"Josephus – I come to you, venerable master, in order to be introduced to the rules and principles of music.
Aloysius – You want, then, to learn the art of composition?
Josephus – Yes.
Aloysius – But are you not aware that this study is like an immense ocean, not to be exhausted even in the lifetime of a Nestor?"
Johann Joseph Fux (1660-1741), Gradus ad Parnassum (1725)

Counterpoint is a term derived from the Latin punctus contra punctum (note against note). It is a piece of music combining two or more contrasting melodies; each of which is an individual melody when played on its own. Pleasing results are achieved when the constituent contrapuntal melodies fit together and complement each other. The integral complexities associated with counterpoint make it, perhaps, the most complicated compositional technique to learn. Yet if it is to sound good and go beyond mere technique, composing counterpoint requires great skill and aesthetic insight.

Nevertheless, the composing of counterpoint is not based on fortuitous chance melodic combinations, nor is its practise restricted to only those possessing musical genius. Rather, it is the result of applying specific rules and guidelines. In other words, it is a skill that can be learned. The most famous means of teaching counterpoint is that developed by Johann Joseph Fux and explained in his dialogue ‘Gradus ad Parnassum' (Latin for "Steps to Parnassus").

In Greek mythology Parnassus was the mountain dwelling of the gods. A composer, having climbed Parnassus, would, according to the metaphor, have achieved a perfect compositional technique. This is achieved by learning species counterpoint.

Species counterpoint is based upon the stylistic conventions of the great Italian composer Palestrina. It has been successfully used as a pedagogical technique for over 300 years. It provides a set of strict rules of increasing complexity concerning the "valid" pitch and duration relationships between the notes found in contrasting melodic parts. The rules are introduced over five separate species of counterpoint. The counterpoint is initially of two parts, one of which, the Cantus firmus (Latin for fixed line; a melody consisting of mainly step-wise movement using notes of a semi-breve duration), is provided for the student. It is over the cantus firmus that the student sets their part using the rules of whatever species of counterpoint has been requested. Thus, a species counterpoint problem is set and the student improves their compositional technique by providing a solution. The intention is that the rules defined by the species counterpoint promote and encourage good compositional practices.

Before describing each of the five species some basic musical theory must be introduced:

Musicians call the differences in pitch between notes an interval. The interval is expressed numerically in terms of the number of notes between the two notes inclusive of the outer notes.

For example, the interval between two notes adjacent in pitch (‘C' and ‘D' for example) is a second (i.e. there are two notes; the lower and the upper). However, the interval between ‘C' and ‘F' is a fourth (as there are four notes between ‘C' and ‘F': C, D, E and F).

The illustration below shows the intervals used in species counterpoint within one octave (any larger intervals can be described as an octave and an xth for example).

It is important to notice that intervals are subdivided into two sets: consonances (that sound ‘nice') and dissonances (that don't). Consonances are further subdivided: the unison, fifth, and octave are called ‘perfect' consonances whereas the sixth and the third are ‘imperfect'.

In addition to the vertical (pitch) differences expressed as intervals, musicians also describe the horizontal movement of and relationship between notes. These can be summarised as follows:

Parallel motion is when two or more parts ascend or descend in pitch by the same distance in the same direction by skip or by step. Below is an example:

The above example is a very specific form of similar (or direct) motion. This is when parts ascend or descend in pitch in the same direction by skip or by step but may include a movement of different distances in each part. The illustration below makes this distinction explicit:

Contrary motion is when parts move by skip or by step in opposite directions to each other. This is demonstrated below:

Oblique motion is when one part moves by skip or by step while the other remains stationary thus:

We are finally in a position to be able to describe and give examples of each species of counterpoint. It must be noted that the rules and conventions that follow have been extracted from two types of source:

• Explicit definitions of species counterpoint rules; where the rule in question is given in a treatise such as Fux's Gradus ad Parnassum or another source on musical theory.
• Implicit conventions or heuristic practices; where the rule in question is derived from a common practice or convention that is often viewed as ‘obvious' within western musical conventions yet is not so obvious to those with little or no musical training (or a computer).

Finally, unless stated otherwise, the rules are compound. For example, the rules for the first species of counterpoint hold over, with certain modifications, into subsequent species.

Generic Features

Species counterpoint rules mainly concern melodic motion and the intervals between the voices. (A voice is a line of music intended for a singer[s] or instrument[s]).

With regard to the combination of intervals and the motion of parts almost any succession of intervals is allowed if the motion between the voices is contrary or oblique, but for similar and parallel motion there are basically two explicit restrictions:

• Parallel motion is only allowed in parts that are separated by imperfect consonances (thirds and sixths).
• Voices must not move in similar motion in parts that lead to either perfect fifths, octaves or unisons.

