Let us say that Alan is talking to Bill in a reasonably quiet room. Bill should have no difficulty following what he is saying. But if Charles joins in and starts talking to Bill on a related subject - at the same volume and at the same time as Alan - Bill is going to have a hard time fully understanding what either of them is saying. The voices do not blend together. Each, to some extent, masks the other, and poor Bill is left in the dark.

In music, however, two 'voices' can complement each other, so that listener Bill can hear both voices clearly and is able to concentrate sometimes more on one, sometimes more on the other. The two voices here are the melody lines of the music.

Now, we cannot simply play any two melodies together and expect them to blend well. The two melodies have to be composed in such a way that they blend. This is the essence of counterpoint: the art of writing two or more independent melodic lines that make a sound together in an interesting and harmonious manner; the key words here are 'interesting' and 'harmonious'.

Consonance and Dissonance

Counterpoint has existed in Western music since about the 9th Century with the start of polyphony¹, and indeed it is almost synonymous with it. The term counterpoint comes from the Latin expression punctus contra punctum, meaning 'point against point', or, more usefully, 'note against note'.

Before polyphony, all Western music (essentially church music) was homophonic plainsong, where, however many voices were heard simultaneously, there was only one melodic line; all of the voices were in unison. Plainsong had existed since the early Christian era, and may have derived from the music of the Jewish synagogue. It also exists in the Eastern Orthodox Church.

Although the idea of consonance and dissonance originated much earlier in ancient Greece, with the advent of polyphony it assumed a new importance. It had been noted that certain notes of the scales then in use, called modes, went well together - they were consonant - while others did not - they were dissonant. The human ear finds consonant notes pleasing, while dissonant notes jar. It has nothing to do with the individual notes themselves; it is how they sound together that matters, specifically the musical distance between them, called the interval. Therefore, we have consonant intervals and dissonant intervals.

The simplest exercise in counterpoint involves writing a second melody that can partner another, such that when both are played or sung together the effect is musically pleasing. Note that the second melody is not just a simple accompaniment to the first; both have something to say musically in the composition - they are partners. Now, given what we know about consonant and dissonant intervals, all we need to do is to write a couple of good melodies, ensuring that the intervals between any notes that sound together are consonant intervals. That is easy enough, it would seem.

Erm… well, yes - but most music has three essential components: melody, harmony and rhythm. If melody is the horizontal component of music - the sequence of notes we see printed from left to right on a page of sheet music - then harmony is the vertical component - the notes that sound together. If both voices in our little two-voice composition have the same rhythm, and we stick to using only intervals (the harmony) that are consonant, we will have written something that is, frankly, boring. It needs both rhythmic variation within the voices and the occasional use of dissonance to give it interest.

The Rules of Counterpoint

The art of counterpoint evolved over many centuries, reaching a pinnacle in around 1600. Subsequently, to aid teaching the art of counterpoint to students, a set of 'rules' were laid down that attempted to codify the best practice of musicians at that time. Rather like in the general way that you need to fully understand the rules of a subject in order to know how to break them constructively, the student of counterpoint was (and still is) taught 'strict counterpoint', before being allowed to move on to using 'free counterpoint', which is used in 'real' music. The rules of strict counterpoint are generally felt to be too rigid to be applied to real-world compositions.

Gradus ad Parnassum

The best-known treatise on the rules of (strict) counterpoint, Gradus ad Parnassum, was published in 1725 by Johann Fux². He advocated that music tutors train students by providing a short, simple melody called a cantus firmus (literally, fixed song), typically with one note to a bar³. The student would then be required to provide variant counter-melodies to the cantus firmus (CF), under each of five of what Fux called species:

• Species 1: the second melody has the same note durations as the CF
• Species 2: for each note in the CF, the second melody has twice, or three times, the number of notes
• Species 3: as 2 above, but with four or six notes to each note of the CF
• Species 4: as 2 above, but with the second note tied over to the first note of the next bar, ie a syncopated melody
• Species 5: using a mixture of the previous four species

For more advanced students there is the option of 'combined counterpoint', in which each added counter-melody is a different species. Although, for training purposes, the exercises given above are limited to two voices, three- or four-part (or even more) counterpoint is common in real-world composition.

