Principles of Counterpoint

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, each member must 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 compelling results.)
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 example, the soprano presents a chorale melody in long notes, the alto develops a neighbor note motive, and the bass has a repeated note motive. (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 the case of non-motivic counterpoint, the difference in the prevailing rhythmic values suffices to set the layers apart.




In this example, typical of a mixed species exercise, each part has its own rhythm. (Note: The “liberties” at the end – the change of chord on the last beat of bar 3, and the accented passing tone on the downbeat in bar 4 – are musically fluent and logical, and should not be prohibited.)


This issue of the degree of similarity between strands in a contrapuntal texture leads us to a new concept here: the notion of musical “planes”. A plane is defined as a musical strand, consisting of one or more parts, which is highly unified in its material. N.B.: The number of planes and the number of real parts (or “voices”) do not necessarily correspond. For example, in Ach wie nichtig, ach wie flüchtig, from Bach’s Orgelbuchlein,the top part contains the chorale melody in long values, the two middle parts imitate each other using a scale motive in 16th notes, and the bass is organized around another motive entirely. In this case, we have three rhythmic and timbral planes, but four parts. To take our social analogy farther, planes can act like subsidiary groups within a community. In the case of a plane consisting of only one part, the relevant analogy would be the individual versus the group.





In this example, from my fifth smphony, the piccolo solo acts as one plane; the low string counterpoint constitutes another. The strings continue seamlessly as the piccolo finishes its phrase and the clarinet begins an answer to the piccolo. Note that such strongly contrasting, stratified counterpoint implies a fairly large form for elaboration.


A counterpoint of multiple polyphonic planes is also possible, for example, in polychoral writing, or in certain operatic ensembles. For example at the end of Act I, Scene 2, in Verdi’s 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. This chattering is itself subdivided contrapuntally into two groups, male and female. Usually, the more in dependant planes there are, the simpler they are, so as not to clog the texture.
For an even more extreme example, see 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 more obscure the overall momentum of the music becomes. (Hence the inertia of Ligeti’s “micropolyphony”.) Less coordinated lines suggest conflict, creating restlessness and tension. (There are perceptual limits: Overly dense textures tend towards inertia, particularly if there is uncertainty about which is the leading line at any given moment. The listener is reduced to trying to decipher the complexity.)
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 direction and a sense of increasingly powerful 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 comes to the foreground and an old one gradually recedes. One of the major differences between Baroque and classical orchestration is that in the former, the layout of the planes tends to be consistent over whole movements, or at least very long sections; classical composers employ more supple transitions between textures.




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 other parts or subgroups avoid, or
  • 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 continually. In studying counterpoint, there are advantages to beginning with stratified textures (there is no need to deal with the developmental implications of characteristic motives), and indeed the species approach is limited almost entirely to such layouts.




Invertible counterpoint is defined as a combination of lines, where each is melodically interesting enough to serve as a leading line and is also designed to act as a functional 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 distinct themes. Without contrast, there is no particular interest in switching the parts around.
There are two main constraints:

  1. Avoiding intervals which create incoherent or unresolved dissonances when inverted.
  2. Not exceeding the interval of inversion between the two parts. This is a direct outgrowth of the need for contrast: Exceeding the interval of inversion produces crossing when inverted, which weakens the distinctness of the inverted combination.

Inversion at intervals other 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 of its positions. The difficulty in constructing a complete fugue out of the various permutations of a given three or four part combination is mainly one of knitting the various inverted combinations into a convincing continuity. The challenge here lies in creating smooth melodic and harmonic joints. 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 also be used to represent the changing 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. Bach simply avoids placing such lines in the bass.




The study of counterpoint normally begins with vocal writing. This is logical, for several reasons:


  • Everyone has a voice; and at least minimal experience with singing.
  • All the parts will have the same timbre, and will blend without special effort, 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 would be quite hard to persuade a listener that a line begun by the violin is continued by the horn! (In the example from my fifth symphony, above, difference of timbre is reinforced by contrast of register and of rhythm.)
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 pedals either play the bass of the secondary plane, or form a separate, third plane. 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 elsewhere momentarily, but melodically the main line does not migrate.
On the other hand, in an orchestral context where timbre is constantly changing, not only will the main line migrate frequently, but subsidiary lines will 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 a fixed number of parts, and the rest filled out as good orchestration, rather than as abstract counterpoint. This opens up a whole world of musically fascinating possibilities, which we explore further in our volume on orchestration.
Finally, let us mention here the way that counterpoint in more than four or five parts can be dramatized by subdividing the whole ensemble into smaller, spatially separated groups, to create stereophonic effects, e.g. in Gabrielli. Real counterpoint in more than five parts, undivided into subgroups, is exceedingly rare; When it does appear it is usually at a climactic moment in a polychoral context.





  • Introduction
  • The pedagogy of counterpoint
  • Stylistic assumptions


  • Voice leading
  • Contour
  • Compound line
  • Accent
  • Melodic structure and ornamentation
  • Motives and coherence
  • Neutral lines


  • Richness
  • Harmonic definition
  • Modulation

Relationships between lines

  • Introduction
  • Classifications of contrapuntal texture
  • Invertible counterpoint: a special case
  • Counterpoint and orchestration

Instrumental Counterpoint

  • Range
  • Crossing
  • Specific instrumental idioms and motives

Contrapuntal forms

  • Fugue
  • Canon
  • Passacaglia and chaconne

Real world uses of counterpoint

  • Counterpoint in non-polyphonic forms

Conclusion, acknowledgments, bibliography