Principles of Counterpoint


The teaching of counterpoint has a long and illustrious history, but its pedagogy is all too often abstracted from musical reality. Perhaps more than any other musical discipline, counterpoint has bred ingrown academic traditions whose relevance to musical practice often seems painfully limited. For example, I recently taught fugue to a talented graduate of a major European conservatory, and discovered that his experience of counterpoint was limited to three years of exercises in 4/4 time, with canti always in whole notes. While this sort of work may be appropriate for a beginner, it hardly constitutes real preparation for composing a musically convincing fugue, or for other, “real life” applications of counterpoint.


The main problem with scholastic approaches is that they often substitute rigid rules for flexible general principles, and thus fail to provide guidance in enough varied musical situations to be useful in practice. At best, of course, an inspiring teacher can fill in the gaps and make the subject seem relevant. But at worst, the student is constrained by a hodge-podge of inconsistent rules, and wastes a great deal of time struggling to avoid situations that are musically unobjectionable. A common fault is to confuse practical rules – say, about the range of a human voice – with pedagogical stages. The former are general principles, which cannot be avoided if the music is to be performable at all; the latter are, by nature, provisional rules of thumb designed to avoid common elementary problems, or to force the student to concentrate on a particular problem and to avoid others that might be confusing. If such pedagogical constraints are presented as global rules, they lead quickly to nonsense.


Here, our aim will be to explain contrapuntal principles so as to provide the most general applications possible. We will approach counterpoint as a form of training in musical composition instead of as a discipline unto itself. We will try to define some general principles of counterpoint, in flexible ways which are transferable to real musical situations, and not limited to the style of one period.


This is not a textbook: We will not repeat, in detail, information easily available elsewhere. Also, we will not propose a detailed method, complete with exercises, although the specifics of such a method are easily derived from our approach, and indeed have been tested in the classroom for years.


In short, this book is more about the “why” of counterpoint than the “what”.


The pedagogy of counterpoint is often a confused mixture of style and method. Most approaches limit themselves more or less closely to one style, and make some attempt at graduated exercises, often derived from the species method of Fux.


Fux’s method does have pedagogical value, but its advantages are best understood independently of stylistic issues. The main advantages to the species approach, especially for beginners, are:


  • By eliminating explicit variety of rhythm in the first four species in favor of a constant, stable, harmonic rhythm, it frees the student to concentrate on matters of line and dissonance. (I say “explicit variety of rhythm” because, even in a line in steady quarter notes, leaps and changes of direction will inevitably imply some rhythmic groupings.)
  • The use of a supplied cantus in whole notes provides a skeleton for the overall form, freeing the student from having to plan a complete harmonic structure from scratch.
  • The limitation to the most elementary harmonies simplifies the understanding of dissonance.
  • The emphasis on vocal writing provides an excellent starting point for contrapuntal study, for three main reasons:
    • Every student has a voice.
    • Most traditional instruments are designed to sing, that is, to imitate the voice.
    • Instruments are much more varied in construction and idiom than voices.
  • The avoidance of motives, at least in the earlier stages, frees the student from the formal consequences they engender.
  • The progression from two part, to three part and four part (etc.) writing is logical, although creating harmonic fullness in two parts poses some unique problems.
  • Each of the first four species focuses effectively on just one or two elements:
    • The first species, eschewing dissonance completely, forces concentration on relationships of contour.
    • The second species introduces the problem of balancing the three simplest forms of linear development between two harmonies: Static elaboration (neighbor notes), gradual development (passing tones), and more dramatic leaping movement (arpeggiation).
    • The third species introduces other idioms for linear development between harmonies: the succession of two passing tones (including the relatively accented passing tone); combinations of passing tones, neighbor notes, and arpeggiation, and (depending on the teacher’s preference) perhaps the cambiata and double neighbor figures as well. In fact, third species counterpoint corresponds almost exactly to the ancient tradition of “differencias”, wherein the student systematically explores all possible ways of filling in the space between two chord tones with a given number of notes. (The technique of differencias was part of the training both of composers and performers; the latter frequently needed to be able to improvise ornamentation.) Schoenberg’s “Preliminary Exercises in Counterpoint” uses a variant of this method.
    • The fourth species focuses on suspensions. With suspensions, for the first time, the student encounters melody and harmony out of phase on the strong beat of the bar. Suspensions are the starting point for many of the richer patterns of elaboration.
    • The fifth species, the culmination of all the previous ones, provides preliminary work in rhythmic flexibility. Apart from a few more elaborate idioms, like the various ornamental resolutions for suspensions, the student works primarily on controlling rhythmic momentum (but without motives).
    • Finally, the mixed species exercises, used in some pedagogical traditions, provide an introduction to stratified textures, and encourage exploration of simultaneous dissonances while maintaining a clear harmonic context.


