$HARMONIC FUNCTIONS ARE THE BASIC RELATIONSHIPS BETWEEN THE
CHORDS -- THE RELATIONSHIPS OF THE ROOTS.  $IT IS NOT INFERRED  THAT THE
ROOTS ARE TO BE HEARD AS A KIND OF IMAGINED BASS LINE.  $NEVERTHELESS, THE
ROOTS MIGHT BE CALLED THE GENERATING TONES OF EACH CHORD, IN THAT THEIR
RELATIONSHIPS TO THE TONIC NOTE USUALLY GIVE FAIR REPRESENTATION OF
EACH CHORD'S FUNCTION.  $CHORDS SEEM TO BE LESS STABLE -- THAT IS,
THEY TEND TO MOVE ON TO OTHER CHORDS -- WHEN THE 3RD, 5TH, OR 7TH APPEARS
IN THE BASS.  $IN FACT, THE SIMPLE 6-4 POSITION (WITH THE 5TH IN THE
BASS) MOST OFTEN HAS NO INDEPENDENT EXISTENCE.*  $USUALLY THE UPPER TWO 
NOTES OF SUCH A CHORD ACT AS APPOGGIATURAS OR NEIGHBORING NOTES TO
A FOLLOWING CHORD.


$EXAMPLE 7

					$NOTE THAT THIS IS THE OPPOSITE
					SITUATION FROM THAT WHEREIN A
					SUSTAINED BASS PEDAL POINT MAY
					HAVE LITTLE OR NO INFLUENCE ON
					THE DETAILS OF HARMONIC FUNCTION.



	$ANOTHER FREQUENT USAGE OF THE 6-4 CHORD OCCURS WHEN THE BASS,
AND PERHAPS OTHER NOTES, MOVE IN A STEPWISE MANNER.  $ASIDE FROM CHORDS
MOVING IN COMPLETE PARALLELISM, THIS PASSING 6-4 CHORD IS THE MAIN
FORMATION THAT CAN BE CALLED A "CONTRAPUNTAL" CHORD RATHER CONSISTENTLY.



$EXAMPLE 8


					$IN A DETALED ANALYSIS, THE
					NUMERALS FOR CHORDS THAT ARE FELT
					TO BE PASSING OR NON-FUNCTIONAL
					SHOULD APPEAR IN PARENTHESES.



	$OF COURSE CHORDS IN OTHER POSITIONS MAY BE FOUND IN SIMILAR
USAGE, BUT THE BASIC ACOUSTICAL SITUATION CAUSED BY THE INTERVAL
OF THE 4TH WITH THE BASS HAS APPARENTLY LED COMPOSERS AWAY FROM A FREER
USE TO THE 6-4 CHORD.

	$IN SPEAKING OF FUNCTIONS, THE CARDINAL PRINCIPLE TO REMEMBER
IS THAT IT IS ONLY THE CONTEXT THAT DETERMINES THE FUNCTION OF EACH CHORD.
$WHEN THE CONTEXT REMAINS UNINFLUENCED BY THE APPEARANCE OF
CHROMATICISM*, THE FUNCTIONS ARE USUALLY SELF-EVIDENT; THE LABELS
APPLIED BY NUMBERING THE SCALE DEGREES OF THE ROOTS USUALLY GIVE
INDICATION OF THE FUNCTIONS.



$EXAMPLE 9




	$THE TWO MAIN PROBLEMS THAT MUST BE FACED IN DIATONIC
SITUATIONS HAVE TO DO WITH SUBSTITUTE FUNCTIONS AND THE DISTINCTION
BETWEEN CHORD TOES AND CONSONANT NON-CHORD TONES.  $ONCE THE
CONCEPT OF SUBSTITUTE FUNCTIONS IS UNDERSTOOD, THE DIFFERENTIATION
BETWEEN CHORD AND NON-CHORD TONES SHOULD OFFER LITTLE DIFFICULTY
(UNTIL WE REACH MUSIC WRITTEN NEAR THE END OF THE TONAL
ERA).  $WHEN DOUBT OCCURS, THE SIMPLEST CHOICE (THAT IS, THE ONE
CLOSEST TO THE MOST COMMON PROGRESSION) IS USUALLY THE RIGHT ONE.

                       --------------


$SUBSTITUTE $FUNCTIONS

	$SUBSTITUTE FUNCTIONS OCCUR IN THOSE SITUATIONS WHERE THE NOTES
OF ONE CHORD ARE FOUND IN A CONTEXT THAT INDICATES THE FUNCTION OF
ANOTHER CHORD.  $THE INTUITIVE USE OF SUBSTITUTE FUNCTIONS MAY HAVE
GROWN OUT OF A NEED FOR A KIND OF PROCESS OF ABBREVIATION THAT
COULD BE APPLIED TO BOTH HARMONIC AND MELODIC SITUATIONS.  $USUALLY THE
DOMINANT FUNCTION IS INVOLVED.  $THE $V$I$I CHORD OFTEN CARRIES A
DOMINANT FEELING AND CAN BE CONSIDERED AS AN ABBREVIATED $V7.  $THE SMALL
S FOLLOWING A $ROMAN NUMERAL GIVES INDICATION OF SUBSTITUTE
FUNCTION.

