octave was merely
22200	a displaced chromatic scale movement and that the substitution of a
22300	sharp on the first note in each case (E%4F%1=D%4S%1, F=E%4S%1) would
22400	make this clear -- to the eye at least.  These spots are further 
22500	complicated because they represent a change in the manner of dealing
22600	with this pattern of long note moving to a short note on the next
22700	degree, followed by a leap.  But when studying the music in terms
22800	of most of the detail (Figure zzz), it is seen that several 
22900	interpretations of this pattern are possible.
23000	
23100	Example
23200	
23300	Figure
23400	
23500		Figure zzz sets forth the main elements of a possible interpretation
23600	which is perhaps obscured by the details in the other two analyses.
23700	The analysis in Figure zzz does not really give a clear
23800	picture of how this music is finally heard.  If all these 
23900	contrapuntally-achieved chords were really taken as functional harmony,
24000	the music would be very difficult to follow in the tonal sense.  However,
24100	once the "Wagnerian method" is understood, the factors shown in
24200	Figures zzza and zzzb stand out in their proper relief.
24300	
24400		These examples from Musorgsky and Wagner have shown us two
24500	methods by which functional ambiguity may be created.  Something
24600	of both methods were found in each example, but with Musorgsky it
24700	was mainly a case of rapidly juxtaposing triads which contained
24800	incompatible chromaticism and supported no single tonic.  With
24900	Wagner it was mainly a case of using chromatic  counterpoint in such a way as
25000	to give little hint in the details about the specific structure of
25100	many chords -- thereby keeping most of the functions in doubt.
25200	
25300	--------------------
25400	
25500		Almost all of Debussy's music is truly tonal, but in his later
25600	works there are many areas which no longer depend on harmonic functions
25700	for their basis of organization.  It is rare, however, that Debussy
25800	transcends tonality by means of extending the "Wagnerian method" 
25900	(although, in his own way, he uses the "method" a great deal -- as,
26000	for example, in the opening section of %2The Afternoon of a Faune%1).
26100	When tonality is dispensed with in his work, it is usually by 
26200	means of presenting successions of functionally unrelated chords,
26300	or by such means as his occasional use of the whole-tone scale,
26400	wherein the "roots" of the various chords employed have significance
26500	only in their contextual sense. In the first four bars of the 
26600	following passage, the B%4F%1 chord is the %2contextual%1 rather than
26700	the %2tonal%1 center.  Roman numerals could be applied to the various 
26800	parallel-moving chords, but they would have no meaning in the sense
26900	that they have been used up to now.  Harmony produced by exact
27000	parallelism is almost always non-functional (see pages zzz-zzz).
27100	In this Prelude the music continues after our example with B%4F%1 as
27200	a true tonal center.
27300	
27400	Example   .  Debussy, Prelude I (...Danseuses de Delphes)
27450				(11 bars from the end)
27475	
27487	
27500	
27600		In Debussy's %2Prelude II%1, functional tonality plays no more
27700	than a distantly associative role.  All of this work, except for five
27800	pentatonic measures, is based on a single whole-tone scale, used so as
27900	to establish a contextual center of C-E with a low B%4F%1 in support.
28000	
28100	Example   .  Debussy, Prelude II (...Voiles)
28200			(first 6 bars, last 2 bars)
28300	
28400	---------------
28500	
28600		With Schoenberg the situation is reversed.  Almost all the 
28700	music he wrote in his last forty-five years (1906-1951) is outside the
28800	realm of functional tonality.  But his beginnings were firmly rooted
28900	in the "Wagnerian method",  as evidenced by the example on page zzz
29000	from his %2Kammersymphonie%1 (1906), composed when he was a young man.
29100	An entire book could be written on the amazing extension of tonality
29200	found in this piece.  The given example is one of the "simpler" parts
29300	of the work and yet there could be many alternative interpretations
29400	add to the analysis offered.
29450		 Picking out which of the notes are 
29500	chord tones is frequently problematical (e.g., see bars 10-11 of the
29550	example).
29600	Sometimes the harmony changes before a chord built on thirds can
29700	appear;$$Note also the "fourth" chord at the beginning of the work,
29800	etc.$ at bars 5 and 6 the chords containing unresolved or "frozen"
29900	accessory tones could be explained as 11th chords.  However, there
30000	is so much of this kind of thing that the make-up of the chords is
30100	often obscured.  Example zzz gives a possible chordal condensation
30200	of the music.  Many of the specific decisions in this matter are
30300	arbitrary.  When playing over the music, the ear sometimes seems to
30400	tell you two things at once.  Much of the chromaticism present is in
30500	terms of appoggiaturas and traditional major-minor alterations
30600	(non-functional).  Especially prevalent is chromaticism in terms
30700	of augmenting and diminishing the fifth of dominant-function chords.
30800	This latter situation produces a chord with a whole-tone potential
30900	which has a far greater ambiguity than even the diminished seventh
31000	chord.
31100	
31200	
31300	Example
31400	
31500		In fact, when a whole-tone chord is found in highly chromatic
31600	surroundings, the ambiguity is total.  Considered as a doubly
31700	altered dominant ninth chord, any of a whole-tone chord's six notes
31800	can be the root.  Or considered as an extended form of augmented
31900	sixth chord, it may resolve to any of six dominants. 6+6=12!  The
32000	role of chromaticism in a whole-tone chord is left in doubt until
32100	other parts of the progression are heard.  When the progression offers
32200	nothing to clarify this role, then the chord can have no tonal
32300	function.  This point is almost reached in the example under study.