Thus, “strict” counterpoint can be useful. However, as the student advances, many of its pedagogical restrictions become stultifying constraints. For example, the student who never works without a cantus firmus never learns to plan a complete harmonic succession on his own. The monotony of harmonic rhythm – not to mention of meter (many texts never even go beyond 4/4 time!) is an enormous omission, leaving the student with no guidance whatsoever about how the mobile bass, which is so typical in contrapuntal textures, affects harmonic momentum and form. The limitation to simple harmony becomes a ludicrous handicap when applied to, say, invertible counterpoint, where the use of seventh chords multiplies the useful possibilities enormously. And so on…


Other approaches to learning counterpoint are usually style based, for the most part attempting to imitate either Palestrina or Bach. While they vary in efficacy, they share a serious limitation: In teaching a specific style, general principles are easily obscured. Also, as Roger Sessions points out in the Foreword to his excellent Harmonic Practice, for a composer, a style is never a closed set of limitations, but a constantly evolving language. For these reasons, this approach seems more appropriate for training musicologists than composers.


Whatever the pedagogical regime, there are two essentials for any successful study of counterpoint:


  • Students must sing the individual lines aloud in turn while listening to the others. The other lines should be sung by other students or played on the keyboard. This is contrapuntal ear training: It directs attention to various lines in turn with the others as background and leads to an intimate knowledge of the music’s inner details that is otherwise unattainable.
  • Quantity counts: The more exercises the student does of each type, the more he becomes familiar with the ways in which notes can be combined. Since the basic movements between chord tones are relatively limited (see below), after a while, many patterns become familiar.


An important pedagogical tool in teaching all musical disciplines is the use of graduated, aural “scales”. By this, we mean encouraging the student to rate the intensity of the effects of various musical situations. This encourages fine distinctions and  refined hearing. For example, instead of just saying that a particular disssonance is “harsh”, compare it to others and try to grade them all on a “scale of harshness”. Then, try to pinpoint which elements determine the force of the effect. This also helps in making distinctions which are useful beyond one particular style.


Finally, we would recommend that any counterpoint exercise, from the simplest to the most elaborate, be discussed as a real composition, with a beginning, a development, and an end. This is the only way to evaluate counterpoint that will be consistently relevant to the real problems faced by a composer.


If we are to see counterpoint in this way – as an aspect of composition and not as a self-contained discipline – we must define the limits of our approach. We repeat here some of our remarks from the first book of this series.


It is difficult to teach composition without making at least some assumptions about formal requirements. The crux of our argument here is that many basic notions enumerated here result from the nature of musical hearing. Let us make clear some of the assumptions behind the phrase “musical hearing”.


We assume first that the composer is writing music meant to be listened to for its own sake, and not as accompaniment to something else. This requires, at a minimum, provoking and sustaining the listener’s interest in embarking on a musical journey in time, as well as bringing the experience to a satisfactory conclusion. Thus, “musical hearing” implies here a sympathetic and attentive listener, at least some of whose psychological processes in listening to the work can be meaningfully discussed in general terms.


We will limit our discussion to western concert music. Non-western music, which often implies very different cultural expectations about the role of music in society or its effect on the individual, is thus excluded from our discussion.


Although some of the notions presented here may also apply to functional music (e.g. music for religious services, ceremonial occasions, commercials, etc.) all of these situations impose significant external constraints on the form: The composer’s formal decisions do not derive primarily from the needs of the musical material. In concert music, by contrast, the composer is exploring and elaborating the chosen material in such a way as to satisfy an attentive musical ear.


Despite my belief that counterpoint is best studied through tonal exercises (it is easier for a beginner to work within a familiar framework than to define a coherent language from scratch), the principles defined here will not be entirely limited to tonal music. The thoughtful reader will quickly see applications which do not depend on tonality.





  • 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