00100		It will be seen that any degree of either a major or minor
00200	scale may be tonicized.  Usually the new tonics will be major or
00300	minor, depending on the normal forms of the various triads in the
00400	original tonic.  When the original key is major, II, III and VI
00500	will most often be tonicized as minor keys, while IV and V will
00600	be major.  VII will rarely be tonicized, since it presents a
00700	diminished chord in the home key.  (The chord built on the
00800	leading tone of C major is B, D, Fn.)  On the other
00900	hand, VII frequently appears as a tonic goal when the first key
01000	is minor.  (The chord built on the seventh tone of the c minor
01100	scale is Bb, D, F.)  With a minor scale we have III, VI,
01200	and VII forming major tonics, and IV and V minor tonics.  Since the
01300	chord on the second degree of the minor scale is normally diminished,
01400	II now becomes rare as a tonic, whereas the major tonic on bII,
01500	the Phrygian second, is often used.  (See Beethoven, Sonata #23 in f,
01600	Op.57, opening bars; Sonata #29 in Bb, Op.106, third movement.)
01700	In actual practice, especially in the music of the 19th century, the
01800	major and minor elements are freely interchangeable.
01900	 
02000		From this point on, the distinction between major and
02100	minor tonics in the upper two levels of an analysis will be indicated
02200	by the use of upper and lower case Roman numerals respectively.  The
02300	functions within the tonics (the lowest level of an analysis) will
02400	continue to be shown by upper case numerals.  Non-functional alterations,
02500	such as the "tierce de Picardie" (I#3 in the minor), may be shown in
02600	the usual fashion.
02700	 
02800		However, when a temporary tonic appears as major after the
02900	preceding music leads one to expect a minor tonic, certain problems
03000	are sometimes raised.  Often such chords are experienced as dominant
03100	functions to chords more closely related to the scale of the
03200	original key, as in in bar 8 following (see also Chapter V).
03300	 
03400	Example 44.  Schubert, Meeres Stille, Op.3, #2
03500	 
03600	 
03700	 
03800	 
03900	 
04000	Figure 44
04100	 
04200	 
04300	 
04400	 
04500	 
04600		Following is a complete table of indications for the possible
04700	temporary tonics that might be found in direct relation to a basic
04800	tonic of C major.  Add the appropriate accidentals when dealing
04900	with other basic tonics.
05000	 
05100	Figure 45
05200	 
05300	 
05400	 
05500	 
05600	 
05700	 
05800	 
05900	 
06000	 
06100		Group 1 lists the tonic chords available from the resources
06200	of the unaltered C scale.  The second group includes tonic chords
06300	that are available as the result of flatting any of the original
06400	scale degrees except the 1st, 4th and 5th; hence, c minor.  (The
06500	bvii, bb, as a tonic is rare, but see the opening of Mozart's
06600	Quartet in C, K.465.)  Group 3 is set apart because it includes the
06700	less common temporary tonics, all of which involve either flatting or
06800	sharping of the 1st, 4th or 5th of the original scale in order to
06900	produce the new tonic chord.  These chords, even when surely approached
07000	as tonics, often prove to be working as dominant or subdominant from the
07100	largest point of view. **********(add examples)***********
07200				(beethoven, bagatelle in f)
07300	 
07400		It will be noted that there is no temporary tonic listed
07500	above that has as its root a sharping of any part of the original
07600	tonic major scale or a flatting of the 1st, 4th or 5th degrees.
07700	It is very difficult to make a case for the existence of such a
07800	direct relationship of tonics.  (See Chapter VI, Alternating
07900	Progression.)
08000	 
08100	                    ------------------------
08200	 
08300	Augmented Sixth Chords
08400	 
08500		It is now clear that chromatic alteration in a chord very often
08600	changes its function.  This will most often be true when the
08700	alteration involves the 1st, 4th, 5th or 7th degree of the scale,
08800	or when it occurs within a phrase rather than at its end.  As stated
08900	before, every judgment must be based on the whole of any particular
09000	context under consideration.
