It will be seen that any degree of either a major or minor
scale may be tonicized.  Usually the new tonics will be major or
minor, depending on the normal forms of the various triads in the
original tonic.  When the original key is major, II, III and VI
will most often be tonicized as minor keys, while IV and V will
be major.  VII will rarely be tonicized, since it presents a
diminished chord in the home key.  (The chord built on the
leading tone of C major is B, D, F%4N%1.)  On the other
hand, VII frequently appears as a tonic goal when the first key
is minor.  (The chord built on the seventh tone of the c minor
scale is B%4F%1, D, F.)  With a minor scale we have III, VI,
and VII forming major tonics, and IV and V minor tonics.  Since the
chord on the second degree of the minor scale is normally diminished,
II now becomes rare as a tonic, whereas the major tonic on bII,
the Phrygian second, is often used.  (See Beethoven, %2Sonata #23 in f%1,
Op.57, opening bars; %2Sonata #29 in B%4F%1, Op.106, third movement.)
In actual practice, especially in the music of the 19th century, the
major and minor elements are freely interchangeable.
 
	%2From this point on, the distinction between major and
minor tonics in the upper two levels of an analysis will be indicated
by the use of upper and lower case Roman numerals respectively%1.  The
functions %2within%1 the tonics (the lowest level of an analysis) will
continue to be shown by upper case numerals.  Non-functional alterations,
such as the "tierce de Picardie" (I%4S%13 in the minor), may be shown in
the usual fashion.
 
	However, when a temporary tonic appears as major after the
preceding music leads one to expect a minor tonic, certain problems
are sometimes raised.  Often such chords are experienced as dominant
functions to chords more closely related to the scale of the
original key, as in bar 8 following (see also Chapter V).
 
Example 46.  Schubert, Meeres Stille, Op.3, #2
 
 
 
 
 
Figure 44
 
 
 
 
 
	Following is a complete table of indications for the possible
temporary tonics that might be found in %2direct%1 relation to a basic
tonic of ↓_C_↓ major.  Add the appropriate accidentals when dealing
with other basic tonics.
 
Figure 45
 
 
 
 
 
 
 
 
 
	Group 1 lists the tonic chords available from the resources
of the unaltered ↓_C_↓ scale.  The second group includes tonic chords
that are available as the result of flatting any of the original
scale degrees except the 1st, 4th and 5th; hence, ↓_c_↓ minor.  (The
%4F%1vii, ↓_b_↓%4F%1, as a tonic is rare, but see the opening of Mozart's
%2Quartet in C%1, K.465.)  Group 3 is set apart because it includes the
less common temporary tonics, all of which involve either flatting or
sharping of the 1st, 4th or 5th of the original scale in order to
produce the new tonic chord.  These chords, even when surely approached
as tonics, often prove to be working as dominant or subdominant from the
largest point of view. **********(add examples)***********
			(beethoven, bagatelle in f)
 
	It will be noted that there is %2no%1 temporary tonic listed
above 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
Progression.)
 
                    ------------------------
 
Augmented Sixth Chords
 
	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:
 
Example 46
 
 
 
 
 
	Strictly speaking, they should be indicated thus:  It.6=IV#6-b1,
G6=IV#6-5-b1, F6=II#6-4-3-b1 (all in C major).  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.
 
 
Example 47
 
 
 
 
	However, since they are so often used as a means of tonicizing
new areas (see Example 30), 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 47, F#
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 dominant role
of the final "resolution" of the A6 chord, since the flatted note is
most easily taken as the b6 of the original tonic.  Thus, augmented
sixth chords will be said to function as part of a tonic a major 3rd
above the lower member of the augmented sixth interval (see Example 47).
 
	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.
 
Example 48
 
 
 
 
 
 
 
Figure 48
 
 
 
 
	Even without recourse to enharmonic change, the F6 chord may work
as the V7-b5 structure of the original key's dominant
(see Example 46.)  One notable use of the V7-b5 occurs at
the end of Schubert's Quintet in C, Op.163.
 
Example 49
 
 
 
 
 
 
	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:
 
 
				might imply
 
 
 
 
 
	For a stronger example, this time employing the G6, we turn to
Schubert's posthumous Sonata in A.  Here, there is little possibility
of confusion with an altered V, since there is no root of V present.
 
Example 50.  Schubert, Sonata in A
 
 
 
 
 
 
 
	Of the two following possible analyses, the second is best.
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 Bb-D-F-G# as an inversion
of A: VII7-b3.
 
Figure 50
 
 
 
 
 
 
 
	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 Sonata, the Bb chord fills a measure and a quarter
before the appearance of the G#.  Thus the relatively simple progression
of I to bII 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 Prelude #23
in F of Chopin, where an Eb is found in the final arpeggiated
chord.  This Eb 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 Eb comes as a welcome bit of
fantasy.
************************** add example??
 
	And then there is the standard "Blues" progression:
 
Example 51
 
 
 
 
Figure 51
 
 
 
 
	Many variants of the main A6 chords may be found in later
tonal music.  But once they 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 potential of a change of
function when any chromaticism is introduced.  Various notes may be
added 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.
 
 
 
 
 
 
 
Exercises for Chapter IV
 
	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.
 
From the 371 Chorales of Bach:*
 
****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.****
	1.  Chorale 11, up to the 34
	2.	"    37
	3.   	"    47
	4.	"    94
	5.	"    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