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Counterpoint Fundamentals including Species Counterpoint

Fundamental Principles
of Counterpoint Study

Though Counterpoint study can be applied to even atonal music, in this course we will deal with the traditional principles, particularly those of Johann Fux (1660-1741), whose teaching informed Mozart, Haydn, Beethoven, and many other composers old and new. Counterpointer does allow you to create your own style sets if you would like to experiment with non-traditional forms of polyphony.

In the following paragraphs you'll find a highly abbreviated introduction to this large topic, which should be enough to help you do the exercises and understand the basic principles. You can use the Bibliography as a starting point if you'd like to study counterpoint in more depth.

Counterpoint study deals chiefly with vocal music, or music in a vocal style. Similar principles can be applied to instrumental music, though with instrumental music it's more difficult to define the style precisely. Instruments are able to leap, for example, with far more agility and speed than the human voice and so can perform music that would not be effective at all if sung. For most exercises we will do best to imagine that each part is a singing voice, but you can also try the Bach Instrumental style set if you'd like to experiment with contrapuntal instrumental writing in the style of Bach's inventions or fugues.

A counterpoint study plan

Species counterpoint is a pedagogical method that breaks the learning task into well-defined graduated stages. Species counterpoint is mostly associated with Johann Fux, who presented the five species in his Gradus Ad Parnassum (Steps to Parnassus) in 1725. Though a prominent composer of his day, Fux is now known chiefly for his book, one of the most influential teaching systems ever devised.

The student should treat the species as did young Joseph Haydn, who as Mann observes, perfectly matched Fux's description of a student "lacking means and a teacher." Haydn began with the First Species and went carefully through all the exercises recommended by Fux. What Haydn lacked was what you, dear reader, have in Counterpointer: a tireless mechanical assistant who can notice errors you might miss and will never complain about being asked to check your 2nd, 3rd or 4th revision of an exercise. This assistant will also play the music for you with your choice of instrument sounds, so with any luck you can do better than poor Haydn.

The below outline of principles will be enough to get you started, though we assume that you already know how to read music, and that you have some familiarity with the concepts of interval and scale. That preparation can be received through Practica Musica if needed. You'll also find tables of rhythms, intervals and scales at the end of this page.

We suggest that you begin with First Species and write accompaniment to Fux's cantus firmi (fixed melodies) in 2, 3, and 4 parts. Then move to Second Species, and take the remaining species in numerical order. Each exercise has a link to the instructions page for that species of counterpoint, and you can also reach those instructions through the table of contents. The exercises using generated cantus firmi are there to provide endless variety in case you tire of the same six melodies: the generated melodies may sometimes be a little quirky but will almost always be different, and can be of any length you desire.

Principles that apply to individual melodies

The ideal of polyphony is voices that are simultaneously independent and cooperative. Each melody should be good in itself but should also combine well with the others. It is the tension between those two requirements that makes the art of counterpoint.

By "good in itself" we mean that the melody is easily sung, not repetitive, and graceful.

"Easily sung" means a relatively close range - generally within a tenth, few large leaps except for the octave, and free of augmented or diminished intervals. There can be additional aids to singability, but these are the most important.

"Not Repetitive" means avoiding both excessively repeated pitches and repeated patterns of pitches, unless the latter are part of a deliberate imitation between voices. You should attempt a variety of shape and rhythm.

"Graceful" is hard to define. Jeppeson makes some attempts to describe grace in his Counterpoint, from which we could conclude that grace may involve meaningful melodic shape, such as a rise of melody to a peak from which it descends, and that grace is made more likely by attention to the various principles of melodic movement and dissonance handling included in the traditional style rules. Grace involves avoidance of extremes, a preference for the subtle.

Principles that apply to the combination of melodies

The three types of melodic motion between two voices are Direct or Similar (both rising or both falling), Contrary, and Oblique (one remains the same while the other rises or falls).

When rhythms are fixed, as in First through Fourth Species counterpoint, independence is supplied mostly though frequent contrary motion of voices and changes of harmony.

Dissonance handling is perhaps the biggest single topic in counterpoint study. Dissonance can be defined either in harmonic terms (a dissonance is a note that is not part of the current chord) or in terms of intervals (a note is dissonant if it is part of a dissonant interval). The older modal counterpoint is more concerned with intervals than the counterpoint of the 18th century and beyond, though it's hard to completely separate intervals and harmony - the idea of polyphony being driven by chords is something that appeared gradually. For species counterpoint exercises, however, we will think mostly in terms of intervals. In species counterpoint a note will be generally considered "dissonant" if it forms a dissonant interval with other notes in the sonority. The exceptions are the cases of the augmented fourth and its inversion, the diminished fifth. In our exercises these will be considered consonant if they are not formed with the bass.

The consonances used in the music being studied are, in order of stability, the octave, fifth, third, and sixth.

The octave, fifth, and fourth are "perfect" consonances (but see below about the fourth).

The thirds and sixths are "imperfect" consonances.

The perfect fourth is special: though acoustically consonant it is considered dissonant if formed with the bass.

All other harmonic combinations are dissonant (2nd, 7th, and all augmented or diminished intervals), with the exception noted above for the diminished fifth and augmented fourth.

Combining an interval with an octave does not change its nature (i.e. compound intervals will be treated the same as simple ones; a tenth is the same as a third for harmonic purposes).

The distinction between "accented" and "unaccented" notes will be important. By "accented" we mean notes that are in a position that is metrically strong with relation to the measure or to neighboring notes. For example, the first note in any measure is always metrically strong. Of four quarters in a measure of 4/4 or 2/2, the 1st and 3rd notes are strong, but if there are just two half notes in that measure you could regard the second as being weak in relation to the first. If you see two notes of equal value and the first is at a metric division point then the first will be stronger than the second. In the following example, asterisks mark the notes that are in relatively strong positions for purposes of counterpoint:

This table summarizes the common intervals:

This table depicts the scales or modes in their untransposed forms:

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