View source for Counterpoint

{{Short description|Polyphonic music with separate melodies}}
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{{Other uses}}
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{{Listen|type=music
| header       = [[File:BachFugueBar.png|frameless|center]]
| filename     = BachBWV862Bar.mid
| title        = Sample of counterpoint
| description  = Extract from [[Fugue]] no. 17 in A-flat major, [[BWV]] 862, from book 1 of ''[[The Well-Tempered Clavier]]'' by [[Johann Sebastian Bach|Bach]]
}}

In [[music theory]], '''counterpoint''' is the relationship of two or more simultaneous [[Part (music)|musical lines]] (also called voices) that are [[harmonically]] dependent on each other, yet independent in [[rhythm]] and [[Pitch contour|melodic contour]].<ref>{{cite book|last1=Laitz|first1=Steven G.|title=The Complete Musician|date=2008|publisher=Oxford University Press, Inc.|location=New York|isbn=978-0-19-530108-3|page=96|edition=2nd}}</ref><!--This doesn't sound like it applies to organum, conductus, discant, English discant, or fauxbourdon, all of which are contrapuntal forms--or even to contrapuntal practice generally in the 13th and 14th centuries.--> The term originates from the [[Latin]] {{lang|la|punctus contra punctum}} meaning "point against point", i.e. "[[Musical note|note]] against note". 

[[John Rahn]] describes counterpoint as follows:

{{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>
{{cite book
 |last= Rahn|first= John|author-link= John Rahn
 |others= intro. and comment. by [[Benjamin Boretz]]
 |title= Music Inside Out: Going Too Far in Musical Essays
 |year= 2000 |publisher= G+B Arts International
 |location= Amsterdam |isbn= 90-5701-332-0
 |oclc= 154331400|page= 177
}}
</ref>
}}

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).

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.

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 [[parallel fifths|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|url-access=subscription}}</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. 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.<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>

==Development==
Some examples of related compositional techniques include: the [[round (music)|round]] (familiar in folk traditions), the [[Canon (music)|canon]], and perhaps the most complex contrapuntal convention: the [[fugue]]. All of these are examples of [[Imitation (music)|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 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. For example, the harmony implied in the opening subject of the [[Fugue]] in [[G-sharp 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.":<ref>Tovey, D. F. (1924, p. 127, Bach 48 Preludes and Fugues, Book II. London, Associated Boards of the Royal Schools of Music.</ref>[[File:Bach prelude in G sharp minor from WTC Book 2.wav|thumb|Bach fugue in G-sharp minor from WTC Book 2]] [[File:Bach prelude in G sharp minor from WTC Book 3.png|thumb|center|500px|Bach fugue in G-sharp minor from WTC Book 2]]

[[Johann Sebastian Bach|Bach]]'s 3-part [[Inventions and Sinfonias (Bach)|Invention in F minor]] combines three independent melodies:
[[File:Bach 3-part Invention BWV 795, bars 7-9.wav|thumb|Bach 3-part Invention BWV&nbsp;795, bars 7–9]]
[[File:Bach 3-part Invention BWV 795, bars 7-9.png|thumb|center|500px|Bach 3-part Invention BWV 795, bars 7–9]]

According to pianist [[András Schiff]], Bach's counterpoint influenced the composing of both [[Wolfgang Amadeus Mozart|Mozart]] and [[Ludwig van Beethoven|Beethoven]]. In the [[development section]] of the opening movement of Beethoven's [[Piano Sonata No. 27 (Beethoven)|Piano Sonata in E minor]], Beethoven demonstrates this influence by adding "a wonderful counterpoint" to one of the main themes.<ref>[[András Schiff|Schiff, A.]] (2006) [https://download.guardian.co.uk/sys-audio/Arts/Culture/2006/12/13/01-27_emin_op90.mp3 "''Guardian'' Lecture on Beethoven Piano Sonata in E minor, Op. 90],  accessed 8 August 2019</ref>
[[File:Beethoven Piano Sonata Op. 90, first movement bars 110-113.wav|thumb|Beethoven Piano Sonata Op.&nbsp;90, first movement bars 110–113]]
[[File:Beethoven Piano Sonata Op. 90, first movement bars 110-113.png|thumb|center|500px|Beethoven Piano Sonata Op. 90, first movement bars 110–113]]

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 (Beethoven)|Symphony No. 9]], bars 116–123. The famous theme is heard on the [[viola]]s and [[cello]]s, while "the [[double bass|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."<ref>[[Antony Hopkins|Hopkins, Antony]] (1981, p. 275) ''The Nine Symphonies of Beethoven.'' London, Heinemann.</ref>
[[File:Beethoven, Symphony No. 9, finale, bars 116-123.wav|thumb|Beethoven, Symphony No. 9, finale, bars 116–123]]
[[File:Beethoven, Symphony No. 9, finale, bars 116-123.png|thumb|center|500px|Beethoven, Symphony No. 9, finale, bars 116–123]]

