COMMENT ⊗   VALID 00003 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	. DEVICE XGP    
C00004 00003	.PAGE←46
C00021 ENDMK
C⊗;
. DEVICE XGP    
.spacing 10*5 mills;
.EVERY HEADING(,{PAGE},)
.AREA TEXT LINES 4 TO 40
.FONT 1 "METL"
.font 2 "METLI"
.font 3 "METS"
.font 4 "MUS[HHA,LCS]"
.font 5 "MUZ[HHA,LCS]"
.FONT 6 "BASL35"
.!XGPLFTMAR←283
.PORTION MAIN;
.PLACE TEXT;
.COMPACT
.<< Put in a footnote. >>
.
.COUNT FOOTNOTE INLINE FROM 1 TO 999 IN PAGE PRINTING ⊂"*****"[1 TO FOOTNOTE]⊃
.<<	(IF THISDEVICE = "XGP" THEN "%51%*" ELSE "[1]");>>
.
.FOOTSEP ← "__________";
.AT "$$" ENTRY "$"
.	⊂
.	NEXT FOOTNOTE;
.	FOOTNOTE!;
.	SEND FOOT
.		⊂
.		BEGIN "NEXT FOOTNOTE"
.		SELECT 1;
.		SINGLE SPACE
.		SPACING 0 MILLS
.		INDENT 0,0,0;
.		(FOOTNOTE! & " ");
ENTRY
.		END "NEXT FOOTNOTE";
.		⊃;
.	⊃;
.
.TURN ON "%↓_↑↓[&]","α"
.PAGE←46
.NEXT PAGE
.begin verbatim
Figure 48
.end
.CENTER
%6⊂⊗⊃L[α%0.53,α%-1.15]:48F.PLT[HHA,LCS]⊂⊗⊃%1
.skip 4
 
.FILL
.INDENT 6
	It will be noted that there is %2no%1 temporary tonic listed
in Figure 47 that has as its %2root%1 a sharping of any part of the original
tonic major scale or a flatting of the 1st, 4th or 5th degrees.
It is very difficult to make a case for the existence of such a
direct relationship of tonics.  (See Chapter VI, Alternating
Progressions.)
 
.CENTER		        
_______________
.BEGIN VERBATIM


Pivot Chords in the Minor
.END
.FILL
.INDENT 6
.adjust
	Because of the ambiguities inherent in the minor scale certain problems
can occur in regard to pivot chords.  In Example 49a the ascending form of the
minor scale produces a chord (IV%4N%1) which can, in a slightly different
context (Example 49b), lead to a brief new tonicization of VII.
.BEGIN VERBATIM

Example 49 
.END
.CENTER
%6⊂⊗⊃L[α%0.03,α%-2.15]:N49X.PLT[HHA,LCS]⊂⊗⊃%1
.SKIP 7

.<<  .BEGIN VERBATIM >>

.<<  Example and Figure 49b >>
.<<  .END  >>
.<<  .CENTER  >>
.<<  %6⊂⊗⊃L[α%0.03,α%-2.20]:NEWX2.PLT[HHA,LCS]⊂⊗⊃%1 >>
.<<  .SKIP 7  >>
 
 
.NEXT PAGE
.fill indent 6
	In the minor, a direct progression from III (with the flatted fifth) 
to V (with the raised third) is somewhat rare.  However the next example may
be analyzed in this way because no real tonicization of III is involved.
.BEGIN VERBATIM
 
Example and Figure 50
.END
.CENTER
%6⊂⊗⊃L[α%0.03,α%-2.42]:N50X.PLT[HHA,LCS]⊂⊗⊃%1
.SKIP 9
 
.fill indent 6
	The III chord may be called a pivot in the minor so long as the conventions
regarding the usage of the various forms of the minor scale are followed.  In
the next example the pivot to III as a tonic is the III chord itself since the
chord appears in a context completely compatible with both ↓_c_↓ and ↓_E%4F%1_↓.
However the return from III to i as the middle-ground tonic involves an abrupt 
chromatic shift.  Thus no pivot is shown.
.BEGIN VERBATIM
 
Example and Figure 51
.END
.CENTER
%6⊂⊗⊃L[α%0.03,α%-2.32]:N51X.PLT[HHA,LCS]⊂⊗⊃%1
 
.NEXT PAGE
.BEGIN VERBATIM

Augmented Sixth Chords
.END
.FILL INDENT 6
	It is now clear that chromatic alteration in a chord very often
changes its function.  This will most often be true when the
alteration involves the 1st, 4th, 5th or 7th degree of the scale,
or when it occurs within a phrase rather than at its end.  As stated
before, every judgment must be based on the whole of any particular
context under consideration.
 

