perm filename C6[HHA,LCS]1 blob sn#424716 filedate 1979-03-12 generic text, type C, neo UTF8
COMMENT ⊗   VALID 00003 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	. DEVICE XGP    
C00004 00003	.SKIP 2
C00019 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]"
.PORTION MAIN;
.PLACE TEXT;
.COMPACT
.PAGE←68
.NEXT PAGE
.<< 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 "%↓_↑↓[&]"
.SKIP 2
.CENTER		
CHAPTER VI
.SKIP 2
.CENTER			
ALTERNATING PROGRESSIONS AND INDIRECT RELATIONSHIPS
.SKIP 1
.INDENT 6
.FILL
.ADJUST
.SELECT 1
 
 
	The simplest form of alternating progression is that in which
a particular chord is approached from two points of view with regard 
to its harmonic function.  In most cases there is not the slightest
doubt as to the primary function (usually dominant) of the final chord.

.BEGIN VERBATIM

Example 65







Figure 65





.END

	Here the delayed resolution of the D7th chord to %2its%1 tonic, ↓_G_↓,
may be shown as above.  The primarily dominant function of the G chord 
is ensured by the immediately preceding subdominant (II%5H%1)
function.  Thus the G major chord is tonicized by the second chord and
"dominantized" by the third chord, the last relationship in the
series being the most influential.  Here, once more, the voice-leading
or contrapuntal element becomes relevant and, from a broad point of
view, the bass notes F%4S%1, A%4F%1, and G form a kind of cambiata figure
which minimizes the effect of the D7th chord as a dominant.$$Many
books on harmony would call this D7 chord simply II%4S3%1.  This seems like
an oversimplification.  A dividing line must be drawn somewhere in these
matters; in this book the sharped 4th and 5th degrees of the scale will only
be admitted as "functional" when they are part of augmented sixth or
augmented fifth chords.$  In detail,
however, the above example %2does%1 offer us the musical effect
indicated by the analysis.

	Similar progressions occur in the Mazurka No.38, Op.59,#3,
of Chopin (measures 16-24):

.begin verbatim

Example 66a
.end
.skip 13


	As the progressions under study become more complex, the
following method for clarifying the relationships may be used.  The
horizontal bars connecting various parts of the Chordal Reduction
serve the purpose of showing which of the harmonies may be directly
related to one another.  %2On any given level, the horizontal bar
connects  chords which all serve the same temporary tonic%1.  It
should be noted that sometimes a chord of substitute function will
be found on a given tonic's bar even though the chord is at the same
time more clearly related to another tonic.  These Chordal Reductions
are not to be confused with the diagrams outlining Tonic Guide Tones.
Tonic Guide Tones will be used solely as a means of clarifying
relationships among the %2tonics%1 involved in any progression.  (See page 55.)

.begin verbatim

Figure 66

Chordal Reduction
.end
.skip 12




	Here the control tonic of III (↓_A_↓) has been established.  The
section in ↓_A_↓ is far too brief to warrant the use of the term
"modulation".  In measure 17 the G and the clearly implied C%4S%1 form
a tritone which is most readily heard as dominant to ↓_D_↓.  However,
measure 18 first offers us a 7th chord on B -- this heard as dominant
to ↓_E_↓.  Then follows a d minor chord, the logical result of measure 17.
In measure 19 is heard an E7th chord (over a tonic A pedal) which is
a substitute for the simple tonic expected after the B7th chord.  At
measure 21 things become a little more complex.  The last chord contains
an A%4S%1, which could be interpreted merely as a chromatic passing note,
but which certainly does tend to tonicize the following B (as the
sixth degree, normally a minor tonic, of ↓_D_↓), which then functions as it
did earlier.  At the end of measure 22, the tonic expected after the
A7th chord of four beats back is replaced by the II%5I%1 of ↓_A_↓.


	Since the successive functions in such music sometimes bear
only a secondary relation to each other, very skillful voice leading,
as in the Chopin example, is necessary in order that the progression
remains clear.  From one point of view, there is no doubt at all that
this passage can be interpreted as a chromatic "working out" of the
A chord.
.begin verbatim

Example 66b.  (Reduction of Example 66a.  The doubling of the
		highest part at the octave below is omitted.)
.end
.skip 8




	However, the particular form the chromaticism takes in this
Mazurka also gives the unmistakable impression of a series of varied
harmonic functions.