$EXAMPLE 10

				$IN A VERY DETAILED ANALYSIS, THE DESIGNATION
				OF A CHORD ACCORDING TO ITS MAKEUP SHOULD
				APPEAR IN PARENTHESES BELOW THE INDICATION
				OF ITS FUNCTION.


	$WHEN THE 13TH OF AN INCOMPLETE $V CHORD LEAPS DIRECTLY TO THE
TONIC A 3RD BELOW, WE MAY OFTEN CONSIDER IT TO BE AN ABBREVATION OF A
THREE-NOTE SCALE MOVEMENT.*


$EXAMPLE 11










	$ABBREVEATIONS DEPEND ON THEIR CONTEXT FOR SPECIFICITY AND SO
ARE SOMEWHAT MORE SUBTLE THAN THEIR SOURCES.  $THE $V$I$I B7 CHORD IS
ALMOST ALWAYS HEARD AS AN ABBREVIATED $V B9.  $BUT IN THIS ABBREVIATED
FORM IT CAN FUNCTION AS THE DOMINANT TO ANY OF FOUR DIFFERENT TONICS,
DEPENDING ONLY ON WHERE THE COMPOSER LEADS IT.


$EXAMPLE 12











	$SIMILARLY, EVEN THE $I$I TRIAD IN THE MINOR MAY SOMETIMES BE
HEARD AS THE UPPER THREE NOTES OF AN INCOMPLETE $V B9.


$EXAMPLE 13









	$WHEN THE DIMINISHED 7TH CHORD APPEARS IN ITS 2ND INVERSION
($V$I$I 4-B3) AND MOVES TO $I IN ROOT POSITION, THE STRONG BASS
MOVEMENT FROM 4 TO 1 GIVES THE IMPRESSION OF A PLAGAL CADENCE.  $IN
SUCH A CASE $V$I$I SEEMS TO BE SUBSTITUTING FOR $I$V.


$EXAMPLE 14










	$LIKEWISE, THE $V$I$I B7 MAY GAIN SOMETHING OF THE SUBDOMINANT
FUNCTION WHEN IT MOVES FROM ITS 3RD INVERSION TO THE ROOT POSITION OF
THE DOMINANT OR TONIC.


$EXAMPLE 15











	$ANOTHER IMPORTANT SUBSTITUTION FOR THE DOMINANT FUNCTION IS
THE TONIC 6-4 CHORD.  $THIS USUALLY IS HEARD AS AN ABBREVIATION
OF THE CONVENTIONAL FORMULA $I 6-4, $V.  $QUITE OFTEN A COMPOSER WILL
BRING THE MUSIC TO THE $I 4-6 CHORD, BUT HEAD OFF IN ANOTHER
DIRECTION BEFORE TAKING THE TIME FOR THE RESOLUTION TO THE $V.  $THE BEST
EXAMPLE OF THIS COMES AT THE BEGINNING OF THE $CLASSIC CONCERTO
CADENZA.  $IN RARE INSTANCES, THE MUSIC CONTINUES DIRECTLY TO THE TONIC
IN ROOT POSITION OR 1ST INVERSION.


$EXAMPLE 16














	$THE CASE OF THE $I$I$I CHORD OF THE MAJOR IMPLYING THE $V13 OR
$I7 PRESENTS A SOMEWHAT DIFFERENT PROBLEM.  $IN COMPLETELY DIATONIC
SITUATIONS THE $I$I$I CHORD SEEMS "STRONGER" THAN ONLY THE $V$I$I.
$PROBABLY THIS IS PARTLY DUE TO THE IDENTIFICATION OF ITS ROOT AND 3RD
WITH THE $I CHORD AND ITS 3RD AND 5TH WITH THE $V CHORD.  $THE EXISTENCE
OF THIS TRIAD AS A TRUE $I$I$I FUNCTION (I.E., NOT AS A SUBSTITUTE
FOR $V OR $I) IS FAIRLY RARE OUTSIDE OF SEQUENTIAL PATTERNS WITH 4TH OR
5TH RELATED ROOTS (SEE $EXAMPLE 9).  $WHEN THE ROOT OF $I$I$I, APPEARING
IN A MELODIC ROLE, MOVE TO $I, $I$I$I FREQUENTLY CARRIES A
DOMINANT FUNCTION.


$EXAMPLE 17