Chapter 3: Relationships between lines
Counterpoint is often defined as the art of combining independent lines. We have already remarked that this is misleading: unless the musical texture makes sense as a whole the result will sound arbitrary or confused. To better make this point, one might use a social analogy: contrapuntal lines are like individual voices in a community, engaged in conversation. All the participants are welcome and active, but for the discussion to remain coherent requires that each member contribute without attempting to overpower the others. (Of course not all conversation is civilized, and one might attempt to musically represent such less "democratic" discourse for dramatic ends. This kind of counterpoint exists, and can even be found in classic operas, where two or more opposing points of view are represented simultaneously. But the challenge in such contexts is still to maintain overall coherence: Simply combining unrelated materials haphazardly does not require any special skill, and usually does not result in artistic interest.)
To return to the issue of linear independence, it may be measured in two (not entirely mutually exclusive) ways. First, independence may result from the motives used.
In this (instrumental) example, the soprano presents the chorale melody in long notes, the alto uses a neighbor note motive, and the bass emphasizes repeated notes. (Incidentally, note how the alto and bass deviate slightly from their respective motives at the cadence. This is typical, and contributes to setting the cadence apart from the rest of the phrase. Schoenberg calls this process "liquidation", a rather oppressive term!)
In this example, typical of a mixed species exercise, each part has its own rhythm. The "liberties" at the end (the change of chord on the last beat of bar 3, and the accented passing tone on the beat f bar 4) are musically fluent and logical, and should not be prohibited. Rather they should be explained to the student.
Finally, even a counterpoint of whole planes is possible, for example in polychoral writing, or certain operatic ensembles in Mozart and Verdi (for example at the end of Act, I Scene 2, in Falstaff, where the young Fenton lyrically sings the praises of his beloved, the other eight characters in the ensemble nervously chatter about what they will do to the wicked Falstaff.). For a more current example, the overlapping movements in some of Elliott Carter’s music, for example the Symphony of Three Orchestras.
In general, the more the individual lines or planes go their own way, the less clear is the overall momentum of the music. For this reason, when Bach wishes to prepare a climax, he often simplifies the texture: Previously independent lines begin to move in a more synchronized fashion. These more coordinated lines create clearer momentum.
Less clearly coordinated lines suggest conflict, creating restlessness and tension. Overly dense textures tend towards inertia, particularly if there is uncertainty about which is the leading line at any given moment. The listener’s effort is focussed on trying to decipher the complexity, instead of following the music’s momentum.
There are many degrees and kinds of inter-relationships between simultaneous lines and planes. The sensitive use of fine gradations along a scale of linear/planar differentiation provides many important resources in composition, particularly at moments of transition, when a new idea may come to the foreground and an old one gradually recede. One of the major differences between Baroque and classical orchestration is that in the former, the layout of the planes tends to be highly consistent over whole movements, or at least very long sections, while the classical composers employ more supple transitions between textures.
Classifications of contrapuntal texture
The layout of rhythmic and motivic planes allows a basic classification for contrapuntal textures as a whole: They may be:-
stratified: Each part or subgroup of parts uses motives which the others parts or subgroups void, or
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imitative: Material is constantly exchanged between parts.
In the first type, the ear is led melodically mainly by one part. In the second type, the leading line migrates. In studying counterpoint there are advantages to beginning with stratified textures, and indeed the species approach is limited almost entirely to such layouts. (Hence the frequent pedagogical difficulty in passing from species writing to imitative work.)
Invertible counterpoint: a special case
Invertible counterpoint is defined as a combination of lines where each is melodically interesting enough to serve as a leading line and also designed to act as a harmonic bass, in another permutation. Since the main use of invertible counterpoint is to create novelty out of an already used combination, it is important that the two lines be fairly contrasting; this is why the technique is normally used to combine different themes. Without contrast, there is no special interest in switching the parts around.There are two main restrictions required to create invertible counterpoint. The first is avoiding intervals which create incoherent or unresolved dissonances when inverted. The other — not exceeding the interval of inversion between the two parts — is a direct outgrowth of the need for contrast: Exceeding the interval of inversion produces crossing when inverted, which weakens the novelty of the inverted combination.
