00100				$C$H$A$P$T$E$R $I$V
00110	
00200	
00300			$F$U$N$C$T$I$O$N$S $O$F $T$H$E $M$I$N$O$R
00350	
00400	
00500	
00600	$MAJOR-MINOR $INTERCHANGEABILITY
00700	
00800		$AS STATED EARLIER, MINOR SCALES WILL BE TREATED AS EXISTING
00900	AS THE RESULT OF A FAIRLY CONSISTENT SET OF ALTERATIONS OF THE
01000	PARALLEL MAJOR SCALES (SEE PAGE ZZZ) AND FOLLOWING).  $WHILE MINOR
01100	SCALES MAY NOT HAVE ORIGINATED IN THIS WAY, IT IS PROBABLE THAT
01200	THEIR USE IN TONAL MUSIC MAY BEST BE APPROACHED FROM THIS POINT
01300	OF VIEW.  $TWO ALTERATIONS SUFFICE TO GIVE THE COMPLETE IMPRESSION
01400	OF MINOR HARMONY -- THE FLATTED THIRD AND THE FLATTED SIXTH.  $IN
01500	SOME CASES, EVEN THE SIXTH NEED NOT BE ALTERED.  $HOWEVER, IF THIS
01600	SCALE DEGREE IS LINGERED UPON, THE MINOR EFFECT WILL BE WEAKENED
01700	UNLESS IT HAS BEEN FLATTED.  $CONVERSELY, THE B6 MAY BE FOUND IN
01800	PROXIMITY TO THE N3 WITHOUT COMPLETELY DESTROYING THE MAJOR
01900	QUALITY.
02000	
02100		$WHEN THE THIRD OR SIXTH OF A SCALE IS FLATTED AND APPEARS AS
02200	THE THIRD OF A CHORD, THERE IS MOST OFTEN NO CHANGE IN THE FUNCTION
02300	OF THE CHORD.  $THE FLATTED SEVENTH OF THE SCALE CAN CHANGE THE
02400	FUNCTION OF THE $V CHORD, ESPECIALLY IF IT IS USED IN SOME
02500	ASCENDING MANNER.  $IT IS RARE THAT A REAL $VB3 CHORD IS HEARD IN A 
02600	POSITION OF STRUCTURAL IMPORTANCE.  $WHEN IT EXISTS, THE $VB3 USUALLY
02700	LOSES ITS "DOMINANT" FUNCTION, UNLESS THE COMPOSER HAS MADE A SPECIAL
02800	EFFORT TO IMPRESS UPON THE LISTENER THAT THE "LEADING TONE" IS
02900	TO BE A WHOLE STEP BELOW THE TONIC NOTE.  $HOWEVER, IT IS ONLY BY
03000	EXAMINING THE WHOLE OF A PHRASE THAT ONE CAN ASCERTAIN WHETHER A
03100	CHORD CONTAINING THE FLATTED SEVENTH OF THE SCALE IS FUNCTIONING
03200	EXCLUSIVELY IN THE ORIGINAL MINOR KEY OR RATHER DUALLY IN THAT KEY
03300	AND THE RELATIVE MAJOR, OR SOME OTHER CLOSELY RELATED KEY.  $IT
03400	SHOULD BE MENTIONED THAT THE "CLOSENESS" OF ANY TWO KEYS TO ONE
03500	ANOTHER DEPENDS LARGELY ON JUST HOW MUCH THEIR SCALES HAVE IN
03600	COMMON, OR SOMETIMES POTENTIALLY HAVE IN COMMON.  ($BY THIS IS
03700	MEANT, THE CONVENTIONAL ASCENDING AND DESCENDING FORMS OF MINOR SCALES
03800	MUST BOTH BE CONSIDERED.)  $THUS $C IS A LITTLE "CLOSER" TO $G THAN
03900	IT IS TO A, BECAUSE ONLY ONE NOTE (THE 4TH) OF THE $C SCALE
04000	MUST BE ALTERED TO PRODUCE THE $G SCALE, BUT TWO NOTES (THE 4TH AND 5TH)
04100	MUST BE ALTERED TO PRODUCE THE ASCENDING FORM OF THE A SCALE.
04200	
04300	$EXAMPLE 41
04400	
04500	
04600	
04700	
04800		$ON THE OTHER HAND, $C IS SOMEWHAT "CLOSER" TO A THAN A IS TO
04900	E OR $E.  $AFTER AN A TONIC IS ESTABLISHED, $C MAY BE TONICIZED MERELY
05000	BY MEANS OF ELEMENTS ALREADY FOUND IN THE CONVENTIONAL
05100	DESCENDING FORM OF THE A SCALE; WHEREAS THE E OR $E SCALE REQUIRES
05200	AT LEAST $D# FOR ITS ESTABLISHMENT.
05300	
05400	$EXAMPLE 42
05500	
05600	
05700	
05800		$IN MUSIC WHERE THERE IS MUCH MAJOR-MINOR ALTERATION, ALMOST
05900	ANY KEYS MAY BE DIRECTLY RELATED.  $AS TO THE PROBLEM OF "CLOSE" OR
