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In [[music theory]], '''counterpoint''' is the relationship
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 [[Consonance and dissonance|dissonance]].▼
==General principles==▼
The term "counterpoint" has been used to designate a voice or even an entire composition.{{sfn|Sachs|Dahlhaus|2001}} Counterpoint focuses on melodic interaction—only secondarily on the harmonies produced by that interaction. In the words of [[John Rahn]]:▼
{{blockquote|It is hard to write a beautiful song. It is harder to write several individually beautiful songs that, when sung simultaneously, sound as a more beautiful polyphonic whole. The internal structures that create each of the voices separately must contribute to the emergent structure of the polyphony, which in turn must reinforce and comment on the structures of the individual voices. The way that is accomplished in detail is ... 'counterpoint'.<ref>
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}}
Counterpoint has been most commonly identified in the [[classical music|European classical tradition]], strongly developing during the [[renaissance music|Renaissance]] and in much of the [[common practice period]], especially in the [[Baroque music|Baroque period]]. In Western [[Music education|pedagogy]], counterpoint is taught through a system of species (see below).
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 music|microtonal]] contexts.<ref>{{Cite journal|last=Mazzola|first=Guerino|date=2017|title=The Topos of Music I: Theory|url=http://dx.doi.org/10.1007/978-3-319-64364-9|journal=Computational Music Science|doi=10.1007/978-3-319-64364-9|isbn=978-3-319-64363-2|s2cid=4399053|issn=1868-0305}}</ref><ref>{{Cite book|last=Mozzalo|first=Guerino|title=The Topos of Music I: Theory : Geometric Logic, Classification, Harmony, Counterpoint, Motives, Rhythm|publisher=Springer International Publishing|year=2017|location=New York}}</ref>▼
▲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 [[Consonance and dissonance|dissonance]].
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. This effect is also used in orchestral arrangements; for instance, in [[Ravel]]’s Bolero #5 the parallel parts of flutes, horn and celesta resemble the sound of an electric organ. In counterpoint, parallel voices are prohibited because they violate the homogeneity of musical texture when independent voices occasionally disappear turning into a new timbre quality and vice versa.<ref>{{Cite book|last=Tangian|first=Andranick|author-link=Andranik Tangian|date=1993|title= Artificial Perception and Music Recognition|series= Lecture Notes in Artificial Intelligence|volume=746|publisher=Springer |location=Berlin-Heidelberg|isbn=978-3-540-57394-4}}</ref><ref>{{Cite journal|last=Tangian|first=Andranick|author-link=Andranik Tangian|year=1994|title=A principle of correlativity of perception and its application to music recognition|journal=[[Music Perception]]|volume=11 |issue=4 |pages=465–502|doi= 10.2307/40285634 |jstor=40285634 }}</ref>▼
▲==General principles==
▲The term "counterpoint" has been used to designate a voice or even an entire composition.{{sfn|Sachs|Dahlhaus|2001}} 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 music|microtonal]] contexts.<ref>{{Cite journal|last=Mazzola|first=Guerino|date=2017|title=The Topos of Music I: Theory|url=http://dx.doi.org/10.1007/978-3-319-64364-9|journal=Computational Music Science|doi=10.1007/978-3-319-64364-9|isbn=978-3-319-64363-2|s2cid=4399053|issn=1868-0305}}</ref><ref>{{Cite book|last=Mozzalo|first=Guerino|title=The Topos of Music I: Theory : Geometric Logic, Classification, Harmony, Counterpoint, Motives, Rhythm|publisher=Springer International Publishing|year=2017|location=New York}}</ref> Another theorist who has tried to incorporate mathematical principles in his study of counterpoint is [[Sergei Taneyev]] (1856-1915). Inspired by [[Baruch Spinoza|Spinoza]],<ref>{{Cite book |last=Grove |first=Paul Richard |url=https://repository.arizona.edu/handle/10150/283986 |title=Sergei Ivanovich Taneev's "Doctrine of the Canon": A translation and commentary |year=1999 |pages=24}}</ref> 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.<ref>{{Cite journal |last=Collins |first=Dennis |year=2018 |title=Approaching Renaissance music using Taneyev's theories of Movable counterpoint |url=https://www.jstor.org/stable/26663520 |journal=Acta Musicologica |volume=90 |issue=8 |pages=181–183 |jstor=26663520 }}</ref>
▲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. This effect is also used in orchestral arrangements; for instance, in [[Ravel]]
==Development==
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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 pair of examples is "[[My Way]]" combined with "[[Life on Mars (song)|Life on Mars]]".<ref>{{YouTube|id=nW0ACEOEq6w&t=1m45s|title="Life on Mars" and "My Way"}}, [[Ukulele Orchestra of Great Britain]]</ref>
[[Johann Sebastian Bach]] is revered as one of the greatest masters of counterpoint.