Earlier, we made reference to consonant and dissonant intervals. Well, it turns out that some consonant intervals are more consonant than others. Consonant intervals come in two flavours: perfect and imperfect. Perfect intervals are those of a unison (both notes are the same), a fifth or an octave; imperfect intervals are major or minor thirds, and sixths.

Leaps and Curves

The rules laid out in Gradus ad Parnassum were designed to avoid music that would be difficult to sing, so large leaps are to be avoided, as are certain awkward intervals. If a voice does make a leap, it must be followed immediately by a step in the opposite direction. The overall aim is a smooth melodic curve.

Constraints were also placed on the ways in which one voice is allowed to move relative to another, what we today call 'voice-leading'. Two voices may move, relative to one another, by:

• Direct motion: both voices move in same direction, either up or down (in pitch)
• Contrary motion: one moves up while the other moves down
• Oblique motion: one stays put while the other moves, either up or down

Fux's four rules governing motion were:

1. Movement from a perfect consonance to another perfect consonance must be by contrary or oblique motion
2. As rule 1, but for movement from an imperfect to a perfect consonance
3. Movement from a perfect consonance to an imperfect consonance can be by any of the three motions
4. As rule 3, but for movement from an imperfect to another imperfect consonance

In addition to the general rules, further specific rules were applied to each species.

Double and Triple Counterpoint

It is very common in contrapuntal music for the same melodic phrase to be passed between the available voices, so that it may be heard first in an upper voice, then later in a lower voice. For example, in a work for solo piano, a melody heard (and played) in an upper register by the right hand, with the left hand providing a counter-melody, may re-appear subsequently being played in a lower register by the left hand, with the right hand now playing the same, or another counter-melody. If the repeated phase is to be an exact replica of the original, the parts must be written in 'invertible counterpoint'. When two voices are involved, invertible counterpoint is called 'double counterpoint'; with three voices, 'triple counterpoint'.

Imitation by Canon

It has long been a love of composers to repeat a melody in another voice, with the second voice starting the melody a little later than the original. This is known as a 'canon'. Canons may be written for two or more voices. Simple instances of canons are catches⁴, and rounds such as 'Three Blind Mice' and 'Frère Jacques'. There are many variations on the canon:

• 'Inverted canon': the intervals of the canon subject appear upside down in the imitating voice (also known as a ‘mirror canon’)
• 'Retrograde canon': the notes of the canon subject appear backwards (also known as a ‘crab canon’)
• 'Retrograde and inverted canon': a combination of the previous two; the imitating voice is backwards and upside down
• 'Canon by augmentation': the imitating voice uses longer duration notes than the original subject
• 'Double canon': two voices participate in one canon, while at the same time two other voices execute a different canon. A ‘triple canon’ is similar, but has three pairs of voices

Fugue is the Sincerest Form of Canon

The 'fugue' takes the canon and develops contrapuntal composition to its highest form. It is written for a defined number of parts or voices, the terminology depending on whether the composition is instrumental or vocal. The first voice enters with a short melodic phrase, known as the fugue's 'subject', in the work's tonic (home) key. Although in principle a fugue could be constructed on any theme, in practice the subject needs to lend itself reasonably well to fugal treatment.

The other parts or voices then enter successively in imitation of each other, the second in the dominant⁵ key of the tonic - the subject now known as the 'answer'; the third back in the tonic key, but now an octave higher or lower than the first voice. In addition to the subject, fugues often have a 'counter-subject'. The counter-subject should be written in invertible counterpoint so that it can readily be placed above or below the subject.