	The alterations that go into making chords of the augmented
sixth (A6) give us a special case.  Such chords evolved as separate
entities from the practice of "freezing" the chromatic passing tone
between the 4th and 5th of the scale.  When these chords are used in
their conventional manner and within a single tonality, they give
us an exception to the rule that the 4th of a scale, as a chord tone,
may not be altered without causing a shift of tonics.  The
traditional names for the three most common augmented sixth chords
are as follows:
.BEGIN VERBATIM

Example 52
.END
.CENTER
%6⊂⊗⊃L[α%0.03,α%-1.00]:N52X.PLT[HHA,LCS]⊂⊗⊃%1
.SKIP 4
 
.FILL INDENT 6
 
	Strictly speaking, they should be indicated thus for a major key such
as ↓_C_↓:
.CENTER
%6⊂⊗⊃L[α%0.03,α%-0.60]:N52Z.PLT[HHA,LCS]⊂⊗⊃%1
.SKIP 3
.FILL INDENT 6
It will generally
suffice to refer to them all in the abbreviated manner, A6.  When
they actually are used as augmented sixth chords, they almost always have
primarily contrapuntal significance, the outer voices expanding by
half step movement.
.BEGIN VERBATIM
 
Example 53
.END
.CENTER
%6⊂⊗⊃L[α%0.03,α%-0.65]:N53X.PLT[HHA,LCS]⊂⊗⊃%1
.SKIP 1
 
.FILL INDENT 6
	However, since they are so often used as a means of tonicizing
new areas (see Example 33), it is usually advisable to make their
presence clear in an analysis.  The augmented sixth interval creates a
situation wherein the dominant tends to be tonicized (Example 53, F%4S%1
leads to G) and at the same time a tonic role for the dominant
is weakened by the effect of presenting its 2nd as flatted (Ab to G).
The actual result is that added strength is given to the %2dominant role%1
of the final "resolution" of the A6 chord, since the flatted note is
most easily taken as the %4F%16 of the original tonic.  Thus, augmented
sixth chords will be said to function as part of a tonic a major 3rd
%2above%1 the %2lower%1 member of the augmented sixth interval (see Example 53).
 

	Because the G6 chord presents the identical acoustical
situation as an ordinary dominant 7th chord (i.e., major 3rd,
minor 3rd, minor 3rd), its enharmonic form will often be used as a
means to move rapidly to a relatively distant tonic.
.BEGIN VERBATIM
 
Example 54
.END
.CENTER
%6⊂⊗⊃L[α%0.03,α%-1.72]:N54X.PLT[HHA,LCS]⊂⊗⊃%1
.NEXT PAGE
.FILL 
 
.FILL INDENT 6
 
	Even without recourse to enharmonic change, the F6 chord may work
as the V%4G%1 structure of the original key's dominant
(see Example 52).  One notable use of the V%4G%1 occurs at
the end of Schubert's %2Quintet in C%1, Op.163.
 
.BEGIN VERBATIM
 
Example 55
.END
.CENTER
%6⊂⊗⊃L[α%0.03,α%-1.02]:N55X.PLT[HHA,LCS]⊂⊗⊃%1
.SKIP 4
.FILL INDENT 6
 
	In this particular case it might be inferred (perhaps
fancifully) that this chord is used to point in the subdominant
direction, a tradition of long standing for endings.  Thus:
 
.skip 2
.CENTER			
might imply
.CENTER
%6⊂⊗⊃L[α%0.09,α%-0.78]:N55F.PLT[HHA,LCS]⊂⊗⊃%1
.skip 2
 
.FILL INDENT 6
 
	For a stronger example, this time employing the G6, we turn to
Schubert's posthumous %2Sonata in A%1.  Here, there is little possibility
of confusion with an altered V, since there is no root of V present.
.BEGIN VERBATIM

Example 56
.END
.CENTER
%6⊂⊗⊃L[α%0.03,α%-1.50]:N56X.PLT[HHA,LCS]⊂⊗⊃%1
.NEXT PAGE
 
.FILL INDENT 6
 
	Of the two following possible analyses, the second is better.
In the first, we assume that since the F is omitted at (*), an
E, though not present, might be implied.  (Even so, this would give the
sound of the subdominant's F6.)  In the second, we more
reasonably assume that the F persists in the memory and that the context
does not lead us to interpret the chord B%4F%1-D-F-G%4S%1 as an inversion
of ↓_A_↓: VII%4G%1.
.BEGIN VERBATIM