[[Johann Sebastian Bach|Bach]]'s 3-part [[Inventions and Sinfonias (Bach)|Invention in F minor]] combines three independent melodies:
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== Species counterpoint ==
{{Image frame|content=<score sound="1">
[[File:Counterpoint species 3.svg|center|thumb|450x450px|Example of "third species" counterpoint]]▼
\new PianoStaff <<
\new Staff \relative c' { d4 e f g | a b c d | e d c b | a b c a | g a b cis | d1 | }
\new Staff \relative c' { d1 | f | g | f | e | d | \bar "|." }
>>
▲
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.<ref>{{cite book |last=Jeppesen |first=Knud |author-link=Knud Jeppesen |others=trans. by [[Glen Haydon]], with a new foreword by Alfred Mann |title=Counterpoint: the polyphonic vocal style of the sixteenth century |orig-year=1939 |url=https://archive.org/details/counterpointpoly0000jepp |url-access=registration |year=1992 |publisher=Dover |location=New York |isbn=0-486-27036-X }}</ref> 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 School (music)|Venetian]] theorist [[Gioseffe Zarlino|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 [[Inversion (music)#Counterpoint|invertible counterpoint]].
[[File:Fux-Gradus-ad-Parnassum.jpg|thumb|''Gradus ad Parnassum'' (1725) by Johann Joseph Fux defines the modern system of teaching 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 [[Nonchord tone|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 solfeggi. 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]].{{Citation needed|date=August 2018}}
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The following rules apply to melodic writing in each species, for each part:
# The [[Mode (music)#Western Church|final]] note must be approached by [[Steps and skips|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{{music|sharp}} is necessary at the [[cadence]].{{sfn|Salzer|Schachter1989|page={{Page needed|date=October 2015}}}}
# 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 [[Steps and skips|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{{music|natural}})<ref>{{Cite book|title=[[The New Oxford Companion to Music]]|date=1983|publisher=Oxford University Press|author1=Arnold, Denis.|author-link=Denis Arnold|author2=Scholes, Percy A.|author2-link=Percy Scholes|pages=1877–1958|isbn=0193113163|oclc=10096883|location=Oxford}}</ref> 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 and dissonance|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 ===
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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. (See [[Steps and skips]].) 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,<ref>{{Cite book|last=Fux|first=Johann Joseph
{{Image frame|width=392|content=<score sound="1">
\relative c'' {
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}
</score>|caption=Short example of "first species" counterpoint}}
# 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 [[Consecutive fifths|parallel fifths or octaves]] between any two parts; and avoid [[Consecutive fifths#Hidden consecutives|"hidden" parallel fifths or octaves]]: that is, movement by [[Contrary motion|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]].)
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In ''second species'' counterpoint, two notes in each of the added parts work against each longer note in the given part.
{{Image frame|content=<score sound="1"> {
# (set-global-staff-size 15)
\relative c' {
<< \new Staff {
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Additional considerations in second species counterpoint are as follows, and are in addition to the considerations for first species:
# It is permissible to begin on an upbeat, leaving a half-rest in the added voice.
# The accented beat must have only consonance (perfect or imperfect). The unaccented beat may have dissonance, but only as a passing tone, i.e. it must be approached and left by step in the same direction.
# Avoid the interval of the unison except at the beginning or end of the example, except that it may occur on the unaccented portion of the bar.
# Use caution with successive accented perfect fifths or octaves. They must not be used as part of a sequential pattern. The example shown is weak due to similar motion in the second measure in both voices. A good rule to follow: if one voice skips or jumps try to use step-wise motion in the other voice or at the very least contrary motion.
===Third species===
{{Image frame|content=<score sound="1"> {
# (set-global-staff-size 16)
\relative c' {
\new PianoStaff <<
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}
>>
}
}
</score>
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===Fourth species===
In ''fourth species'' counterpoint, some notes are sustained or ''suspended'' in an added part while notes move against them in the given part, often creating a [[Consonance and dissonance|dissonance]] on the beat, followed by the suspended note then changing (and "catching up") to create a subsequent [[Consonance and dissonance|consonance]] with the note in the given part as it continues to sound. As before, fourth species counterpoint is called ''expanded'' when the added-part notes vary in length among themselves. The technique requires chains of notes sustained across the boundaries determined by beat, and so creates [[syncopation]].
