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CHAPTER II
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.CENTER			
DIATONIC FUNCTIONS
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.BEGIN VERBATIM

Scales and Tonality
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	A particular tonality is defined by a few essential interval
relations in any succession of tones.  Paradoxically, in the music
here to be dealt with, the tonal center itself is not a note
that need figure in any of the essential intervals.  In fact, an
unheard note on the tonal center may achieve its role through a
kind of musical default, wherein all other possibilities are
ruled out.  First of all it must be realized that in tonal music
the minor mode has no separate existence, but represents merely
a fairly consistently applied group of alterations -- flattings --
of certain parts of the major mode.  These alterable parts of the
major scale are the 7th, 6th, 3rd, and even the 2nd (most often
as the root of the "Neapolitan" chord or as a non-chord auxiliary.)
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Example 1
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	The remaining notes, the 5th, 4th and 1st, can never be
altered, as functional tones,$$See page zzz regarding the exception
of the Augmented Sixth Chord.$ without causing at least a tendency
to shift tonal centers.  (It should be noted that chromatically
%2raising%1 any note of the %2major%1 scale causes some tendency to shift tonality.
See following chapters.)  However, the presence of a potential 1st,
4th and 5th may still be tonally inconclusive without
the appearance of the leading tone -- major 7th of the scale.
In minor keys especially, the lowered 7th may often be
heard, but -- in the broadest sense -- almost always as a
descending auxiliary tone.
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Example 2
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.skip  11
	When the %4F%*7th degree appears as a chord tone and is not, in
some sense, passing downward toward the 5th, the tonal center
tends to shift.
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Example 3
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	Continuing this approach, we find that the %2tritone%1 (augmented
4th or diminished 5th) may be thought of as the tonality-defining
interval, since its presence between the 4th and 7th is
unique in relation to all the other intervals found between the
degrees of a %2major%1 scale.
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Example 4
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.skip 10
	However, one more note must be involved so that we may be
made aware of the particular role of each part of the tritone.
Since, in a %2major key%1, one or the other of the parts of a tritone
must be the unalterable 4th of the scale, the whole step above it
%2must%1 be the equally unalterable 5th.
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Example 5
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.skip 7
	It follows that when a note is heard a half-step above either
part of a tritone, it must be the tonic.
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Example 6
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.skip 6
	Thus, in the major mode, we have two groups of three notes,
either of which may suffice to define a tonal center -- the 1st,
4th, and 7th, or the 5th, 4th, and 7th.  It must be noted that
these intervals need not occur between %2adjacent%1 tones only.
Other less critical notes may separate these scale degrees 
within a melodic unit.  An important thing to remember is that the
tritones formed as the result of the alterations (flattings) that
create the %2minor%1 scale do not serve the same purpose of tonic
definition.  Of course, composers often take advantage of this
obvious possibility of ambiguity in order to shift tonics.  The
"altered" notes in the original key become "unaltered" notes in
the new key, etc.
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Example 7
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.skip 7
	The next example shows how the various temporary tonics of
a somewhat chromatic line might be ascertained.  Among the notes
heard in measure 17 and the first two beats of measure 18, two
tritone relations may be found -- A%4F%1-D and F-B.

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Example 8.  Mozart, Sonata in F, K.189e (280), first movement.
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.skip 12
	It  is  clear  that the A%4F%1-D cannot be the critical tritone, since
the E%4N%1, a whole step above D, rules  out E%4F%1 as tonic.  The context of  the
passage makes it doubtful that A%4F%1 could be interpreted as G%4S%1, because  the
G%4N%1 is a  normal goal  for the  flatted sixth  in C  Major-minor.  No  such
problems come with the interpretation of (G)-F-B-(C) as the tonic-defining
intervals, and so C is  the tonic at that point.   It should be seen  that
there is no reason to indicate the tritone relation between notes such  as
the E and B%4F%1 of measure 18.  The E%4N%1 becomes altered to E%4F%1 and unless there
is some reason to call the E%4F%1  now D%4S%1, there is no tonic-defining  element
present, but rather a move into the minor mode.  The same line of  thought
will apply to the rest of the passage, due to its sequential nature.

	The preceding  discussion  has  been  in  terms of a succession of
tones -- a melodic  line.  The same  things prove to  be true when  dealing
with the interval relations in chord progressions, since chords, in  tonal
music, may be  thought of  as simultaneous vertical  occurrences of  scale
parts.  Every  chord  progression is  inextricably  bound up  with  linear
implications;  chords  grow   out  of  the   verticalization  of   melodic
combinations and melodies  are directed  so as  to serve  the purposes  of
particular chord progressions.  Since music never exists in a static form,
the  linear  impulse  --  the  impulse  to  move  forward  --  is   always
predominant.   However,  early   in  the  history   of  tonal  music   the
relationships of the vertical elements  became so conventional that  their
abstract manifestations were clear to all.  Strike any dominant 7th  chord
before even the  most untrained listeners  and they will  be able to  sing
back the notes  of the expected  tonic chord, but  without any  particular
regard for voice leading between the two chords.  Thus in tonal music  the
simple melodic impulse must share primacy with the impulse of the harmonic
progression.

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.BEGIN VERBATIM

Harmonic Functions
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	Harmonic functions are the basic relationships between the
chords -- the relationships of the %2roots%1.  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 %4A%1 position (with the 5th in the
bass) most often has no independent existence.$$See section on substitute
functions, p.zzz.$  Usually the upper two
notes of such a chord act as appoggiaturas or neighboring notes to
a following chord.


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Example 9
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	Another frequent usage of the %4A%1 chord occurs when the bass,
and perhaps other notes, move in a stepwise manner.  Aside from chords
moving in complete parallelism, this passing %4A%1 chord is the main
formation that can be called a "contrapuntal" chord rather consistently.


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Example 10
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.skip 9
	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 of the %4A%1 chord.
	It must be remembered that there will always be some exceptions
to the general rules given here.  One prominent exception in regard to
the use of %4A%1 chords occurs when the lowest voice is serving in a
primarily melodic role.  In this sort of situation the lowest voice may
sometimes work as a kind of "misplaced" soprano, with the true bass line
being only implied.  Also it is not really rare to find a V chord  in the
%4A%1 position, but then the bass will usually move in a stepwise manner.
(See next example.)
	In some rather chromatic situations it may be best to give the
%4A%1 position status equal to that of other positions.  This may occur
when the usual resolution of the %4A%1 chord does not appear or when 
the chord acts as a pivot to a new tonic.
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Example 11
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.skip 9
	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,$$Since the normal usage of the minor mode includes much
chromaticism, the following discussion will generally refer to
situations in the major.$
 the functions are usually self-evident; the labels
applied by numbering the scale degrees of the roots usually give
indication of the functions.


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Example 12
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.skip 10
	The two main problems that must be faced in diatonic
situations have to do with substitute functions and the distinction
between chord tones 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.
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