Figure 56
.END
.CENTER
%6⊂⊗⊃L[α%0.03,α%-1.20]:N56F.PLT[HHA,LCS]⊂⊗⊃%1
.SKIP 4

.FILL INDENT 6
 
	It should be pointed out again that no chord may be evaluated
until all its parts have been heard.  However, no set rules can be
given for this; as usual, the context must be the determining factor.
In the Schubert %2Sonata%1, the B%4F%1 chord fills a measure and a quarter
before the appearance of the G%4S%1.  Thus the relatively simple progression
of I to %4F%1II has time to be accepted before the function is altered by
the addition of a fourth pitch.  Such particulars are certainly open to
varying interpretations.  In both of these Schubert pieces, such ambiguous
procedures are possible because of the extremely firm establishment of
the main tonic in the preceding passages.

 
	A case with some similarity is presented in the %2Prelude #23
in F%1 of Chopin, where an E%4F%1 is found in the final arpeggiated
chord.  This E%4F%1 is usually heard merely as an intensification of
the already present 7th partial of the bass note's overtone series.
However, it is undeniable that some tendency toward the subdominant,
a tonal area which is almost completely neglected in the piece, is
heard.  At the end of a piece devoted to almost nothing more than
figuration on I and V, this E%4F%1 comes as a welcome bit of
fantasy.
.begin verbatim

Example 57.  Chopin, Prelude, Op.28, #23
.end
.CENTER
%6⊂⊗⊃L[α%0.00,α%-1.87]:N57X.PLT[HHA,LCS]⊂⊗⊃%1
.skip 10
	And then there is the standard "Blues" progression:
.begin verbatim

Example 58
.end
.CENTER
%6⊂⊗⊃L[α%-0.08,α%-1.80]:N58X.PLT[HHA,LCS]⊂⊗⊃%1
.skip 8
.FILL INDENT 6
 
	Many variants of the main A6 chords may be found in later
tonal music.  But once they are recognized for what they are, they should
cause no difficulties in an analysis.  Similarly, there are many
chromatic variants of the dominant, subdominant (the A6 is one!), and
other functions, except for the I function.$$But remember that 
there is always the %2potential%1 of a change of
function when any chromaticism is introduced.$  Various notes may be
%2added%1 to tonic function, and the root may even be omitted, but if
the root or 5th are altered, the tonic function becomes dubious.

 
	Chromaticism has always caused composers trouble with
notation.  The augmented sixth and diminished seventh chords in
particular have raised problems, because of the ambiguity of
the situations in which they are often found.  Composers cannot be
totally consistent in notating such chords when enharmonic
equivalence is involved.  It will always be necessary to determine
the function or functions of chromatic chords by studying their
surroundings rather than by taking their notation at face value.
 
.CENTER		        
_______________
.NEXT PAGE
.begin verbatim

Exercises for Chapter IV

.end
.FILL INDENT 6
	Analyze the following works.  Show the distinctions between
major and minor tonics through the use of upper and lower case
numerals on the two highest levels of the analyses.
.begin verbatim

 
From the 371 Chorales of Bach:*

	1.  Chorale  11, up to the 3/4.
	2.  Chorale  37, all.
	3.  Chorale  47
	4.  Chorale  94
	5.  Chorale  223
 

From the Sonatas of Mozart:
 
	6.  Sonata in D, K.205b (284), last movement, Variation VII.
 
	7.  Sonata in a, K.300d (310), first movement, 24 bars
		starting at recapitulation.  (In cases where there are
		many suspensions and appoggiaturas it is usually best
		to write out a chordal reduction of the passage before
		working out the analysis.)
 
	8.  Sonata in C, K.300h (330), second movement, first 20 bars.
 

From the Preludes, Op.28, of Chopin:
 
        9.  Prelude  1, in C
       10.  Prelude  6, in b
       11.  Prelude 20, in c

_____________
* Note that all bass lines in the Bach Chorales are probably
intended to be doubled at the octave below.  Hence, even if the
notation of the bass part crosses above the tenor part, the bass 
part remains the true bass.
.end
.NEXT PAGE