<score sound="1">
\relative c' {
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==See also==
{{portal|Music}}
* [[Counter-melody]]
* [[Hauptstimme]]
* [[Polyphony]]
* [[Polyrhythm]]
* [[Voice leading]]
==References==
{{Reflist}}
'''Sources'''
* {{cite book|first1=Klaus-Jürgen|last1=Sachs|first2=Carl|last2=Dahlhaus|author2-link=Carl Dahlhaus|chapter=Counterpoint|title=[[The New Grove Dictionary of Music and Musicians]]|edition=second|editor1=Stanley Sadie|editor-link=Stanley Sadie|editor2=John Tyrrell|editor2-link=John Tyrrell (musicologist)|location=London|publisher=Macmillan Publishers|year=2001}}
* {{cite book|last1=Salzer|first1=Felix|author1-link=Felix Salzer|last2=Schachter|first2=Carl|author2-link=Carl Schachter|title=Counterpoint in Composition: The Study of Voice Leading|location=New York|year=1989|publisher=Stanley Persky, City University of New York|isbn=023107039X}}
==Further reading==
* Kurth, Ernst (1991). "Foundations of Linear Counterpoint". In ''Ernst Kurth: Selected Writings'', selected and translated by Lee Allen Rothfarb, foreword by Ian Bent, p. 37–95. Cambridge Studies in Music Theory and Analysis 2. Cambridge and New York: Cambridge University Press. Paperback reprint 2006. {{ISBN|0-521-35522-2}} (cloth); {{ISBN|0-521-02824-8}} (pbk)
* {{cite book |last1=Agustín-Aquino |first1=Octavio Alberto |last2=Junod |first2=Julien |last3=Mazzola |first3=Guerino |title=Computational Counterpoint Worlds: Mathematical Theory, Software, and Experiments |date=2015 |location=Cham |publisher=Springer |isbn=978-3-319-11235-0 |doi=10.1007/978-3-319-11236-7 |s2cid=7203604 |ref=none}}
* Prout, Ebenezer (1890). ''Counterpoint: Strict and Free''. London: Augener & Co.
* Spalding, Walter Raymond (1904). ''Tonal Counterpoint: Studies in Part-writing''. Boston, New York: A. P. Schmidt.
* Mann, Alfred (1965). ''The Study of Counterpoint: from Johann Joseph Fux's "Gradus ad Parnassum".'' W.W. Norton.
==External links==
{{EB1911 poster|Counterpoint}}
{{EB1911 poster|Contrapuntal Forms}}
* [http://www.lindsaydavidson.co.uk/counterpoint/ An explanation and teach yourself method for Species Counterpoint]
* [http://ntoll.org/article/species-counterpoint ntoll.org: Species Counterpoint] by Nicholas H. Tollervey
* [https://web.archive.org/web/20030823070750/http://www.o-art.org/history/early/Seeger.html Orima: The History of Experimental Music in Northern California: On Dissonant Counterpoint] by David Nicholls from his ''American Experimental Music: 1890–1940''
* [http://dictionary.onmusic.org/terms/1104-dissonant_counterpoint Virginia Tech Multimedia Music Dictionary: Dissonant counterpoint examples and definition]
* [http://www.ars-nova.com/cpmanual Counterpointer:Software tutorial for the study of counterpoint] by Jeffrey Evans
* [http://whybach.crosstownbooks.com/chapter.html "Bach as Contrapuntist"] {{Webarchive|url=https://web.archive.org/web/20201112013705/http://whybach.crosstownbooks.com/chapter.html |date=2020-11-12 }} by Dan Brown, music critic from Cornell University, from his web book ''Why Bach?''
* [http://www.maison-de-contrapuntal.com "contrapuntal—a collaborative arts project by Benjamin Skepper"]
* [https://alanbelkinmusic.com/site/en/index.php/ Principles of Counterpoint]{{Dead link|date=September 2024 |bot=InternetArchiveBot |fix-attempted=yes }}, by Alan Belkin
{{Counterpoint & polyphony}}
{{Texture (music)}}
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