Careful
weighing of these four criteria will prove invaluable when faced with
the great diversity of harmonic content which can affect each of the
twelve classified types of sequences.
The very nature
of the type 1 sequence which, as we have already emphasized, circulates
through a descending circle of fifths, the selfsame structure
considered to form the foundation of the tonal discourse, makes it an ideal
field for research and observation. To
begin, our study will be limited to surface variants or, in other
words, those that do not affect the sequence of roots.
a. Surface variants
The type 1 sequence from a modulating perspective
In a modulating context, this sequence can incorporate several different harmonic structures:
1.
A circle of fifths where we change keys with each chord. This event
occurs most frequently as a series of dominant- or diminished-seventh
chords. In the case of a parallelism of diminished-seventh chords, it is
sometime possible, depending on the context, to assign to the passage an ornamental
status that excludes harmonic movement; in ambiguous cases, we should
always refer to the criteria stated previously.
Figure 35
In figure 35, we have deliberately chosen the analysis or instead of for the sake of convenience, but essentially what we find here is an evaded
cadence gesture where the function V of IV is substituted for the
expected function I.
Example 423 : J.S. Bach : The Well-Tempered Clavier, vol. II, Prelude no 18, BWV 887 (mm 33-36)
Type 1 sequence
Example 424 : Schumann : Frauenliebe und -leben, op. 42, no 2 (mm 54-60)
Type 1 sequence
Very
often we find this structure of a modulating circle of fifths amplified
in time and space within the development section of a simply constructed classical sonata form:
Example 425 : J. Haydn : Piano sonata, Hob. XVI:47, I, Moderato (mm 42-46)
Type 1 sequence
Example 426 : W.A. Mozart : Symphony no 41, "Jupiter", K. 551, IV (mm 169-189)
Type 1 sequence
Example 427 : L.V. Beethoven : Symphony no 1, op. 21, I (mm 108-122)
Type 1 sequence
2.
Formulas treated in sequence, progressing by descending steps or
half-steps. For example, one of the most common ones:
characterized
by the alternation of a minor chord (the only structure that can fill
the role of function I and function II at the same time) and a structure that
can take the role of V:
Figure 36
Example 428 : J. Brahms : Symphony no 2, op. 73, I (mm 66-71)
Type 1 sequence
characterized
by the alternation of a major chord built on the 2nd degree lowered by
a semi-tone and of a structure which can function as V:
Figure 37
Example 429 : F. Chopin : Prelude, op. 28, no 17 (mm 51-57)
Type 1 sequence
The following example employs sometimes II, sometimes N:
Example 430 : R. Wagner : Die Walküre, Act I, Scene 1 (end)
Type 1 sequence
Figure 38
Example 431 : F. Chopin : Piano sonata no 1, op. 4, I (mm 95-97)
Type 1 sequence
The type 1 sequence from a non-modulating perspective
In a non-modulating context, the type 1 sequence can appear either:
1. Without secondary functions
meaning only with chords (in root position or inversion) native to the
given key, to which altered chords, resulting from the use of the
Neapolitan chord or from the application of mode mixture, may be added
2. With secondary functions by far the most frequent among these being secondary dominants which
appear in the form of one or another of the seven structures already
identified:
Figure 39
Example 432 : F. Chopin : Prelude, op. 28, no 17 (mm 23-27)
Type 1 sequence
The secondary polarization can also be expanded and thus provoke secondary functions other than dominants:
Example 433 : J.S. Bach : The Well-Tempered Clavier, vol. I, Fugue no 6, BWV 851 (mm 9-13)
Type 1 sequence
A secondary
polarization can even, given the necessary symmetry, omit an explicit statement of the secondary tonic itself (as seen in example 432)
and continue directly on to an imitation of the model in the principal key which in turn can also be very well
established without the appearance of its tonic chord. In fact, we can say
that a key is clearly designated from the moment that its dominant
function is identified as such:
Example 434 : F. Chopin : Etude, op. 10, no 12 (mm 65-77)
Type 1 sequence
A non-modulating perspective is appropriate here given the
context (section A' of an ABA' form) of the last 44 measures of the
etude in which this fragment is situated:
This
same phenomenon (of a secondary polarization occuring without a
statement of the secondary tonic) can also be observed in the
context of other types of sequences:
Example 435 : E. Grieg : Sonata for cello and piano, op. 36, I (mm 366-390)
Type 7 sequence
Example 436 : F. Mendelssohn : Variations sérieuses, op. 54 (mm 1-4)
a) IV - V - I without the function I and b) type 4 sequence
Finally, modulating and non-modulating perspectives can be juxtaposed when
several different structures of the type 1 sequence are strung
together:
Example 437 : W.A. Mozart : Fantasy, K. 475 (mm 73-77)
Type 1 sequence
b. Core variations
All
the procedures for diversification discussed until now have done
nothing but modify the internal composition of the chords without
altering in any way the normal sequence of roots. Other modes of
variation involving the harmonic content provoke more serious
ramifications and disrupt the expected root movement, without, however,
inhibiting identification of the restructured sequence.