Further rules (both implicit and explicit) that are concerned with ensuring an interesting yet conventionally sounding result include:

• The range (distance between the lowest and highest possible notes) of a voice should not be more than an interval of a tenth (in keeping with a comfortable range for the human voice).
• Stepwise motion should predominate (to encourage a smooth melodic line).
• In all but third species counterpoint, avoid more than five consecutive notes in the same direction (to make sure the melody has an undulating, and thus interesting, shape). In third species counterpoint avoid more than nine consecutive notes in the same direction.
• Avoid simultaneous leaps (i.e. if one voice leaps the other should move stepwise).
• A leap greater than a third should be followed by either a move back to the originating note (only possible if the leap is a fourth) or a leap in the opposite direction that does not exceed the original leap (only possible if the leap is a fifth with the subsequent leap usually being a fourth) or a step in the opposite direction (by far the most predominant solution).
• Do not cross voices (i.e. do not let the upper voice's notes stray below the lower voices and vice versa).
• Avoid repetitions of notes (to ensure variety in the melodic line).
• Begin and end on the same note as the cantus firmus (although counterpoints above the cantus firmus may begin with an interval of a fifth).
• Approach the final note by step in contrary motion to the cantus firmus.
• Approach the penultimate note by step or small leap(i.e. no larger than the interval of a third).

It should be noted that when writing out species counterpoint it is common practice to write a number denoting the size of the interval between the notes in the separate lines of music. Thus, ‘5' means an interval of a fifth, ‘3' a third and ‘8' an octave. In addition to making the relationship between the melodic lines explicit it also forces the person writing the species counterpoint to think about the various rules relating to musical intervals.

First Species

First species counterpoint can best be described as note for note counterpoint. In other words, for every note in the cantus firmus the first species provides a note to compliment it. As a result the first species of counterpoint provides the same number of semibreves as the cantus firmus.

The rules for this species can be summarised thus:

• Use only consonances.
• Unisons can only occur at either the beginning or end of the piece.
• The only leaps allowed are thirds, perfect fourths and fifths and an ascending minor sixth, but step movement is preferred.
• Use no more than three intervals of a parallel third, sixth (or tenth) in direct succession (to encourage differentiation in musical texture).

Second species

The second species of counterpoint adds two important features to the writing of a melody:

• The introduction of oblique motion where one has to provide two notes in the counterpoint for each note in the cantus firmus. Thus two minims are provided in the counterpoint for every semibreve in the cantus firmus.
• The use of dissonant notes (intervals of a second, fourth or seventh) is allowed in certain circumstances.

The rules for second species counterpoint can be summarised thus:

• The use of dissonant notes is allowed on the second minim of a bar only when connecting two notes by a solely stepwise motion.
• The use of parallel perfect consonances (intervals of a fifth and octave) on the first minim of consecutive bars is not allowed (as this gives the impression of parallel motion between perfect consonances which is not allowed in the rules defined previously).
• A stepwise connection between two instances of the same (consonant) note may be used if and only if the middle note is also a consonance, this is often called a neighbour-note figure.

• The counterpoint may start with a single minim's rest.
• The final note is always the same length and name as that used in the cantus firmus.

Third Species

In third species counterpoint the oblique motion is subdivided into four notes in the counterpoint against one note in the cantus firmus. The rules for this species are very similar to the second species but include some modifications to incorporate the new rhythmic texture.

• The counterpoint can start with a crotchet rest.
• The final note of the counterpoint conforms to the practice defined in second species counterpoint.
• The first note of every bar should be a consonance.
• Notes on the second, third and fourth beats can also be consonant or unison.
• Dissonances can occur on the second, third and fourth beats only when part of a stepwise movement between consonances.
• Dissonances cannot be adjacent to each other (implied by the above rule).

There are only two exceptions to the above rules concerning the placement of dissonances.

• The so-called double-neighbour rule that consists of a four note figure starting on the first beat that begins and ends on the same note with the second note a step above the original and the third note a step below the original. This will sometimes lead to a (legal) leap from a dissonance.

• Nota cambiata (translated as exchanged note) is a five note figure acting as an embellishment to the melodic contour from beat one (or three) to the next beat one (or three) inclusive. The contour of a nota cambiata is a step down, a leap down a third followed by two upward steps. The first, third and fifth notes must be consonances but the second and fourth can be dissonant. There are only two possible starting intervals for counterpoint written above or below the cantus firmus. An upper counterpoint's nota cambiata can begin on either an interval of an octave or a sixth whereas a lower counterpoint's nota cambiata can begin on either an interval of a fifth or a third.

Both the above exceptions to the rule may be inverted in pitch (turned upside down). However, this is rarely used and also causes the starting intervals that can be used to be inverted from the upper to lower (and vice versa) practice. (An inverted nota cambiata in an upper counterpoint can only start on an interval of a fifth or a third whereas in a lower counterpoint the starting intervals can only be an octave or a sixth.)

