00100		The III as a substitute continuation of I is sometimes found
00200	in the I-III-IV progression.
00300	.begin verbatim
00400	 
00500	Examples 18a, 18b
00550	.end
00600	.skip 10
01700		In Examples 18a and 18b the functions involved are clearly
01800	similar, since the B sounds as a passing note, en route to A, in both
01900	cases.  However, with the same upper parts and a new bass line
02000	(Examples 19a and 19b) the substitute character of the III tends
02100	to disappear.  Now, due to the strength of the 5th descent in the
02200	bass, three functions might be heard instead of two.  The  tied-over C
02300	can be heard as a suspension with the following B as its resolution.
02400	.begin verbatim
02500	 
02600	Examples 19a, 19b
02700	.end
02800	.skip 10
04000		The very special effect of the %2ascending%1 3rd progression
04100	may be seen as occasional characteristic of Brahms' work.
04200	.begin verbatim
04300	 
04400	Example 20.  Brahms, Romance, Op.118,#5
04500	.end
04600	.skip 15
05600		Any two-note  chord  (or  even  a  single  note)  can  be  a
05700	substitute function whose numeral designation depends entirely on the
05800	context.  In two-part tonal counterpoint the clearly  implied  roots
05900	of  chords  are  very  often omitted.  When doubt does arise in such
06000	music,  usually  the  analysis  which  shows   the   simplest,   most
06100	conventional  progression,  or  one  which  is part of an established
06200	pattern or sequence, is the right one.
06300	.begin verbatim
06400	 
06500	Example 21
06600	.end
06700	.skip 10
07300		Quite subtle is the relationship between II, especially
07400	II 6-5, and IV.  It is clear that when the II in root
07500	position moves to V its function will not be confused with that
07600	of IV.  However, in cadential formulas the sense of II 6-5 or II 6
07700	is certainly heard as subdominant -- with the root of II being heard
07800	usually as an anticipation or added 6th or passing tone.
07900	.begin verbatim
08000	 
08100	Example 22
08200	.end
08300	.skip 10
09400		In cases as above, where the bass (and often the soprano too)
09500	moves stepwise, the problem of harmony versus counterpoint presents one
09600	of its most perplexing facets.  In Example 22 it is completely
09700	possible to conceive of the entire II 6-5 as a passing chord
09800	between the I6 and the V.  It is argued by some that all harmonies
09900	that occur over stepwise bass movement (excepting those that come
10000	at the high or low point of such movement) have no functional significance.
10100	If this view is accepted, some distinction (though not a hard an fast
10200	one) must be made between the "structural" and "contrapuntal"
10300	chords of a progression.  In situations including chromatic alteration
10400	the problem is often simplified, since in most cases the alterations
10500	serve to lead our attention to the main chords.
10600	 
10700	 
10800	                ----------------------
10900	 
11000	 
11100		The following examples serve to illustrate that the context
11200	is the chief consideration in designating the relative importance of
11300	chords.
11400	.begin verbatim
11500	 
11600	Example 23.  Mozart, Sonata in A, K.300i (331)
11700	.end
11800	.skip 12
11900	 
12000		Heard alone, the above is a simple ↓_D_↓: IV-V-I progression;
12100	but heard in its continuing context (Example 24) the I chord
12200	retrospectively becomes a pseudo 6-4 chord.  Because of the use of the
12300	A pedal at the starred (*) points and the fact that each of the two bar
12400	groups presents the A chord on the strong beats, the F# and D of the
12500	D chord, even when moved to the bass, are heard as auxiliaries to E and
12600	C# of the A chord.
12650	.begin verbatim
12700	 
12800	Example 24.
12900	.end
13000	.skip 16
13100	 
13200		Despite the two-part presentation, the essential movement of the
13300	following passage from Bach's Partita #5 is clearly heard as a
13400	descending series of chords; VI-V-IV-III-II.  Needless to
13500	say, the progression found in the details (VI-II:V7-I :IV-VII :
