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.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
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.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
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%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
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%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		        
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