perm filename CH2A[HHA,LCS]3 blob
sn#412593 filedate 1979-01-20 generic text, type T, neo UTF8
00100 CHAPTER II
00200
00300 DIATONIC FUNCTIONS
00400
00500 Scales and Tonality
00600
00700 A particular tonality is defined by a few essential interval
00800 relations in any succession of tones. Paradoxically, in the music
00900 here to be dealt with, the tonal center itself is not a note
01000 that need figure in any of the essential intervals. In fact, an
01100 unheard note on the tonal center may achieve its role through a
01200 kind of musical default, wherein all other possibilities are
01300 ruled out. First of all it must be realized that in tonal music
01400 the minor mode has no separate existence, but represents merely
01500 a fairly consistently appled group of alterations -- flattings --
01600 of certain parts of the major mode. These alterable parts of the
01700 major scale are the 7th, 6th, 3rd, and even the 2nd (most often
01800 as the root of the "Neapolitan" chord or as a non-chord auxiliary.)
01900
02000 Example 1
02100
02200
02300
02400
02500
02600
02700 The remaining notes, the 5th, 4th and 1st, can never be
02800 altered, as functional tones,* without causing at least a tendency
02900 to shift tonal centers. (It should be noted that chromatically
03000 raising any note of the major scale causes some tendency to shift tonality.
03100 See following chapters.) However, the presence of a potential 1st,
03200 4th and 5th may still be tonally inconclusive without
03300 the appearance of the leading tone -- major 7th of the scale.
03400 In minor keys especially, the lowered 7th may often be
03500 heard, but -- in the broadest sense -- almost always as a
03600 descending auxiliary tone.
03700
03800 Example 2
03900
04000
04100
04200
04300 Auxiliary tones will
04400 often be marked X.
04500
04600
04700
04800
04900
05000 When the b7th degree appears as a chord tone and is not, in
05100 some sense, passing downward toward the 5th, the tonal center
05200 tends to shift.
05300
05400 Example 3
05500
05600
05700
05800
05900
06000
06100
06200 Continuing this approach, we find that the tritone (augmented
06300 4th or diminished 5th) may be thought of as the tonality-defining
06400 interval, since its presence between the 4th and 7th is
06500 unique in relation to all the other intervals found between the
06600 degrees of a major scale.
06700
06800 Example 4
06900
07000
07100
07200
07300
07400
07500
07600
07700
07800
07900
08000
08100 However, one more note must be involved so that we may be
08200 made aware of the particular role of each part of the tritone.
08300 Since, in a major key, one or the other of the parts of a tritone
08400 must be the unalterable 4th of the scale, the whole step above it
08500 must be the equally unalterable 5th.
08600
08700 Example 5
08800
08900
09000
09100
09200
09300
09400
09500
09600
09700
09800 It follows that when a note is heard a half-step above either
09900 part of a tritone, it must be the tonic.
10000
10100 Example 6
10200
10300
10400
10500
10600
10700
10800
10900 Thus, in the major mode, we have two groups of three notes,
11000 either of which may suffice to define a tonal center -- the 1st,
11100 4th, and 7th, or the 5th, 4th, and 7th. It must be noted that
11200 these intervals need not occur between adjacent tones only.
11300 Other less critical notes may separate these scale degrees
11400 within a melodic unit. An important thing to remember is that the
11500 tritones formed as the result of the alterations (flattings) that
11600 create the minor scale do not serve the same purpose of tonic
11700 definition. Of course, composers often take advantage of this
11800 obvious possibility of ambiguity in order to shift tonics. The
11900 "altered" notes in the original dey become "unaltered" notes in
12000 the new key, etc.
12100
12200 Example 7
12300
12400
12500
12600
12700
12800
12900
13000
13100
13200
13300
13400 The next example shows how the various temporary tonics of
13500 a some what chromatic line might be ascertained. Among the notes
13600 heard in measure 17 and first two beats of measure 18, two
13700 tritone relations may be found -- Ab-D and F-B.