13600	III7-VI:II) does exist.  But the context causes us to hear the
13700	alternate chords (II,I,VII,VI) as subsidiary to the other
13800	chords.  The fact that VI-V-IV-III-II hardly constitutes an
13900	exciting harmonic progression does not alter our hearing of this
14000	passage.  It must be understood that, in the largest sense, this passage
14100	gives us a movement from VI to II.  In relative terms, the main
14200	harmonies in between are passing chords, each elaborated by chords
14300	at the 4th above.  However, the %2particular%1 effect of the
14400	example depends on the functions of all the harmonic details -- VI-II
14500	V7-I -- etc.
14550	.begin verbatim
14600	 
14700	Example 25.  Bach, Partita #5, Praeambulum
14750	.end
14800	.skip 22
14900	 
15000		Undoubtedly the internal structure of this passage may be
15100	heard on many different levels.  The number of levels may vary but,
15200	generally, the use of three in an analysis will suffice to give a clear
15300	picture of the way in which a piece can be heard.  The primary level of this
15400	sort of analysis will indicate the key of the particular area of the
15500	piece under consideration.  The secondary level will show the
15600	larger harmonic motions within the area, and the tertiary level will give
15700	virtually all the harmonic details.  The middle level will offer the
15800	greatest problems, since it is listening at this level (i.e., not
15900	concentrating on every detail and, at the same time, maintaining
16000	a harmonic awareness of more than just the end points) that the most
16100	variety occurs.  In returning to the example from the Partita we see that
16200	the first level may considered for now as ↓_C_↓: I.  Because of the clear
16300	stepwise descent of the bass from first beat to first beat of each bar,
16400	which is concluded only on the low D, we can say that the movement on
16500	the second level is simply VI-II (or alternatively, because of the
16600	patterns of the upper part, the passage may be heard in two-bar groups
16700	 -- VI-I, IV-VI, II).  The third level offers -- without
16800	going into the details of minute chord inversions -- the analysis given
16900	under the example.  Putting the three levels together we have:
16950	.begin verbatim
17000	 
17100	Figure 25
17200	.end
17300	.skip 10
17400	 
17500		1.  The key is established (although the I chord occupies no
17600	prominent position).
17700		2.  The main movement with the key is from VI to II (or the
17800	alternative mentioned above).
17900		3.  The details of harmonic elaboration are given.
18000	 
18100	             --------------
18200	 
18300		For a somewhat more complicated example we turn to a passage from
18400	Schubert's Piano Sonata in Bb (fourth movement, measure 86).
18450	.begin verbatim
18500	 
18600	Example 26
18700	.end
18800	.skip 22
18900		Here the first level gives us ↓_F_↓: I.  In cases where the
19000	second level becomes quite subtle, it is often advisable to bypass it
19100	and return later from the third level.  The third level offers no more
19200	problems than did the Bach example.  Here the progression is:
19250	.begin verbatim
19300	 
19400	Figure 26a
19500	.end
19600	.skip 10
19700		Although this passage certainly does not sound "weak", all
19800	the direct progressions in the first four bars are by 2nds and 3rds.  If
19900	wee apply the concept of substitute functions to the 3rd relations,
20000	the situation becomes more clear.  Thus III may serve for I and VI
20100	may serve for IV.  The II 6-4 is non-functional, since its upper
20200	two notes resolve stepwise to the final VI.  This may be indicated:
20250	.begin verbatim
20300	 
20400	Figure 26b
20500	.end
20600	.skip 10
20700		However, the descending figure of two notes in the soprano in
20800	each of the last four bars draws one's attention to the last note
20900	%2and%1 chord in each bar.  The first beat in each of these bars may be
21000	considered a kind of harmonized appoggiatura, even though the bass does
21100	not always move in a stepwise manner.  Now:
21150	.begin verbatim
21200	 
21300	Figure 26c
21400	.end
21500	.skip 9
21600	becomes our second level.  The three levels together form:
21650	.begin verbatim
21700	 
21800	Figure 26d
21900	.end
22000	.skip 12
22100		In the foregoing discussion, the word "levels" is used in
22200	full realization that its use in this connection could become confused with
22300	its use in the overlapping and somewhat similar realm of pure harmonic
22400	functions.  Decisions concerning the broader structural levels
22500	heard in a piece will generally be much less specific than those
22600	concerning the levels of harmonic function.  In the former
22700	category, the totality of a piece must be dealt with; in the latter,
22800	one must deal primarily with an abstraction of the relations between
22900	the vertical occurrences of a piece -- i.e., harmony.  It is
23000	believed that the development of consistent terminology for the discussion
23100	of harmonic functions must supercede the total analysis of
23200	music.  In the following chapters, "levels" will be
23300	used with regard to harmonic functions.
23400	 
23500	 
23600	                 -----------------
23650	.next page
23700	.begin verbatim
23800	 
23900	Exercises for Chapter II
24000	 
24100	I.	Write out the following passages.  Show each tritone
24200		relationship and indicate the half or whole steps on 
24250		either side of the tritone.  From this, ascertain the 
24350		various temporary tonics involved.  Follow the form 
24450		used in Example zzz on page zzz.
24600	 
24700		From the Mozart Sonatas:
24800	 
24900		1.  Sonata in Bb, K.189f(281), first movement, bar 48 to
25000				first note of bar 54 (both hands).
25100	 
25200		2.  Sonata in a, K.300d(310), last movement, bars 52-59
25300			(right hand only).
25400	 
25500		3.  Phantasie (nr.4) in c, K.475, six bars, starting
25600			from 12 before Andantino (both hands).
25700	 
25800		4.  Sonata in C, K.545, bars 29-42 (right hand only).
25900	 
26000	II.	Analyze the following diatonic passages.  Show all 
26050		substitute functions and "passing" or "contrapuntal" 
26150		chords.
26200	 
26300		From the 371 Chorales of Bach:
26400	 
26500		1.  Chorale 1, first 10 bars
26600		2.  Chorale 5, first 6 bars
26700		3.  Chorale 14, first 6 bars
26800		4.  Chorale 125, first 4 bars
26900		5.  Chorale 209, last 5 bars
27000	 
27100		From the Mozart Sonatas:
27200	 
27300		6.  Sonata in G, K.189h(283), first movement, bars 1-10
27400		7.  Sonata in G, K.189h(283) second movement, bars 1-4
27500		8.  Sonata in C, K545, third movement, last 10 bars
27600		9.  Sonata in D, K.284c(311), second movement, bars 1-11
27700	.end