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."<ref>[[Gordon Jacob|Jacob, Gordon]] (1953, p. 14) Wagner Overture ''Die Meistersinger''. Harmondsworth, Penguin</ref> 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."<ref>[[Donald Tovey|Tovey, Donald Francis]] (1936, p. 127) ''Essays in Musical Analysis'', Volume IV. Oxford University Press.</ref>
[[File:Wagner Meistersinger Vorspiel bars 158-161.wav|thumb|Wagner Meistersinger Vorspiel bars 158–161]]
[[File:Wagner Meistersinger Vorspiel bars 158-161.png|thumb|center|500px|Wagner Meistersinger Vorspiel bars 158–161]]

One spectacular example of 5-voice counterpoint can be found in the finale to Mozart's [[Symphony No. 41 (Mozart)|Symphony No 41]] ("Jupiter" Symphony). Here five tunes combine simultaneously in "a rich tapestry of dialogue":<ref>[[Simon P. Keefe|Keefe, Simon P.]] (2003, p. 104) ''The Cambridge Companion to Mozart''. Cambridge University Press.</ref>
[[File:Mozart Jupiter Finale final section, bars 389-397 all five themes together.wav|thumb|Mozart Symphony No.&nbsp;41 Finale, bars 389–396]]
[[File:Mozart Jupiter Finale final section, bars 389-396 all five themes together.png|thumb|center|600px|Mozart Symphony No.&nbsp;41 Finale, bars 389–396]]
See also [[Invertible counterpoint]].

== Species counterpoint ==
{{Image frame|content=<score sound="1">
\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 "|." }
>>
</score>|align=center|caption=Example of "third 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.<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 [[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]].{{Citation needed|date=August 2018}}

===Considerations for all species===
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 ===
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.<ref>
{{cite web | url=https://finearts.uvic.ca/music/current/theory_materials/Counterpoint%20online.pdf | archive-url=https://web.archive.org/web/20181023092047/https://finearts.uvic.ca/music/current/theory_materials/Counterpoint%20online.pdf | url-status=dead | archive-date=23 October 2018 |author=Anon. |title=Species Counterpoint | publisher=Faculty of Fine Arts, University of Victoria, Canada | access-date=16 May 2020}} (archive from 23 October 2018)</ref>

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 1660–1741|url=https://catalyst.library.jhu.edu/catalog/bib_275485|archive-url=https://web.archive.org/web/20201003205348/https://catalyst.library.jhu.edu/catalog/bib_275485|url-status=dead|archive-date=October 3, 2020|title=The study of counterpoint from Johann Joseph Fux's Gradus ad parnassum|series=The Norton library, N277|date=1965|publisher=W. W. Norton|edition=Rev.|location=New York}}</ref><!--Who says that most later counterpoint teachers give these rules?--> are as follows.
{{Image frame|width=392|content=<score sound="1">
\relative c'' {
  <<
    \new Staff { \clef "treble" d1 a b d cis d }
    \new Staff { \clef "treble" d,1 f g f e d }
  >>
}
</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]].)

===Second species===
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 {
r2 a' d c b e d a b cis d1
\bar "|." }
\new Staff {
d,1 f g f e d} >>
}
}
</score>
<br />Short example of "second species" counterpoint
}}

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 may be consonant (perfect or imperfect), the unaccented beat may then have dissonance, in the form of three kinds of melodic embellishment: Passing Note (scalic movement between two consonances), Neighbour Note (a step away from a consonance and back to the same consonance) or an Escape Tone (a step in one direction to a dissonance followed by a leap in the opposite direction to a consonance).
The accented beat may have dissonance as well, but the unaccented beat that follows it must be consonant. This is known as Accented Dissonance, and takes the form of either a Neighbour note or a Passing note, which must resolve down to a consonance on the offbeat. 
# 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 <<
\new Staff {
d e f g a b c d
e d c b a b c a g a b cis d1
\bar "|." }
\new Staff {
d,1 f g f e d
}
>>
}
}
</score>
<br />Short example of "third species" counterpoint
}}
In ''third species'' counterpoint, four (or three, etc.) notes move against each longer note in the given part.

Three special figures are introduced into third species and later added to fifth species, and ultimately outside the restrictions of ''species writing''. There are three figures to consider: The ''nota [[cambiata]]'', ''double neighbor tones'', and ''double passing tones''.

