Modality and the Melodic Foreground
Roger Solie
Part IV
[24] RHYTHM GAMMA 
Some uncomplicated instances:
EXAMPLE 24-1
Sym D.944/i
Sym Op.125/iv, 92
Pf Son K.333/ii
SQ H.74/ii
By Principal Four above, the second term is not generally connected forward, at any pitch-level, with a trill or a turn. The only apparent exception to this is interesting:
EXAMPLE 24-2
Ser K.388/iv, 96
If one interprets, as I do, the larger rhythm as at "A" and (in outline) "B," then
indeed we here have a genuine exception, a turn on a strong beat connecting the
2° forward to a weak beat. However, if we decide instead we have a
gavotte-rhythm here, as at "C," then the turn falls on a weak beat, as in Fl-Hp
Conc K.299/iii and Ser K.525/ii (EX 24-2). Gavotte-rhythms seem to be an auditory
analog of the visual effect known as the "Necker cube"
in that the interest lies in the ambiguity: are
alternating beats in the foreground (strong beats) or in the background (weak
beats)? Here, it's precisely the third-measure turn-figure that makes the
fourth-measure downbeat feel like the arrival of a relatively stronger beat,
calling into question the higher-level meter of the incipit.
Pitch-level 3-4-5° incipits in gamma rhythms are a Beethoven specialty:
EXAMPLE 24-3
Cons House Ov Op.124, 88
Duo WoO 27#2/i, 43
Sym Op.125/iv, 92
Str Trio Op.9#3/ii
Septet Op.20/i, 86
Most elaborations (there aren't many) in gamma, epsilon, and zeta rhythms are made with simple interpolated pitches in the basic outline. (The fact that there are few motivic elaborations of these rhythms is largely an artifact of their definition: elaborating a simple line with a repeated motive usually results in a pattern whose elements are of equal duration, which the units of these rhythms, by definition, are not.)
[25] RHYTHM EPSILON 
Some simple examples of PT incipits in this rhythm:
EXAMPLE 25-1
Bar Trio H.69/ii, trio
Vc Son Op.5#2/i, 106
SQ K.589/iv
Pf Son D.575/iv, 3
Here, in accordance with the principles above, trills and turns are permitted, so the 2nd term can be connected with the third (even though the durational pattern already does so)-except that 2°→1° trills are still avoided:
EXAMPLE 25-2 (representative
examples)
Rondo, Vn & orch, K.269, 43
Minuet WoO 9/#4
Pf Son K.283/iii
Pf Son K.545/ii
Pf Son Op.31#3/i, 65
SQ K.589/i
Sym H.82/i, 70
[26] RHYTHM ZETA 
Simple examples of PTs in this rhythm:
EXAMPLE 26-1
SQ H.77/ii
SQ K.499/iv, 44
Str Trio Op.3/iv, 35
Pf Son D.279/i, 45
Even though there is nothing to forbid them, not many trills and especially few
turns occur on the second note-the nontonic pitch-of this rhythm, apparently
because there's usually too little time. That is, there are very few examples such
as
Instead, one frequently finds
turn-ornaments and written-out turn-figures applied to the first note, or
to the end of it, often with the second pitch delayed and shortened:
EXAMPLE 26-2
Sym K.338/ii
Pf Son H.36/i, 12
Vn-Pf Conc K.315f, 99
Sym Op.36/i, 34
Pf Conc Op 73/i, 11
Pf Conc K.482/i, 77
Ob 4t K.370/i
Pf Conc K.415/i, 93
Vn Son K.376/i, 48
Pf Conc K.503/i, 170
Pf Conc K.491/iii, 165
Pf Son K.331/i, var vi
The only genuine turns I find on the nontonic note are shown in:
EXAMPLE 26-3
Entf
K.384 / #16
Str 5t sketch K.514a
and also Bar Trio H.83/i (EX 23-3)
Presumably for similar reasons, trills in this rhythm are likewise relatively infrequent; here are basically all of them:
EXAMPLE 26-4
2-Pf Conc K.365/iii, 45
Vc Son Op.69/i, 65
Vn Son K.296/iii
BarTrio H.76/i
BarTrio H.90/i
Pf-Orch Rondo, K.386
One of the very few incipit [3°- trilled 2° -1°] PT formations in this whole repertory, and the only weak-beat example, occurs in the final incipit of EX 26-4 (the Pf-Orch Rondo, K.386). (For the other two, see ¶ [27] just below.)
