In music theory, counterpoint is the relationship of two or more simultaneous musical lines (also called voices) that are harmonically dependent on each other, yet independent in rhythm and melodic contour. The term originates from the Latin meaning "point against point", i.e. "note against note". Counterpoint has been most commonly identified in the European classical tradition, strongly developing during the Renaissance and in much of the common practice period, especially in the Baroque period. In Western pedagogy, counterpoint is taught through a system of species (see below).
There are several different forms of counterpoint, including imitative counterpoint and free counterpoint. Imitative counterpoint involves the repetition of a main melodic idea across different vocal parts, with or without variation. Compositions written in free counterpoint often incorporate non-traditional harmonies and chords, chromaticism and dissonance.
General principles The term "counterpoint" has been used to designate a voice or even an entire composition. Counterpoint focuses on melodic interaction—only secondarily on the harmonies produced by that interaction.
Work initiated by Guerino Mazzola (born 1947) has given counterpoint theory a mathematical foundation. In particular, Mazzola's model gives a structural (and not psychological) foundation of forbidden parallels of fifths and the dissonant fourth. Octavio Agustin has extended the model to microtonal contexts. Another theorist who has tried to incorporate mathematical principles in his study of counterpoint is Sergei Taneyev (1856–1915). Inspired by Spinoza, Taneyev developed a theory which covers and generalizes a wide range of advanced contrapuntal phenomena, including what is known to the English-speaking theorists as invertible counterpoint (although he describes them mainly using his own, custom-built terminology), by means of linking them to simple algebraic procedures.
In counterpoint, the functional independence of voices is the prime concern. The violation of this principle leads to special effects, which are avoided in counterpoint. In organ registers, certain interval combinations and chords are activated by a single key so that playing a melody results in parallel voice leading. These voices, losing independence, are fused into one and the parallel chords are perceived as single tones with a new timbre. In counterpoint, parallel voices are prohibited because they violate the heterogeneity of musical texture when independent voices occasionally disappear turning into a new timbre quality and vice versa.
Development Some examples of related compositional techniques include: the round (familiar in folk traditions), the canon, and perhaps the most complex contrapuntal convention: the fugue. All of these are examples of imitative counterpoint.
Examples from the repertoire There are many examples of song melodies that are harmonically interdependent yet independent in rhythm and melodic contour. For example, "Frère Jacques" and "Three Blind Mice" combine euphoniously when sung together. A number of popular songs that share the same chord progression can also be sung together as counterpoint. A well-known example is "My Way" combined with "Life on Mars?"., Ukulele Orchestra of Great Britain
Johann Sebastian Bach is revered as one of the greatest masters of counterpoint. For example, the harmony implied in the opening subject of the Fugue in G minor from Book II of the Well-Tempered Clavier is heard anew in a subtle way when a second voice is added. "The counterpoint in bars 5-8... sheds an unexpected light on the tonality of the Subject.":Tovey, D. F. (1924, p. 127, Bach 48 Preludes and Fugues, Book II. London, Associated Boards of the Royal Schools of Music.
Bach's 3-part Invention in F minor combines three independent melodies:
According to pianist András Schiff, Bach's counterpoint influenced the composing of both Mozart and Beethoven. In the development section of the opening movement of Beethoven's Piano Sonata in E minor, Beethoven demonstrates this influence by adding "a wonderful counterpoint" to one of the main themes.Schiff, A. (2006) "Guardian Lecture on Beethoven Piano Sonata in E minor, Op. 90, accessed 8 August 2019
A further example of fluid counterpoint in late Beethoven may be found in the first orchestral variation on the "Ode to Joy" theme in the last movement of Beethoven's Symphony No. 9, bars 116–123. The famous theme is heard on the violas and cellos, while "the basses add a bass-line whose sheer unpredictability gives the impression that it is being spontaneously improvised. Meantime a solo bassoon adds a counterpoint that has a similarly impromptu quality."Hopkins, Antony (1981, p. 275) The Nine Symphonies of Beethoven. London, Heinemann.
In the Prelude to Richard Wagner's opera Die Meistersinger von Nürnberg, three themes from the opera are combined simultaneously. According to Gordon Jacob, "This is universally and justly acclaimed as an extraordinary feat of virtuosity."Jacob, Gordon (1953, p. 14) Wagner Overture Die Meistersinger. Harmondsworth, Penguin However, Donald Tovey points out that here "the combination of themes ... unlike classical counterpoint, really do not of themselves combine into complete or euphonious harmony."Tovey, Donald Francis (1936, p. 127) Essays in Musical Analysis, Volume IV. Oxford University Press.
One spectacular example of 5-voice counterpoint can be found in the finale to Mozart's Symphony No 41 ("Jupiter" Symphony). Here five tunes combine simultaneously in "a rich tapestry of dialogue":Keefe, Simon P. (2003, p. 104) The Cambridge Companion to Mozart. Cambridge University Press.
See also Invertible counterpoint.