Fourth species

Fourth species counterpoint introduces the concept of a suspension. This is when a consonance in the counterpoint is held over as the cantus firmus changes note so that it becomes a dissonance. Furthermore, it is essential that the now dissonant note ‘resolves' in a downwards direction onto an adjacent consonant note. Thus, a suspension can be thought of in three parts:

• A preparation that must be a consonance.
• The suspension itself that is a dissonance.
• A resolution down to an adjacent consonance.

As a result, the fourth species introduces the possibility of a dissonance at the start of a bar.

When writing fourth species counterpoint one changes pitch in the second half of the bar with a minim note (the preparation) that is tied over to another minim of the same pitch (the suspension) before moving to a new pitch that acts as both the resolution for the current suspension and preparation for the next.

Strictly speaking a suspension includes a resolving dissonance. However, one need not tie notes together to cause a dissonance and thus form a suspension. It is quite possible to leave out a suspension and tie notes of the same pitch that form consonances with the two different notes in the cantus firmus. In other words, step two of the suspension is changed into a consonance.

Fourth species counterpoint can be summarised with the following rules:

• The counterpoint starts with a minim rest. The first heard note follows normal conventions.
• The final note conforms to the practice defined in second species counterpoint.
• Use tied notes (as described above) as much as possible. If this is not possible one should revert to second species counterpoint for as short a period as possible.
• The only dissonances allowed as suspensions are the movement of an interval of a seventh down to a sixth or the movement of a fourth down to a third. Sometimes a movement of a ninth to an octave is used (infrequently).
• If the note that is tied over is a consonance (i.e. there is no suspension) then the note need not resolve down. As a result, movement in any direction by step or leap is allowed so long as it moves to a consonance and follows the generic species counterpoint rules concerning movement.
• The penultimate bar must include a move from a seventh down to a sixth type suspension.
• Include as many suspensions as possible but do not allow more than three of the same type in succession (to avoid repetitiveness and an endlessly downward moving counterpoint).
• Use leaps of an octave if the two parts are getting close to each other.
• Use leaps after consonances to add interest to the the counterpoint.

Fifth species

Fifth species counterpoint is a combination of the other four types with a few new decorative techniques introduced. As J.J.Fux stated in Gradus ad Parnassum, "As a garden is full of flowers so this species of counterpoint should be full of excellences of all kinds…" (Fux ed. Mann, 1943, p.64). In other words, a liberal mixture of all the previous species will produce the best results.

The most obvious new technique is the use of quavers as decoration to the counterpoint. Nevertheless, as in all things to do with species counterpoint, their use is specific and very clearly defined.

Fifth species counterpoint can be summarised as follows:

• The opening note of fifth species counterpoint should use the same conventions as the fourth species starting note.
• The penultimate and final bars should also use the same conventions as the fourth species.
• Quavers (always used in pairs) are only allowed on the ‘weak' second and fourth beats.
• They can only be used in two possible ways:
  • As a neighbour-note figure (a stepwise connection between two instances of the same (consonant) note may be used if and only if the middle note is also a consonance).
    
  • As passing notes that connect two consonant notes an interval of a fourth apart (rarely used).
    
• All quaver notes should be entered into and left by step.
• Only use quaver figures once in a bar.
• Do not over use quaver figures. Do not use them more than once every three bars.
• Suspensions that make use of a movement from a seventh to a sixth sound especially good if the suspension is decorated with a neighbour-note quaver figure.
• Further embellishments to fourth species suspensions come from its combination with elements of the third species:
  • The resolution can be anticipated by a crotchets worth duration. In other words, whereas before a suspension consisted of two minims of the same pitch tied together, this is replaced with a minim tied to a crotchet of the same pitch on the first beat followed by the resolution on the second beat.
  • Make use of an &eactue;chappée (escape) note. This is where the minim preparation note is tied to a crotchet suspension that is followed by a crotchet note a step directly above the suspension note followed by the appropriate resolution note.
  • Finally, the crotchet suspension note can be temporarily abandoned with a descending consonant leap to a crotchet consonant note before leaping back up to the expected consonant resolution note.

The above three rules are demonstrated in the following illustration:

• As in the fourth species the preparation of a suspension always starts on the third beat of a bar and ties over to the first beat of the next bar.
• Do not make use of semibreves in any part of the counterpoint except the last bar. To do so would cause the counterpoint to sound empty and dilatory.
• The use of minims starting on the second or fourth beats of a bar (as tied crotchets) is not allowed.
• The rhythm of two crotchets and a minim in one bar is not good unless it is preceded by a bar ending with two crotchets.

Concluding Remarks on Counterpoint

By digesting the information on this page it is hoped that the reader will have reached their own Parnassus of understanding concerning the five species of counterpoint. Nevertheless, it should be pointed out that the only way in which one can truly claim understanding is if a successful completion of practical species counterpoint problems can be demonstrated.

This can only come with practise and a process of evolving one's technique so that a solution is derived from a creative and intuitive process as opposed to a clumsy adherence to a set of rules.