[27] RHYTHM DELTA
(the nontonic "dissonance" occurring in the strongest metric position) 
Representative uncomplicated examples:
EXAMPLE 27-1
Vn Conc Op.61/ii
SQ H.37/ii, trio
SQ K.170/ii
Lied D.911/#1, 71
There occur very few trills or turns on the nontonic pitch-the second note-in PTs in this rhythm, presumably for the reasons of metric stability mentioned above. The only two I find, both off db0, are given in
EXAMPLE 27-2
Sym H.64/iii
Vn Son K.306/iii, 30
It's odd that, even though off db0, both of these should be the otherwise avoided 2°→1° trill, although if the reason this trill is avoided in 321° PT incipits is because the 2°→1° trill is saved as a closing gesture, then there is less reason to avoid it when the 1° arrives less conclusively on a weak beat.
It's clear from examples like these that sometimes a trill, like other quick ornaments, functions to stress a note, to mark out a relatively strong beat that might otherwise be masked (in these two cases, by the contour), and/or to establish the beginning of a rhythmic group. How one systematically distinguishes between a trill that connects a weak beat forward to a stronger, and one that serves to mark a relatively strong beat that might otherwise be misinterpreted, I'm not sure. (And of course, sometimes trills and other ornaments stress a relatively weak beat that is also meant to connect forward). The use of the 2°→1° trill in the two examples above seems related to its use with an NT-figure in the two incipits below:
(EXAMPLE 27-2)
Pf Son H.37/i
Vn Son K.296/i, 44
On the other hand, if a trill is required to stress the midbar 2° in K.306/iii, 30 in this example, why is it not similarly required in Pf Conc K.503/iii, 163 (EX 27-2)?
[28] | RHYTHM ETA (the middle note here represents the nontonic
"dissonance"; the end-accented rhythm 
ends on a tonic
pitch which is, unless noted, db0)
Some straightforward examples:
EXAMPLE 28-1
Schspl K.484/#4, 6
Pf Trio H.11/i, 60
Pf Son Op.106/i, 62
Waltz D.779/#15
Trills and turns should be quite possible in this rhythm, and they do indeed occur:
EXAMPLE 28-2
trills:SQ Op.132/iii,47
Bar Trio H.107/ii
Contradance K.267/#2, 16
turns: BarTrio H.4/ii
Lira Conc H.4/i
Idomeneo K.366/#9
Notice that most of these are off db0, evidently because the relative metric hierarchy in a 3-note group, of which the second bears a trill or a turn, is presumptively 1-3-2 (as in an alpha rhythm), while a two-note upbeat to db0 must be readily understandable as 2-3-1 or 2-2-1, metrically. The reasoning behind the Mozart K.267 example would be that in a gavotte you want the (notated) downbeats weakened, and the (notated) midpoint weak-beats strengthened, to achieve the gavotte-rhythm equipoise and ambiguity; and that's what the trill here does: weakens somewhat the third note with respect to the first.
On the 5°-8° region of the scale
[29]
5678° incipits in general
There are relatively few obvious general principles behind the treatment of individual pitches in PT-formations in this region of the scale, and it does not seem necessary to sort them out by rhythmic type, as we have done for PT incipits in the 1-5° region.
The one dominating principle is that the 7° ought not to be separated from the
8°. Thus the few trills and turns that occur within 5-6-7-8° incipits are
preponderantly on the 7°, tying it forward to the tonic, as in Sym H.71/i, 8
(EXAMPLE 29-1) A standard 4-note turn on
the 6° would tend to tie the 7° back, so we don't find: 
However, a five-note turn which includes both
6° and 7° obviously preserves or strengthens the 7°-8° connection
and so this kind of turn on 6° is useful: Pf Son Op.22/iii, and Vn Son
K.301/i, 44 (EX 29-1). And a trill on 6° which follows a pre-established
pattern, is counteracted by the dotted rhythm (which connects 7° to 8°),
and occurs after db0, apparently does not contradict this principle: SQ
K.458/ii, trio (EX 29-1).
Incomplete 5-8° figures:
These are incipits with pseudo PT-figures that proceed [5-7-8°] or
[5-6-8°]. Most of these (roughly 22) are [5-7-8°]-figures:
EXAMPLE 29-2
SQ H.36/ii
SQ K.159/i
Cl-Pf Trio Op.11/i, 47
SQ D.112/iv
There are at least four examples of [5-6-8°]-figures:
(EXAMPLE 29-2)
Bar Trio H.15/iii
Sym H.100/i, 24
Lied D.776, 8
Pf Son D.845/iii, trio, 4
Notice that in these the middle term-6° or 7°-can be metrically either weak or strong with respect to the third pitch, the 8° (cf. ¶ [30] just below).