13800
13900 Example 8. Mozart, Sonata in F, K.189e (280), first movement.
14000
14100
14200
14300
14400
14500
14600
14700
14800
14900
15000
15100
15200
15300
15400
15500
15600
15700
15800
15900 It is clear that the Ab-D cannot be the critical tritone, since
16000 the E!, a whole step above D, rules out Eb as tonic. The context
16100 of the passage makes it doubtful that Ab could be interpreted as
16200 G#, because the G! is a normal goal for the flatted sixth
16300 in C Major-minor. No such problems come with the interpretation
16400 of (G)-F-B-(C) as the tonic-defining intervals, and so C is the
16500 tonic at that point. It should be seen that there is no reason
16600 to indicate the tritone relation between notes such as the E and
16700 Bb of measure 18. The E! becomes altered to Eb and unless
16800 there is some reason to call the Eb now D#, there is no tonic-defining
16900 element present, but rather a move into the minor mode. The same
17000 line of thought will apply to the rest of the passage, due to
17100 its sequential nature.
17200
17300 The preceding discussion has been in terms of a succession
17400 of tones == a melodic line. The same things prove to be tru
17500 when dealing with the interval relations in chord progressions,
17600 since chords, in tonal music, may be thought of as simultaneous
17700 vertical occurrences of scale parts. Every chord progression
17800 is inextricably bound up with linear implications; chords grow
17900 out of the verticalization of melodic combinations and melodies
18000 are directed so as to serve the purposes of particular chord
18100 progressions. Since music never exists in a static form, the
18200 linear impulse -- the impulse to move forward -- is always
18300 predominant. However, early in the history of tonal music the
18400 relationships of the vertical elements became so conventional that
18500 their abstract manifestations were clear to all. Strike any
18600 dominant 7th chord before even the most untrained listeners
18700 and they will be able to sing back the notes of the expected tonic
18800 chord, but without any particular regard for voice leading between
18900 the two chords. Thus in tonal music the simple melodic impulse
19000 must share primacy with the impulse of the harmonic progression.
19100
19200 --------------------------
19300
19400 Harmonic Functions
19500
19600
19700 Harmonic functions are the basic relationships between the
19800 chords -- the relationships of the roots. It is not inferred that the
19900 roots are to be heard as a kind of imagined bass line. Nevertheless, the
20000 roots might be called the generating tones of each chord, in that their
20100 relationships to the tonic note usually give fair representation of
20200 each chord's function. Chords seem to be less stable -- that is,
20300 they tend to move on to other chords -- when the 3rd, 5th, or 7th appears
20400 in the bass. In fact, the simple 6-4 position (with the 5th in the
20500 bass) most often has no independent existence.* Usually the upper two
20600
20700 notes of such a chord act as appoggiaturas or neighboring notes to
20800 a following chord.
20900
21000
21100 Example 7
21200 Note that this is the opposite
21300 situation from that wherein a
21400 sustained bass pedal point may
21500 have little or no influence on
21600 the details of harmonic function.
21700
21800
21900 Another frequent usage of the 6-4 chord occurs when the bass,
22000 and perhaps other notes, move in a stepwise manner. Aside from chords
22100 moving in complete parallelism, this passing 6-4 chord is the main
22200 formation that can be called a "contrapuntal" chord rather consistently.
22300
22400
22500 Example 8
22600 In a detaled analysis, the
22700 numerals for chords that are felt
22800 to be passing or non-functional
22900 should appear in parentheses.
23000
23100
23200
23300
23400 Of course chords in other positions may be found in similar
23500 usage, but the basic acoustical situation caused by the interval
23600 of the 4th with the bass has apparently led composers away from a freer
23700 use to the 6-4 chord.
23800 In speaking of functions, the cardinal principle to remember
23900 is that it is only the context that determines the function of each chord.
24000 When the context remains uninfluenced by the appearance of
24100 chromaticism*, the functions are usually self-evident; the labels
24200 applied by numbering the scale degrees of the roots usually give
24300 indication of the functions.