Inversion at other intervals than the octave or the fifteenth creates new harmonic colors; such intervals should be used specifically to create these colors. For example invertible counterpoint at the twelfth engenders an interesting play between sixths and sevenths. Invertible counterpoint at the tenth, by avoiding parallel intervals entirely, allows doubling at the third and sixth for richness without fear of creating parallel octaves and fifths.
Invertible counterpoint is best taught allowing a fairly rich harmonic vocabulary. Seventh chords are especially useful, since they have more possible inversions than simple triads, and because the second inversion is not constrained in the same way as the plain 6/4 chord.
As Tovey points out, in his magisterial discussion of invertible counterpoint (in his analysis of Bach’s Art of the Fugue), when properly designed, an invertible combination will work in all its positions. The difficulty then becomes one of smoothly knitting the inverted passages into the overall texture. In particular, the leading line must seem to lead into the inverted passage without a bump.
The most common applications of invertible counterpoint, in fugue, include countersubjects, multiple fugue subjects, and recurring episodes.
Apart from these, there are occasional examples in opera and other dramatic contexts, since the technique can be used to represent the dominance of one character over another.
We should also mention here a procedure very common in Bach, but seemingly never discussed in textbooks: we call this procedure semi-invertible counterpoint. By this we mean lines designed to be interchanged, but without being usable as bass lines.
Counterpoint and orchestration
The study of counterpoint normally begins with vocal writing. This is logical: Everyone has a voice, and all the parts have the same timbre, allowing the student to ignore questions of timbral balance and contrast. While we will consider the contrapuntal use of instrumental idioms in the next chapter, we must here examine how timbre and contrapuntal planes interact.When there is more than one tone color present, all other things being equal, the ear separates the musical texture into strands based on color differences. It is normally quite hard to persuade a listener that a line begun by the violin is continued by the horn! Polytimbral writing is often associated with stratified texture, as in many Bach chorale preludes for organ, where the cantus appears on one keyboard, accompanied on another rhythmic plane by a second keyboard with a different sound. The pedal either is the bass of the secondary plane, or may form a third plane on its own. What is unusual about this situation is that the listener’s attention is directed in a much more stable way to one "leading" plane. Of course harmonic events may attract attention momentarily to another part, but melodically the main line does not migrate.
On the other hand, in an orchestral context where timbre is constantly changing, not only does the main line migrate frequently, but subsidiary lines move about as well. (In fact, in an orchestral fugue the number of "real" parts can be ambiguous at times.) Further, creating an auditory landscape that is orchestrally interesting and rich may even require adding filler material, lines that fade in and out of contrapuntal writing, and perhaps even some heterophonic doubling. In this situation the best way for the student to proceed is to make a sketch of the main line, changing tone color at musically logical phrase divisions. Other parts should be sketched in without too much attention to maintaining any given number of parts, and the rest should be filled out as good orchestration rather than as abstract counterpoint. This opens up a whole world of musically fascinating possibilities, but their discussion must await our forthcoming volume on orchestration.
Finally, let us mention here the way counterpoint in more than four or five parts can be dramatized by polychoral effects, either through spatial separation (e.g. Gabrielli) or by contrasting timbral choirs, or both. Whole planes can come and go, creating a counterpoint of masses, where each plane behaves like a line in simple counterpoint. (Incidentally, ignoring the importance of such independent phrasing between parts is another major lacuna is the species approach.) In fact, as the number of parts increases, the attention which can be paid to each part individually diminishes, creating a need for subgrouping — planes - within the overall texture to maintain aural coherence.
© Alan Belkin, 2000. Legal proof of copyright exists. The material may be used free of charge provided that the author's name is included.