[30] 8-7-6-5° incipits in general
In these, a trill can act to group the 6° forward (and thus the 7° back
with the tonic), or instead it can connect the 7° forward to the 6°. I
haven't found any deep principles here; there aren't many incipits in total to
work from, except in rhythms like beta, where the figure works out well
harmonically:
EXAMPLE 30-1
Pf Trio H.6/ii
SQ H.35/ii, trio
Vn Conc H.3/ii
Sym K.162/i, 38
Pf Son D.279/i
Incomplete 8-5° figures (viz, 8-6-5° or 8-7-5°):
Here, there are many [8-6-5°] examples; in most (but not all) the 6° is
metrically weak with respect to the following 5°:
EXAMPLE 30-2
Bar Trio H.39/ii
Sym H.58/iv
Pf Son Op.27#1/iv
Sym Op.125/ii, 438
In the [8-7-5°]'s, the 7° is usually (but not always) stronger than the 5°:
(EXAMPLE 30-2)
Sym H.42/iii
Don G. K.527/#23, 16
Sym Op.125/iv, 851
Waltz D.146/#8
[31]
We have, in summary, been able to say about PT-figures in this repertory:
In general, very little residue of the special treatment afforded to the 4-5°, 2-3°, or 2-1° progressions in AP- and NT-figures appears to remain when they occur within PT-formations. The only real hint of special treatment for the 4-5° step might be that only Beethoven writes 3-4-5° gamma rhythms (¶ [24]).
In spite of the many ways these simple three-note scale-fragments might be elaborated, we have found it useful to speak of a few common methods: the addition of a trill or turn, elaborations by motive (generally with alpha rhythms), articulated elaborations (mostly at the 1-2-3° pitch-level, as in [1-2°, 2-3°] ), and elaborations by interpolated pitches.
In alpha-rhythm 1-2-3° and 5-4-3° PT-figures, the middle term-the one containing the "nontonic" pitch-is generally pivoted, rather than grouped back or forward with a trill or a turn, except that a 6/8 turn-figure is quite possible here.
In incipit 3-2-1° PT-figures of any rhythm, the 2° is not trilled (but a turn on the 2° readily occurs).
In rhythms in which the second term is not weaker than the third term-i.e., beta, delta, and gamma rhythms-the middle term of a PT-figure, the nontonic note, does not generally carry a trill or a turn.
In 5-6-7-8° PT formations, the 7° is not tied back (away from the tonic) by a trill or turn on the 6°.
[32] Concluding
What we have established can hardly be considered a complete account of the modal
principles in Classic melody. [19]
We have considered themes by just four composers, in the major mode only, and by
no means all of those. We now have a few principles to which to appeal, to account
for certain cases of failed translation, of "diatonic transposition" applied to a
perfectly satisfactory Classic theme producing an unsatisfactory result. A melody
beginning
is so unsatisfactory compared to its original, Schubert's Rosamunde D797/ballet, 139 (EX 20-2), for example, because it attempts, via a turn-figure, to connect forward the 2° in a 1-2-3° alpha-rhythm incipit, which we noted (¶ [19]) is instead generally pivoted in this style.
But in many other cases we can readily devise, the reason why a given melodic fragment sits uncomfortably in a certain region of the scale remains elusive. Consider the Mozart Clarinet Concerto theme with which we began this inquiry:
and its obviously unsuccessful translation down a third:
In spite of the pages we've just spent trying to find a few modal principles, none really seem to cast any specific aspersions on the translated version, even though its inadequacy is scarcely in doubt.
It might be that the trouble with this, and many other examples one can manufacture at will, is just that it's somehow not suggestive, not fruitful; it seems to leave little room for interesting continuation, jumping with both feet on the tonic as it does already in the second measure. If we change that, we get an incipit that at least one can continue:
No one would mistake this for Mozart, but it might have been good enough for a lesser composer on a busy day. And if an incipit can be unsatisfactory, not for internal reasons, but rather because it is simply not capable of playing its part in a larger melodic scheme, then we need to learn in more detail what those larger schemes are, and exactly how they relate to the incipit.
[19] It's unclear exactly what an inquiry like this has to do with the ongoing music perception project prominent in recent music theory and psychology, especially as it attempts to map the qualities of scale-degrees in Western tonal music (for recent summaries of this literature see Cross (1997) and Lerdahl (2001, chapter 2)). How exactly, for example, does one connect a chart like that of Lerdahl (2001, p.163) representing the relative "attraction" of nontonic pitches in the diatonic major scale to the tonic pitches, with the actual practice of composers? We read on this diagram, for example, that 2° in the major key is "attracted to" the tonic more than it is to the 3° (by a ratio of .5 to .375), yet we have seen that in 123° alpha-rhythm PT situations the composers considered here prefer to poise the 2° in the middle, attached neither to the 1° nor the 3° (¶ [19]). The same chart also gives the attraction strength for 4°→5° and 6°→5° as .375, the same as for 2°→3°; yet in almost all musical circumstances we have here considered these progressions are handled quite differently, especially the 4°→5°. A chart like this may indeed perfectly embody the results of well-designed perceptual experiments on musically-experienced subjects, and let us grant that it reflects the mind of Schubert and his listeners too; in what way, then, does it influence Schubert's choice of notes?