Welcome :: Glossary :: About / Contact us :: Thanks / Credits :: Website plan

PART 1 - 1.1 - Genesis of the analytical model :: 1.2 - Description of the analytical model :: 1.3 - A practice of analysis in the tonal harmonic discourse from Bach to Wagner :: 1.4 - By way of a general conclusion


1.3 - A practice of analysis in the tonal harmonic discourse from Bach to Wagner ||
A) FORMULAS - 1. Definition of a formula :: 2. Presentation of the little catalogue of harmonic vocabulary :: 3. User's guide to the little catalogue and various instructions :: 4. Examples illustrating the little catalogue (motifs: 1, 2, 3, 4, 5, 6a, 6b, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, motifs in combination)
B) SEQUENCES - 1. Definition of a harmonic sequence :: 2. Classifying sequences :: 3. Melodic formulations: characteristic motifs :: 4. The tonal nature of the harmonic sequence :: 5.The tripartite structure of the harmonic sequence :: 6. A modulating sequence or not? :: 7. Diversification of harmonic content :: 8. The harmonic sequence as a place of subversion :: 9. Conclusion

7. DIVERSIFICATION OF HARMONIC CONTENT

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
a

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



a

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
a

Example 428 : J. Brahms : Symphony no 2, op. 73, I (mm 66-71)
Type 1 sequence


a

 

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
a

Example 429 : F. Chopin : Prelude, op. 28, no 17 (mm 51-57)
Type 1 sequence


a

The following example employs sometimes II, sometimes N:

Example 430 : R. Wagner : Die Walküre, Act I, Scene 1 (end)
Type 1 sequence


a

Figure 38
a

Example 431 : F. Chopin : Piano sonata no 1, op. 4, I (mm 95-97)
Type 1 sequence


a

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


a

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

See also example 398.

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:


a

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


a

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


a

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


a

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
a

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


a

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


a

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


a

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


8. THE HARMONIC SEQUENCE AS A PLACE OF SUBVERSION