Having completed the subject or answer, a voice then moves on to the counter-subject, while the next voice is giving the subject or answer. Tonic and dominant, and subject and answer, alternate until all of the voices have entered. There then follows the first of a series of 'episodes' which connect successive returns to a canonical treatment of the fugue's subject and counter-subject. These episodes provide not only contrast but a means of modulating to other keys, the juxtaposition of which are an important feature of fugues. The canonical passages, alternating with episodes, continue until the subject has returned to the home key and the fugue is worked out.

Great Exponents of Counterpoint - the Contrapuntalists

Historically, there have been three peaks in the use of counterpoint: the first during the Renaissance with the intricate motets and masses of Josquin Desprez; the second in the latter half of the 16th Century with composers like Palestrina; and the third during the Baroque period, the greatest exponent at this time being JS Bach.

Josquin Desprez (c1440 - 1521)

Desprez is regarded as one of the greatest musicians ever to have lived; his work strongly influencing those after him for a century or more. His compositions include 18 masses, over 100 motets, and other secular music. He made extensive use of the technique called 'pervasive imitation', in which short motifs and phrases are passed backwards and forwards between pairs of voices, usually in canon.

Giovanni Pierluigi da Palestrina (c1555 - 1594)

Palestrina composed a vast quantity of music, all of it vocal, most of it highly contrapuntal, and much of it full of technical devices; complete editions of his work run to over 30 volumes. It was Fux's study of Palestrina's work that led to Gradus ad Parnassum.

Johann Sebastian Bach (1685 - 1750)

JS Bach was the Baroque era's technical guru on counterpoint. He was able to not only appreciate its infinite possibilities, in much the same way as a mathematician appreciates the elegant beauty of an equation, but had the mathematical-like skills to actually implement these possibilities in music of outstanding quality. Two works by Bach were written expressly to demonstrate the possibilities of counterpoint: 'The Musical Offering' BWV1079⁶ and the 'Art of Fugue' BWV1080.

'The Musical Offering' is a set of two fugues (one three-part, one six-part), ten canons and a trio sonata. The fugues and canons take as their starting point a theme - the thema regium (royal theme) - written and given to Bach by Frederick II, king of Prussia, on the occasion of Bach's visit to the royal court at Potsdam in 1747. The three-part fugue was reputedly improvised by Bach on the spot, while the others were composed very shortly afterwards and sent to the king as a printed presentation.

Bach's 'Art of Fugue' was left unfinished at his death. It comprises a set of 14 fugues and four canons worked upon a single theme. The fugues increase in complexity, the only clue to the order in which they should be played. No indications are given as to instrumentation, and it may well be that Bach never intended the work for performance, rather as an intellectual exercise to demonstrate how far the theme could be developed.

Counterpoint Lives On

Even in Bach's time, the fugue was starting to be considered old-fashioned. After him, it virtually disappeared as a musical entity. However, the fugal device remained, recurring endlessly in the work of composers down the centuries, from the late string quartets of Beethoven to Verdi's 'Requiem' and Bartók's 'Music for Strings, Percussion and Celesta'. Even in a post-tonal world, the key principles of balance between voices and forward musical momentum by progression are still evident.

Counterpoint is by no means exclusive to so-called classical music; it is equally relevant to 'popular' music. While it is true that examples of fugues and mirror canons in popular music are a bit thin on the ground, when we remember that counterpoint is the interaction between concurrent melodies, it should be no surprise that it is found in music of all genres. One area that is likely to be an exception is solo vocalist-led material - contrapuntal Kylie, probably not. But in the interplay between instrumental lines, eg rhythm and lead guitar, or lead guitar and bass guitar, counterpoint will be in evidence.

You can also find instances of overlapping vocal lines, eg in the harmonies of some Beach Boys tracks. Think also of the beginning of The Beatles' 'Paperback Writer'. And who would dare to say that Andrew Lloyd Webber's musicals are strangers to counterpoint?

Counterpoint is ever-changing, but rarely absent from music of great quality.