Once again,
it is at the instigation of the foundational pair that these core
variations, seeking to reproduce the most common substitutes for the
tonic chord in the dominant-tonic couple, will be introduced. We know
that a principal polarization is often established with the help of a
substitute for the principal tonic. In the same manner, a secondary
polarization, in comparable cases, can resort to the same substitutes,
namely those that we observe in the context of deceptive
or evaded cadences.
Let
us recall that all constitutive chords of a key (major, minor, or
mixed) that take the form of perfect chords (major or minor) as well as
the Neapolitan chord are capable of filling the role of a secondary
tonic (designated as x). In the context of a sequence, substitutes for x in the secondary pair V of x - x can be grouped into the following two categories:
1. V of x - V of the next function in the circle of fifths: 1st substitute
The expected secondary tonic chord (x) is transformed into the dominant of the function following x
in the cycle (in a sequence, this situation can only occur in the
context of a type 1 sequence). This relationship corresponds to what we
observe in a V - V of IV evaded cadence and the chain of dominant functions
can persist under the condition that the relationship between the roots of
the two chords articulates a perfect fifth. This observation implies
that the first category of substitutes results only in surface
variants which have already been illustrated in examples 397, 399 and 432.
The second category is entirely another matter.
2. V of x - VI of x or IV of x: 2nd substitute
The expected secondary tonic chord (x) is replaced by a sub-mediant or sub-dominant chord of x.
This relationship corresponds to that which we observe in the deceptive
cadence (V - VI or V - IV). In this case, at the moment where the symmetrical
treatment is interrupted, the chord acting as VI of x or IV of x will have a double function: the first with respect to the secondary
tonic and the second with respect to the principal tonic. It is from
this second function that the closing formula begins.
Example 438 : W.A. Mozart : Piano sonata, K. 280, I (mm 35-43)
Type 7 sequence
Example 439 : J.S. Bach : Orgelbüchlein, BWV 622, O Mensch, bewein' dein' Sunde gross, Adagio assai (end)
Type 7 sequence
Example 440 : F. Schubert : String quartet, Death and the Maiden, D. 810, I, Allegro (mm 15-19)
Type 7 sequence
Substituting
VI for I in the foundational pair (by far the most common substitution)
can lead to yet another form of imitation, independant of any secondary polarization:
Figure 40
Here again, the characteristic melodic motif (in the outer voices) belongs to a type 1 sequence.
Example 441 : J.S. Bach : The Well-Tempered Clavier, vol. II, prelude no 15, BWV 884 (mm 7-13)
Type 1 sequence on the model V - VI
Example 442 : J. Brahms : Intermezzo, op. 119, no 2 (mm 15-17)
Type 1 sequence on the model V - VI
Lastly,
other variants involving the content of sequences are caused by inserting
functions within a given outline that corresponds to one of the
classified types
of sequences; this graft usually takes place within the limits of an
expanded secondary polarization:
Example 443 : J. Haydn : Piano sonata, Hob XVI:37, I (mm 46-49)
Type 4 sequence with grafts
Example 444 : W.A. Mozart : Piano sonata, K. 280, I (mm 17-26)
Type 1 sequence with grafts
The abbreviation a.a. refers to the expression "altered by analogy," which will be explained later.
Example 445 : W.A. Mozart : String quintet, K. 581, III, Trio (mm 17-23)
Type 7 sequence with grafts
We can even find an entire formula grafted into a sequence.
Example 446 : W.A. Mozart : Concerto for clarinet, K. 622, II, Adagio (mm 76-83)
Type 7 sequence with a graft of the formula III-II-V-I
or 
instead of 
for the sake of convenience, but essentially what we find here is an evaded
cadence gesture where the function V of IV is substituted for the
expected function I.
