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CHAPTER IV
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FUNCTIONS OF THE MINOR
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.BEGIN VERBATIM

Major-minor Interchangeability
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	As stated earlier, minor scales will be treated as existing
as the result of a fairly consistent set of alterations of the
parallel major scales (see page 8 and following).  While minor
scales may not have originated in this way, it is probable that
their use in tonal music may best be approached from this point
of view.  Two alterations suffice to give the complete impression
of minor harmony -- the flatted third and the flatted sixth.  In
some cases, even the sixth need not be altered.  However, if the
sixth degree is lingered upon, the minor effect will be weakened
unless it has been flatted.  Conversely, the %4F%16 may be found in
proximity to the %4N%13 without completely destroying the major
quality.
 

	When the third or sixth of a scale is flatted and appears as
the third of a chord, there is most often no change in the function
of the chord.  The flatted seventh of the scale %2can%1 change the
function of the V chord, especially if it is used in some
ascending manner.  It is rare that a real V%4F3%1 chord is heard in a
position of structural importance.  When it exists, the V%4F3%1 usually
loses its "dominant" function, unless the composer has made a special
effort to impress upon the listener that the "leading tone" is
to be a whole step below the tonic note.  However, it is only by
examining the whole of a phrase that one can ascertain whether a
chord containing the flatted seventh of the scale is functioning
exclusively in the original minor key or rather dually in that key
and the relative major, or some other closely related key.  It
should be mentioned that the "closeness" of any two keys to one
another depends largely on just how much their scales have in
common, or sometimes %2potentially%1 have in common.  (By this is
meant, the conventional ascending and descending forms of minor scales
must %2both%1 be considered.)  Thus ↓_C_↓ is a little "closer" to ↓_G_↓ than
it is to ↓_a_↓, because only one note (the 4th) of the ↓_C_↓ scale
must be altered to produce the ↓_G_↓ scale, but two notes (the 4th and 5th)
must be altered to produce the ascending form of the ↓_a_↓ scale.
 
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Example 43
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	On the other hand, ↓_C_↓ is somewhat "closer" to ↓_a_↓ than ↓_a_↓ is to
↓_e_↓ or ↓_E_↓.  After an ↓_a_↓ tonic is established, ↓_C_↓ may be tonicized merely
by means of elements already found in the conventional
descending form of the ↓_a_↓ scale; whereas the ↓_e_↓ or ↓_E_↓ scale requires
at least D%4S%1 for its establishment.
 
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Example 44
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	In music where there is much major-minor alteration, almost
any keys may be directly related.  As to the problem of "close" or
"far", the absolute number of chromatic changes required to establish
a new key will not be so important as the question of just what
role the altered notes play in each of the scales involved.  The
problem of the larger relationships between keys will be dealt with
in subsequent chapters.
 
 
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	When we truly have a group of functions based on the natural
minor scale (i.e., third, sixth, and seventh degrees flatted both ascending
and descending), we may say that the harmony formed therefrom
is %2modal%1.  Following is an example of modal and tonal treatments
of the same melodic fragment.
 
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Examples 45a,b.  Bach, Chorale 28
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	The analysis of the first phrase is as follows:
 
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Figure 45a
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	The %4N%13 in the third chord must be indicated, since it is a
deviation from the norm.  The %4S%13 is shown in the second bar, since
the V now becomes a true tonal dominant.  (The second chord may be
analyzed either as II or IV; in any case, the function is
subdominant.) 
The last phrase gives:$$Note that the auxiliary tone E 
(instead of E%4S%1)weakens the tonic effect of the f%4S%1 chord.  
It seems to refer back to the modal V of the first phrase.$
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Figure 45b1
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	We hear much more harmonic activity in this phrase, so our
diagram becomes more complicated.  It might be argued that the
last eighth note of bar 1 does not form a new function.  There is in
the alto, however, a very distinctive leap of a 4th across the
bar line which tends to make us hear the B as a chord note.  A
broader interpretation of this passage, based on the stepwise
movement of the outer voices at this point, would lead us
to the omission of both the last eighth of bar 1 and the first
eighth of bar 2 as structural chords.  Thus:
 
.begin verbatim
 
Figure 45b2
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	Either of these two analyses of the last phrase is acceptable,
the choice depending on how much detail is desired.  The important
thing is that the details be comprehended.
 
	Many examples of modality may be found in 19th-century music,
especially in the works of Chopin (see Mazurka #15, Op.24, #2,
second section, Lydian mode; Mazurka #26, Op.41, #1, Phrygian
mode.)  These self-conscious exoticisms might be called "modal
tonality" (as opposed to major-minor tonality) and are most often presented
as clear deviations from the norm.  The functions of the various
modally-formed chords are no different, but these chords can serve as
direct pivots to tonal areas which might be more distant from an ordinary
major-minor tonality.
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