06000	"FAR", THE ABSOLUTE NUMBER OF CHROMATIC CHANGES REQUIRED TO ESTABLISH
06100	A NEW KEY WILL NOT BE SO IMPORTANT AS THE QUESTION OF JUST WHAT
06200	ROLE THE ALTERED NOTES PLAY IN EACH OF THE SCALES INVOLVED.  $THE
06300	PROBLEM OF THE LARGER RELATIONSHIPS BETWEEN KEYS WILL BE DEALT WITH
06400	IN SUBSEQUENT CHAPTERS.
06500	
06600	
06700			--------------------------
06800	
06900	
07000		$WHEN WE TRULY HAVE A GROUP OF FUNCTIONS BASED ON THE NATURAL
07100	MINOR SCALE (I.E., THIRD, SIXTH, AND SEVENTH DEGREES FLATTED BOTH ASCENDING
07200	AND DESCENDING), WE MAY SAY THAT THE HARMONY FORMED THEREFROM
07300	IS MODAL.  $FOLLOWING IS AN EXAMPLE OF MODAL AND TONAL TREATMENTS
07400	OF THE SAME MELODIC FRAGMENT.
07500	
07600	************** EXPAND A BIT ON 'MODAL' ***********
07700	
07800	$EXAMPLES 43A,B.  $BACH, $CHORALE 28
07900	
08000	
08100	
08200		$THE ANALYSIS OF THE FIRST PHRASE IS AS FOLLOWS:
08300	
08400	$FIGURE 43A
08500	
08600	
08700		$THE N3 IN THE THIRD CHORD MUST BE INDICATED, SINCE IT IS A
08800	DEVIATION FROM THE NORM.  $THE #3 IS SHOWN IN THE SECOND BAR, SINCE
08900	THE $V NOW BECOMES A TRUE TONAL DOMINANT.  ($THE SECOND CHORD MAY BE
09000	ANALYZED EITHER AS $I$I OR $I$V; IN ANY CASE, THE FUNCTION IS 
09100	SUBDOMINANT.)
09200	
09300		$THE LAST PHRASE GIVES:
09400	
09500	$FIGURE 43B1
09600	
09700	
09750	***$NOTE THAT THE AUXILIARY TONE $E (INSTEAD OF $E#)WEAKENS THE TONIC
09775	EFFECT OF THE F# CHORD.  $IT SEEMS TO REFER BACK TO THE MODAL $V OF
09787	THE FIRST PHRASE.
09800	
09900		$WE HEAR MUCH MORE HARMONIC ACTIVITY IN THIS PHRASE, SO OUR
10000	DIAGRAM BECOMES MORE COMPLICATED.  $IT MIGHT BE ARGUED THAT THE
10100	LAST EIGHTH NOTE OF BAR 1 DOES NOT FORM A NEW FUNCTION.  $THERE IS IN
10200	THE ALTO, HOWEVER, A VERY DISTINCTIVE LEAP OF A 4TH ACROSS THE 
10300	BAR LINE WHICH TENDS TO MAKE US HEAR THE $B AS A CHORD NOTE.  $A
10400	BROADER INTERPRETATION OF THIS PASSAGE, BASED ON THE STEPWISE
10500	MOVEMENT OF THE OUTER VOICES AT THIS POINT, WOULD LEAD US
10600	TO THE OMISSION OF BOTH THE LAST EIGHTH OF BAR 1 AND THE FIRST
10700	EIGHTH OF BAR 2 AS STRUCTURAL CHORDS.  $THUS:
10800	
10900	$FIGURE 43B2
11000	
11100	
11200	
11300		$EITHER OF THESE TWO ANALYSES OF THE LAST PHRASE IS ACCEPTABLE,
11400	THE CHOICE DEPENDING ON HOW MUCH DETAIL IS DESIRED.  $THE IMPORTANT
11500	THING IS THAT THE DETAILS BE COMPREHENDED.
11600	
11700		$MANY EXAMPLES OF MODALITY MAY BE FOUND IN 19TH-CENTURY MUSIC,
11800	ESPECIALLY IN THE WORKS OF $CHOPIN (SEE $MAZURKA #15, $OP.24, #2,
11900	SECOND SECTION, $LYDIAN MODE; $MAZURKA #26, $OP.41, #1, $PHRYGIAN
12000	MODE.)  $THESE SELF-CONSCIOUS EXOTICISMS MIGHT BE CALLED "MODAL
12100	TONALITY" (AS OPPOSED TO MAJOR-MINOR TONALITY) AND ARE MOST OFTEN PRESENTED
12200	AS CLEAR DEVIATIONS FROM THE NORM.  $THE FUNCTIONS OF THE VARIOUS
12300	MODALLY-FORMED CHORDS ARE NO DIFFERENT, BUT THESE CHORDS CAN SERVE AS
12400	DIRECT PIVOTS TO TONAL AREAS WHICH MIGHT BE MORE DISTANT FROM A GIVEN
12500	MAJOR-MINOR TONALITY.
12600	
12700	************* MENTION LATE 19TH CENT. FRENCH?
12800	
12900			-----------------------