32400	
32500	Example    .  Schoenberg, Kammersymphonie, Op.9
32600	
32700	
32800	Figure
32900	
33000		In measure 1, the A major %4A%1 chord is probably best called
33100	a Vs -- although such substitute functions cannot be assumed
33200	as surely here as with earlier music.  The F%4S%1 may be taken to
33300	change the function or it may be taken as an added sixth, a "frozen"
33400	accessory tone.  In older music, the effect of the added sixth 
33500	appears often with non-tonic chords (e.g., II%4B%1=IV+6, VII%4B%1=II+6,
33600	III%4B%1=V+6, or V%4Z%1, etc.), but it is not until the late 
33700	19th century that the %2tonic%1 with the added sixth is used as a
33800	relatively stable chord.  A similar problem occurs with the E (major
33900	or minor∞ chord in bar 11.
34000	
34100		The functions of detail (there are several possible
34200	interpretations) in bars 1 and 2 seem weak in comparison to the
34300	slower, main harmonic movements, and so are placed in parentheses.
34400	In bar 2 the possible (even probable) dominant or G%46%1 function
34500	of the chord is not immediately realized, so the C%4N%1 may be
34600	heard as the lower neighboring note to C%4S%1 (see also page zzz).
34700	There is no sure way of ascertaining the functions in bars 5 and 6.
34800	The A%4F%1-D%4F%1 progression may be heard as #=D=#%4F%1: V-I
34900	almost as easily as #=A=#%4F%1: I-IV.  This latter interpretation
35000	seems best, however, since #=A=#%4F%1 is closer to #=E=#%4F%1, the
35100	altered dominant of which appears in bars 4 and 7.  The cadence from
35200	bar 7 to bar 8 (and at the end) is reminiscent of that noted in
35300	Schubert's %2Piano Sonata%1 in A (see page zzz).  The tendency
35400	toward the subdominant is unmistakable, although in a texture as 
35500	rich as Schoenberg's, the presence of a lowered seventh in a tonic
35600	(or any other) chord does not necessarily influence its function.
35700	(This is just one more bit of ambiguity.)  However, the subdominant
35800	tendency is also an important element in the over-all design of the
35900	entire work; the first of the largest formal units opens in #=E=#,
36000	moves finally to #=A=#, and then closes there.  (It is curious to note
36100	that this same interval relationship plays an important part in
36200	Schoenberg's twelve-tone works.)
36300	
36400		The designation of temporary tonics in bars 9 to 11 is highly
36500	arbitrary.  The highest melodic line seems to have a #=d=# 
36600	quality, but the other voices form harmonies, most of which are only
36700	indirectly related to #=d=#.  Perhaps a main source of ambiguity
36800	in this fragment is the large number of whole-tone-potential chords
36900	(marked x in the analysis).  They all can be derived from the same
37000	whole-tone scale and thus are all possible dominant functions to
37100	#=A=# ... or #=B=# (or could they be augmented sixth chords in
37200	#=D=#∞  However, because of their vertical positions, some of the
37300	forms of this whole-tone chord can be heard quite readily as dominants
37400	of #=E=#%4F%1 or #=G=#.  After listening to the example several
37500	times, it is possible to hear as an important relationship the 
37600	movement of #=A=#-#=E=#%4%F%1-#=A=#, wherein the #=E=#%4F%1
37700	is the %4F$1II of #=D=#; or in functional terms, #=A=#  ###SEE BOOK###.
37800	In bar 4 the dominant of #=E=#%4F%1 (or is it A%46%1 of #=D=#∞
37900	grows out of #=f=#%4S%1 (or is the melodic D%4S%1 more than an added
38000	sixth∞, but the melodic line in the following bars emphasizes the
38100	#=D=#-#=A=# relationship almost in spite of the harmony.
38150	
38200	
38300		It is significant that #=E=#%4F%1 somehow seems linked with #=D=# in
38400	this excerpt.  As pointed out earlier, a direct tritone relationship
38500	between two tonics is difficult to achieve in any functional sense (see
38600	page 46).  In order to bring about this relationship, even indirectly, a
38700	rather complex texture is necessary.  (Conversely, the simplest way to
38800	ensure "atonality" is through the liberal use of tritones.)  However, as
38900	the texture increases in complexity, the relative value of tonal functions
39000	in the music decreases and what was a %2means%1 (the context) of 
39100	clarifying and elaborating the functions becomes an %2end%1 (replacing
39200	tonality).
39300	
39400		While it is true that there is much 20th-century music in the
39500	new idiom which uses chords built on thirds and which even has an 
39600	occasional functional progression, it is generally worse than useless
39700	to analyze this music from a tonal point of view.  Almost any
39800	relationships can be gleaned from any such music, but how valuable
39900	are answers (even right ones) when the questions are wrong?  Even
40000	music such as that of the Schoenberg example might better be analyzed
40100	in contextual terms -- a basic element of the context being ambiguous
40200	tonal references based on chords whose specific constitution is
40300	frequently unclear.  Procedures for the analysis of contextual music will
40400	not likely become fully developed until composers have finally explored,
40500	in their intuitive manner, all the most fruitful potentials of this
40600	basis of organization.  However, in the tonal music which stylistically
40700	precedes the 20th century, the application of the principles of analysis 
40800	here set forth should give the musician a clear understanding of the
40900	harmonic role of each sound structure in the musical continuum.  The
41000	primary purpose of this study is to increase the awareness of just what
41100	particular progressions within the tonal conventions produce what
41200	%2musical%1 effects on the individual.  It must again be emphasized
41300	that tonal music is made up of a great deal more than harmony alone,
41400	but all else is essentially rhythmic and melodic elaboration of the
41500	functional harmonic relationships.  It is mainly by means of the
41600	great variety and subtlety of these relationships that this music is
41700	able to express such a wide range of human emotions.