Species counterpoint Species counterpoint was developed as a pedagogical tool in which students progress through several "species" of increasing complexity, with a very simple part that remains constant known as the cantus firmus (Latin for "fixed melody"). Species counterpoint generally offers less freedom to the composer than other types of counterpoint and therefore is called a "strict" counterpoint. The student gradually attains the ability to write free counterpoint (that is, less rigorously constrained counterpoint, usually without a cantus firmus) according to the given rules at the time. The idea is at least as old as 1532, when Giovanni Maria Lanfranco described a similar concept in his Scintille di musica (Brescia, 1533). The 16th-century Venetian theorist Zarlino elaborated on the idea in his influential Le institutioni harmoniche, and it was first presented in a codified form in 1619 by Lodovico Zacconi in his Prattica di musica. Zacconi, unlike later theorists, included a few extra contrapuntal techniques, such as invertible counterpoint.
In 1725 Johann Joseph Fux published Gradus ad Parnassum (Steps to Parnassus), in which he described five species:
Note against note; Two notes against one; Four notes against one; Notes offset against each other (as suspensions); All the first four species together, as "florid" counterpoint.
A succession of later theorists quite closely imitated Fux's seminal work, often with some small and idiosyncratic modifications in the rules. Many of Fux's rules concerning the purely linear construction of melodies have their origin in solfeggio. Concerning the common practice era, alterations to the melodic rules were introduced to enable the function of certain harmonic forms. The combination of these melodies produced the basic harmonic structure, the figured bass.
Considerations for all species The following rules apply to melodic writing in each species, for each part:
The final note must be approached by step. If the final is approached from below, then the leading tone must be raised in a minor key (Dorian, Hypodorian, Aeolian, Hypoaeolian), but not in Phrygian or Hypophrygian mode. Thus, in the Dorian mode on D, a C is necessary at the cadence. Permitted melodic intervals are the perfect unison, fourth, fifth, and octave, as well as the major and minor second, major and minor third, and ascending minor sixth. The ascending minor sixth must be immediately followed by motion downwards. If writing two skips in the same direction—something that must be only rarely done—the second must be smaller than the first, and the interval between the first and the third note may not be dissonant. The three notes should be from the same triad; if this is impossible, they should not outline more than one octave. In general, do not write more than two skips in the same direction. If writing a skip in one direction, it is best to proceed after the skip with step-wise motion in the other direction. The interval of a tritone in three notes should be avoided (for example, an ascending melodic motion F–A–B) as is the interval of a seventh in three notes. There must be a climax or high point in the line countering the cantus firmus. This usually occurs somewhere in the middle of exercise and must occur on a strong beat. An outlining of a seventh is avoided within a single line moving in the same direction.
And, in all species, the following rules govern the combination of the parts:
The counterpoint must begin and end on a perfect consonance. Contrary motion should dominate. Perfect consonances must be approached by oblique or contrary motion. Imperfect consonances may be approached by any type of motion. The interval of a tenth should not be exceeded between two adjacent parts unless by necessity. Build from the bass, upward.
First species In first species counterpoint, each note in every added part (parts being also referred to as lines or voices) sounds against one note in the cantus firmus. Notes in all parts are sounded simultaneously, and move against each other simultaneously. Since all notes in first species counterpoint are whole notes, rhythmic independence is not available. (archive from 23 October 2018) An example is shown below.
In the present context, a "step" is a melodic interval of a half or whole step. A "skip" is an interval of a third or fourth. An interval of a fifth or larger is referred to as a "leap".
A few further rules given by Fux, by study of the Palestrina style, and usually given in the works of later counterpoint pedagogues, are as follows.
Begin and end on either the unison, octave, or fifth, unless the added part is underneath, in which case begin and end only on unison or octave. Use no unisons except at the beginning or end. Avoid parallel fifths or octaves between any two parts; and avoid "hidden" parallel fifths or octaves: that is, movement by similar motion to a perfect fifth or octave, unless one part (sometimes restricted to the higher of the parts) moves by step. Avoid moving in parallel fourths. (In practice Palestrina and others frequently allowed themselves such progressions, especially if they do not involve the lowest of the parts.) Do not use an interval more than three times in a row. Attempt to use up to three parallel thirds or sixths in a row. Attempt to keep any two adjacent parts within a tenth of each other, unless an exceptionally pleasing line can be written by moving outside that range. Avoid having any two parts move in the same direction by skip. Attempt to have as much contrary motion as possible. Avoid dissonant intervals between any two parts: major or minor second, major or minor seventh, any augmented or diminished interval, and perfect fourth (in many contexts).
In the adjacent example in two parts, the cantus firmus is the lower part. (The same cantus firmus is used for later examples also. Each is in the Dorian mode.)
Second species In second species counterpoint, two notes in each of the added parts work against each longer note in the given part. An example is shown below.
Additional considerations in second species counterpoint are as follows, and are in addition to the considerations for first species: