The III as a substitute continuation of I is sometimes found
in the I-III-Iv progression.
 
 
Examples 18a, 18b
 
 
 
 
 
 
 
 
 
 
 
	In Examples 18a and 18b the functions involved are clearly
similar, since the B sounds as a passing note, en route to A, in both
cases.  However, with the same upper parts and a new bass line
(Examples 19a and 19b) the substitute character of the III tends
to disappear.  Now, due to the strength of the 5th descent in the
bass, three functions might be heard instead of two.  The  tied-over C
can be heard as a suspension with the following B as its resolution.
 
 
Examples 19a, 19b
 
 
 
 
 
 
 
 
 
 
 
 
 
	The very special effect of the ascending 3rd progression
may be seen as occasional characteristic of Brahms' work.
 
 
Example 20.  Brahms, Romance, Op.118,#5
 
 
 
 
 
 
 
 
 
 
 
	Any two-note  chord  (or  even  a  single  note)  can  be  a
substitute function whose numeral designation depends entirely on the
context.  In two-part tonal counterpoint the clearly  implied  roots
of  chords  are  very  often omitted.  When doubt does arise in such
music,  usually  the  analysis  which  shows   the   simplest,   most
conventional  progression,  or  one  which  is part of an established
pattern or sequence, is the right one.
 
 
Example 21
 
 
 
 
 
 
 
	Quite subtle is the relationship between II, especially
II 6-5, and IV.  It is clear that when the II in root
position moves to V its function will not be confused with that
of IV.  However, in cadential formulas the sense of II 6-5 or II 6
is certainly heard as subdominant -- with the root of II being heard
usually as an anticipation or added 6th or passing tone.
 
 
Example 22
 
 
 
 
 
 
 
 
 
 
 
 
	In cases as above, where the bass (and often the soprano too)
moves stepwise, the problem of harmony versus counterpoint presents one
of its most perplexing facets.  In Example 22 it is completely
possible to conceive of the entire II 6-5 as a passing chord
between the I6 and the V.  It is argued by some that all harmonies
that occur over stepwise bass movement (excepting those that come
at the high or low point of such movement) have no functional significance.
If this view is accepted, some distinction (though not a hard an fast
one) must be made between the "structural" and "contrapuntal"
chords of a progression.  In situations including chromatic alteration
the problem is often simplified, since in most cases the alterations
serve to lead our attention to the main chords.
 
 
                ----------------------
 
 
	The following examples serve to illustrate that the context
is the chief consideration in designating the relative importance of
chords.
 
 
Example 23.  Mozart, Sonata in A, K.300i (331)
 
 
 
	Heard alone, the above is a simple D: IV-V-I progression;
but heard in its continuing context (Example 24) the I chord
retrospectively becomes a pseudo 6-4 chord.  Because of the use of the
A pedal at the starred (*) points and the fact that each of the two bar
groups presents the A chord on the strong beats, the F# and D of the
D chord, even when moved to the bass, are heard as auxiliaries to E and
C# of the A chord.
 
Example 24.
 
 
 
	Despite the two-part presentation, the essential movement of the
following passage from Bach's Partita #5 is clearly heard as a
descending series of chords; VI-V-IV-III-II.  Needless to
say, the progression found in the details (VI-II:V7-I :IV-VII :
III7-VI:II) does exist.  But the context causes us to hear the
alternate chords (II,I,VII,VI) as subsidiary to the other
chords.  The fact that VI-V-IV-III-II hardly constitutes an
exciting harmonic progression does not alter our hearing of this
passage.  It must be understood that, in the largest sense, this passage
gives us a movement from VI to II.  In relative terms, the main
harmonies in between are passing chords, each elaborated by chords
at the 4th above.  However, the particular effect of the
example depends on the functons of all the harmonic details -- VI-II
V7-I -- etc.
 
Example 25.  Bach, Partita #5, Praeambulum
 
 
	Undoubtedly the internal structure of this passage may be
heard on many different levels.  The number of levels may vary but,
generally, the use of three in an analysis will suffice to give a clear
picture of the way in which a piece can be heard.  The primary level of this
sort of analysis will indicate the key of the particular area of the
piece under consideration.  The secondary level will show the
larger harmonic motions within the area, and the tertiary level will give
virtually all the harmonic details.  The middle level will offer the
greatest problems, since it is listening at this level (i.e., not
concentrating on every detail and, at the same time, maintaining
a harmonic awareness of more than just the end points) that the most
variety occurs.  In returning to the example from the Partita we see that
the first level may considered for now as C: I.  Because of the clear
stepwise descent of the bass from first beat to first beat of each bar,
which is concluded only on the low D, we can say that the movement on
the second level is simply VI-II (or alternatively, because of the
patterns of the upper part, the passage may be heard in two-bar groups
 -- VI-I, IV-VI, II).  The third level offers -- without
going into the details of minute chord inversions -- the analysis given
under the example.  Putting the three levels together we have:
 
Figure 25
 
 
 
	1.  The key is established (although the I chord occupies no
prominent position).
	2.  The main movement with the key is from VI to II (or the
alternative mentioned above).
	3.  The details of harmonic elaboration are given.
 
             --------------
 
	For a somewhat more complicated example we turn to a passage from
Schubert's Piano Sonata in Bb (fourth movement, measure 86).
 
Example 26
 
 
	Here the first level gives us F: I.  In cases where the
second level becomes quite subtle, it is often advisable to bypass it
and return later from the third level.  The third level offers no more
problems than did the Bach example.  Here the progression is:
 
Figure 26a
 
 
	Although this passage certainly does not sound "weak", all
the direct progressions in the first four bars are by 2nds and 3rds.  If
wee apply the concept of substitute functions to the 3rd relations,
the situation becomes more clear.  Thus III may serve for I and VI
may serve for IV.  The II 6-4 is non-functional, since its upper
two notes resolve stepwise to the final VI.  This may be indicated:
 
Figure 26b
 
 
	However, the descending figure of two notes in the soprano in
each of the last four bars draws one's attention to the last note
and chord in each bar.  The first beat in each of these bars may be
considered a kind of harmonized appoggiatura, even though the bass does
not always move in a stepwise manner.  Now:
 
Figure 26c
 
 
becomes our second level.  The three levels together form:
 
Figure 26d
 
 
	In the foregoing discussion, the word "levels" is used in
full realization that its use in this connection could become confused with
its use in the overlapping and somewhat similar realm of pure harmonic
functions.  Decisions concerning the broader structural levels
heard in a piece will generally be much less specific than those
concerning the levels of harmonic function.  In the former
category, the totality of a piece must be dealt with; in the latter,
one must deal primarily with an abstraction of the relations between
the vertical occurrences of a piece -- i.e., harmony.  It is
believed that the development of consistent terminology for the discussion
of harmonic functions must supecrede the total analysis of
music.  In the following chapters, "levels" will be
used with regard to harmonic functions.
 
 
                 -----------------
 
 
Exercises for Chapter II
 
I.	Write out the following passages.  Show each tritone
	relationship and indicate the half or whole steps on either
	side of the tritone.  From this, ascertain the various
	temporary tonics involved.  Follow the form used in
	Example zzz on page zzz.
 
	From the Mozart Sonatas:
 
	1.  Sonata in Bb, K.189f(281), first movement, bar 48 to
			first note of bar 54 (both hands).
 
	2.  Sonata in a, K.300d(310), last movement, bars 52-59
		(right hand only).
 
	3.  Phantasie (nr.4) in c, K.475, six bars, starting
		from 12 before Andantino (both hands).
 
	4.  Sonata in C, K.545, bars 29-42 (right hand only).
 
II.	Analyze the following diatonic passages.  Show all substitute
	functions and "passing" or "contrapuntal" chords.
 
	From the 371 Chorales of Bach:
 
	1.  Chorale 1, first 10 bars
	2.  Chorale 5, first 6 bars
	3.  Chorale 14, first 6 bars
	4.  Chorale 125, first 4 bars
	5.  Chorale 209, last 5 bars
 
	From the Mozart Sonatas:
 
	6.  Sonata in G, K.189h(283), first movement, bars 1-10
	7.  Sonata in G, K.189h(283) second movement, bars 1-4
	8.  Sonata in C, K545, third movment, last 10 bars
	9.  Sonata in D, K.284c(311), second movement, bars 1-11