09100	 
09200		The alterations that go into making chords of the augmented
09300	sixth (A6) give us a special case.  Such chords evolved as separate
09400	entities from the practice of "freezing" the chromatic passing tone
09500	between the 4th and 5th of the scale.  When these chords are used in
09600	their conventional manner and within a single tonality, they give
09700	us an exception to the rule that the 4th of a scale, as a chord tone,
09800	may not be altered without causing a shift of tonics.  The
09900	traditional names for the three most common augmented sixth chords
10000	are as follows:
10100	 
10200	Example 46
10300	 
10400	 
10500	 
10600	 
10700	 
10800		Strictly speaking, they should be indicated thus:  It.6=IV#6-b1,
10900	G6=IV#6-5-b1, F6=II#6-4-3-b1 (all in C major).  It will generally
11000	suffice to refer to them all in the abbreviated manner, A6.  When
11100	they actually are used as augmented sixth chords, they almost always have
11200	primarily contrapuntal significance, the outer voices expanding by
11300	half step movement.
11400	 
11500	 
11600	Example 47
11700	 
11800	 
11900	 
12000	 
12100		However, since they are so often used as a means of tonicizing
12200	new areas (see Example 30), it is usually advisable to make their
12300	presence clear in an analysis.  The augmented sixth interval creates a
12400	situation wherein the dominant tends to be tonicized (Example 47, F#
12500	leads to G) and at the same time a tonic role for the dominant
12600	is weakened by the effect of presenting its 2nd as flatted (Ab to G).
12700	The actual result is that added strength is given to the dominant role
12800	of the final "resolution" of the A6 chord, since the flatted note is
12900	most easily taken as the b6 of the original tonic.  Thus, augmented
13000	sixth chords will be said to function as part of a tonic a major 3rd
13100	above the lower member of the augmented sixth interval (see Example 47).
13200	 
13300		Because the G6 chord presents the identical acoustical
13400	situation as an ordinary dominant 7th chord (i.e., major 3rd,
13500	minor 3rd, minor 3rd), its enharmonic form will often be used as a
13600	means to move rapidly to a relatively distant tonic.
13700	 
13800	Example 48
13900	 
14000	 
14100	 
14200	 
14300	 
14400	 
14500	 
14600	Figure 48
14700	 
14800	 
14900	 
15000	 
15100		Even without recourse to enharmonic change, the F6 chord may work
15200	as the V7-b5 structure of the original key's dominant
15300	(see Example 46.)  One notable use of the V7-b5 occurs at
15400	the end of Schubert's Quintet in C, Op.163.
15500	 
15600	Example 49
15700	 
15800	 
15900	 
16000	 
16100	 
16200	 
16300		In this particular case it might be inferred (perhaps
16400	fancifully) that this chord is used to point in the subdominant
16500	direction, a tradition of long standing for endings.  Thus:
16600	 
16700	 
16800					might imply
16900	 
17000	 
17100	 
17200	 
17300	 
17400		For a stronger example, this time employing the G6, we turn to
17500	Schubert's posthumous Sonata in A.  Here, there is little possibility
17600	of confusion with an altered V, since there is no root of V present.
17700	 
17800	Example 50.  Schubert, Sonata in A
17900	 
18000	 
18100	 
18200	 
18300	 
18400	 
18500	 
18600		Of the two following possible analyses, the second is best.
18700	In the first, we assume that since the F is omitted at (*), an
18800	E, though not present, might be implied.  (Even so, this would give the
18900	sound of the subdominant's F6.)  In the second, we more
19000	reasonably assume that the F persists in the memory and that the context
19100	does not lead us to interpret the chord Bb-D-F-G# as an inversion
19200	of A: VII7-b3.
