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		CHAPTER II

		DIATONIC FUNCTIONS

Scales and Tonality

A particular tonality iss 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 appled 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.)

		Example 1






The remaining notes, the 5th, 4th and 1st, can never be
altered, as functional tones,* without causing at least a tendency
to shift tonal centers.  (It should be noted that chromatically
raising any note of the major 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.

		Example 2




						Auxiliary tones will
						often be marked X.





When the b7th degree appears as a chord tone and is not, in
some sense, passing downward toward the 5th, the tonal center
tends to shift.

		Example 3







Continuing this approach, we find that the tritone (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 major scale.

		Example 4












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 major key, one or the other of the parts of a tritone
must be the unalterable 4th of the scale, the whole step above it
must be the equally unalterable 5th.

		Example 5










It follows that when a note is heard a half-step above either
part of a tritone, it must be the tonic.

		Example 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 adjacent 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 minor 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 dey become "unaltered" notes in
the new key, etc.

		Example 7











The next example shows how the various temporary tonics of
a some what chromatic line might be ascertained.  Among the notes
heard in measure 17 and first two beats of measure 18, two
tritone relations may be found -- Ab-D and F-B.

  Example 8.  Mozart, Sonata in F, K.189e (280), first movement.



















It is clear that the Ab-D cannot be the critical tritone, since
the E!, a whole step above D, rules out Eb as tonic.  The context
of the passage makes it doubtful that Ab could be interpreted as
G#, because the G! 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
Bb of measure 18.  The E! becomes altered to Eb and unless
there is some reason to call the Eb now D#, 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 tru
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.

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

Harmonic Functions