24400
24500
24600 Example 9
24700
24800
24900
25000
25100
25200
25300
25400
25500
25600
25700
25800 The two main problems that must be faced in diatonic
25900 situations have to do with substitute functions and the distinction
26000 between chord toes and consonant non-chord tones. Once the
26100 concept of substitute functions is understood, the differentiation
26200 between chord and non-chord tones should offer little difficulty
26300 (until we reach music written near the end of the tonal
26400 era). When doubt occurs, the simplest choice (that is, the one
26500 closest to the most common progression) is usually the right one.
26600
26700 --------------
26800
26900 Substitute Functions
27000
27100 Substitute functions occur in those situations where the notes
27200 of one chord are found in a context that indicates the function of
27300 another chord. The intuitive use of substitute functions may have
27400 grown out of a need for a kind of process of abbreviation that
27500 could be applied to both harmonic and melodic situations. Usually the
27600 dominant function is involved. The VII chord often carries a
27700 dominant feeling and can be considered as an abbreviated V7. The small
27800 s following a Roman numeral gives indication of substitute
27900 function.
28000
28100 Example 10
28200 In a very detailed analysis, the designation
28300 of a chord according to its makeup should
28400 appear in parentheses below the indication
28500 of its function.
28600
28700
28800
28900
29000 When the 13th of an incomplete V chord leaps directly to the
29100 tonic a 3rd below, we may often consider it to be an abbrevation of a
29200 three-note scale movement.*
29300
29400
29500 Example 11
29600
29700
29800
29900
30000
30100
30200
30300
30400
30500
30600 Abbreveations depend on their context for specificity and so
30700 are somewhat more subtle than their sources. The VII b7 chord is
30800 almost always heard as an abbreviated V b9. But in this abbreviated
30900 form it can function as the dominant to any of four different tonics,
31000 depending only on where the composer leads it.
31100
31200 Example 12
31300
31400
31500
31600
31700
31800
31900
32000
32100
32200
32300 Similarly, even the II triad in the minor may sometimes be
32400 heard as the upper three notes of an incomplete V b9.
32500
32600 Example 13
32700
32800
32900
33000
33100
33200
33300
33400
33500
33600
33700
33800
33900
34000 When the diminished 7th chord appears in its 2nd inversion
34100 (VII 4-b3) and moves to I in root position, the strong bass
34200 movement from 4 to 1 gives the impression of a plagal cadence. In
34300 such a case VII seems to be substituting for IV.
34400
34500 Example 14
34600
34700
34800
34900
35000
35100
35200
35300
35400
35500
35600
35700
35800
35900 Likewise, the VII b7 may gain something of the subdominant
36000 function when it moves from its 3rd inversion to the root position of
36100 the dominant or tonic.
36200
36300 Example 15
36400
36500
36600
36700
36800
36900
37000
37100
37200
37300
37400
37500
37600
37700 Another important substitution for the dominant function is
37800 the tonic 6-4 chord. This usually is heard as an abbreviation
37900 of the conventional formula I 6-4, V. Quite often a composer will
38000 bring the music to the I 4-6 chord, but head off in another
38100 direction before taking the time for the resolution to the V. The best
38200 example of this comes at the beginning of the Classic concerto
38300 cadenza. In rare instances, the music continues directly to the tonic
38400 in root position or 1st inversion.
38500
38600 Example 16
38700
38800
38900
39000
39100
39200
39300
39400
39500
39600
39700
39800 The case of the III chord of the major implying the V13 or
39900 I7 presents a somewhat different problem. In completely diatonic
40000 situations the III chord seems "stronger" than only the VII.
40100 Probably this is partly due to the identification of its root and 3rd
40200 with the I chord and its 3rd and 5th with the V chord. The existence
40300 of this triad as a true III function (i.e., not as a substitute
40400 for V or I) is fairly rare outside of sequential patterns with 4th or
40500 5th related roots (see Example 9). When the root of III, appearing
40600 in a melodic role, move to I, III frequently carries a
40700 dominant function.
40800
40900 Example 17