19300	 
19400	Figure 50
19500	 
19600	 
19700	 
19800	 
19900	 
20000	 
20100	 
20200		It should be pointed out again that no chord may be evaluated
20300	until all its parts have been heard.  However, no set rules can be
20400	given for this; as usual, the context must be the determining factor.
20500	In the Schubert Sonata, the Bb chord fills a measure and a quarter
20600	before the appearance of the G#.  Thus the relatively simple progression
20700	of I to bII has time to be accepted before the function is altered by
20800	the addition of a fourth pitch.  Such particulars are certainly open to
20900	varying interpretations.  In both of these Schubert pieces, such ambiguous
21000	procedures are possible because of the extremely firm establishment of
21100	the main tonic in the preceding passages.
21200	 
21300		A case with some similarity is presented in the Prelude #23
21400	in F of Chopin, where an Eb is found in the final arpeggiated
21500	chord.  This Eb is usually heard merely as an intensification of
21600	the already present 7th partial of the bass note's overtone series.
21700	However, it is undeniable that some tendency toward the subdominant,
21800	a tonal area which is almost completely neglected in the piece, is
21900	heard.  At the end of a piece devoted to almost nothing more than
22000	figuration on I and V, this Eb comes as a welcome bit of
22100	fantasy.
22200	************************** add example??
22300	 
22400		And then there is the standard "Blues" progression:
22500	 
22600	Example 51
22700	 
22800	 
22900	 
23000	 
23100	Figure 51
23200	 
23300	 
23400	 
23500	 
23600		Many variants of the main A6 chords may be found in later
23700	tonal music.  But once they recognized for what they are, they should
23800	cause no difficulties in an analysis.  Similarly, there are many
23900	chromatic variants of the dominant, subdominant (the A6! is one), and
24000	other functions, except for the I function.
24100	But remember that there is always the potential of a change of
24200	function when any chromaticism is introduced.  Various notes may be
24300	added to tonic function, and the root may even be omitted, but if
24400	the root or 5th are altered, the tonic function becomes dubious.
24500	 
24600		Chromaticism has always caused composers trouble with
24700	notation.  The augmented sixth and diminished seventh chords in
24800	particular have raised problems, because of the ambiguity of
24900	the situations in which they are often found.  Composers cannot be
25000	totally consistent in notating such chords when enharmonic
25100	equivalence is involved.  It will always be necessary to determine
25200	the function or functions of chromatic chords by studying their
25300	surroundings rather than by taking their notation at face value.
25400	 
25500	 
25600	 
25700	 
25800	 
25900	 
26000	 
26100	Exercises for Chapter IV
26200	 
26300		Analyze the following works.  Show the distinctions between
26400	major and minor tonics through the use of upper and lower case
26500	numerals on the two highest levels of the analyses.
26600	 
26700	From the 371 Chorales of Bach:*
26800	 
26900	****Note that all bass lines in the Bach Chorales are probably
27000	intended to be doubled at the octave below.  Hence, even if the
27100	notation of the bass part
27200	crosses above the tenor part, the bass part remains the true bass.****
27300		1.  Chorale 11, up to the 34
27400		2.	"    37
27500		3.   	"    47
27600		4.	"    94
27700		5.	"    223
27800	 
27900	From the Sonatas of Mozart:
28000	 
28100		6.  Sonata in D, K.205b (284), last movement, Variation VII
28200	 
28300		7.  Sonata in a, K.300d (310), first movement, 24 bars
28400			starting at recapitulation.  (In cases where there are
28500			many suspensions and appoggiaturas it is usually best
28600			to write out a chordal reduction of the passage before
28700			working out the analysis.)
28800	 
28900		8.  Sonata in C, K.300h (330), second movement, first 20 bars
29000	 
29100	From the Preludes, Op. 28, of Chopin:
29200	 
29300		9.  Prelude 1, in C
29400	      10.  Prelude 6, in b
29500	      11.  Prelude 20, in c