Double neighbor tones: the figure is prolonged over four beats and allows special dissonances. The upper and lower tones are prepared on beat 1 and resolved on beat 4. The fifth note or downbeat of the next measure should move by step in the same direction as the last two notes of the double neighbor figure. Lastly a double passing tone allows two dissonant passing tones in a row. The figure would consist of 4 notes moving in the same direction by step. The two notes that allow dissonance would be beat 2 and 3 or 3 and 4. The dissonant interval of a fourth would proceed into a diminished fifth and the next note would resolve at the interval of a sixth.{{sfn|Salzer|Schachter1989|page={{Page needed|date=October 2015}}}}
[[File:Ascending Double Passing Tone.jpg|thumb|Example of a double passing tone in which the two middle notes are a dissonant interval from the cantus firmus, a fourth and a diminished fifth]]
[[File:Descending Double Neighbor Figure.jpg|thumb|Example of a descending double neighbor figure against a cantus firmus]]
[[File:Ascending Double Neighbor Figure.jpg|thumb|Example of an ascending double neighbor figure (with an interesting tritone leap at the end) against a cantus firmus]]

===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]]. A dissonant interval is allowed on beat 1 because of the syncopation created by the suspension. While it is not incorrect to start with a half note, it is also common to start 4th species with a half rest.
<score sound="1">
\relative c' {
\new PianoStaff <<
\new Staff {
\set Staff.explicitKeySignatureVisibility = #all-invisible
a'2 d~ d c~ c bes~
\key d \minor bes
a b cis d1 \bar "|."
}
\new Staff {
d, f g f e d \bar "|."
}
>>
}
</score>Short example of "fourth species" counterpoint

===Fifth species (florid counterpoint)===
In ''fifth species'' counterpoint, sometimes called ''florid counterpoint'', the other four species of counterpoint are combined within the added parts. In the example, the first and second bars are second species, the third bar is third species, the fourth and fifth bars are third and embellished fourth species, and the final bar is first species. In florid counterpoint it is important that no one species dominates the composition.
<score sound="1">
\relative c' {
\new PianoStaff <<
\new Staff {
r2 a' d c b4 c d e f e d2~ d4 cis8 b cis2 d1 \bar "|."
}
\new Staff {
d, f g f e d \bar "|."
}
>>
}
</score>
Short example of "Florid" counterpoint

==Contrapuntal derivations==
Since the [[Renaissance music|Renaissance]] period in European music, much contrapuntal music has been written in imitative counterpoint. In imitative counterpoint, two or more voices enter at different times, and (especially when entering) each voice repeats some version of the same melodic element. The [[fantasia (music)|fantasia]], the [[ricercar]], and later, the [[Canon (music)|canon]] and [[fugue]] (the contrapuntal form ''par excellence'') all feature imitative counterpoint, which also frequently appears in [[choir|choral]] works such as [[motet]]s and [[madrigal (music)|madrigals]]. Imitative counterpoint spawned a number of devices, including:

;[[Melodic inversion]]: The inverse of a given fragment of melody is the fragment turned upside down—so if the original fragment has a rising major third (see [[interval (music)|interval]]), the inverted fragment has a falling major (or perhaps minor) third, etc. (Compare, in [[twelve-tone technique]], the inversion of the tone row, which is the so-called prime series turned upside down.) (Note: in ''invertible counterpoint'', including ''double'' and ''triple counterpoint'', the term ''inversion'' is used in a different sense altogether. At least one pair of parts is switched, so that the one that was higher becomes lower. See [[Inversion (music)#Counterpoint|Inversion in counterpoint]]; it is not a kind of imitation, but a rearrangement of the parts.)
;[[Retrograde (music)|Retrograde]]: Whereby an imitative voice sounds the melody backwards in relation to the leading voice.
;[[Retrograde inversion]]: Where the imitative voice sounds the melody backwards and upside-down at once.
;[[Augmentation (music)|Augmentation]]: When in one of the parts in imitative counterpoint the note values are extended in duration compared to the rate at which they were sounded when introduced.
;[[Diminution]]: When in one of the parts in imitative counterpoint the note values are reduced in duration compared to the rate at which they were sounded when introduced.

==Free counterpoint==
Broadly speaking, due to the development of harmony, from the Baroque period on, most contrapuntal compositions were written in the style of free counterpoint. This means that the general focus of the composer had shifted away from how the intervals of added melodies related to a ''[[cantus firmus]]'', and more toward how they related to each other.{{Citation needed|date=August 2018}}<ref>{{Cite web |last=Kornfeld |first=Jono |title=Free Counterpoint, Two Parts |url=http://www.jkornfeld.net/free.pdf |access-date=6 February 2023}}</ref>

Nonetheless, according to [[Kent Kennan]]: "....actual teaching in that fashion (free counterpoint) did not become widespread until the late nineteenth century."<ref>{{cite book|last1=Kennan|first1=Kent|author-link=Kent Kennan|title=Counterpoint|year=1999|publisher=Prentice-Hall|location=Upper Saddle River, New Jersey|isbn=0-13-080746-X|pages=4|edition=fourth}}</ref> Young composers of the eighteenth and nineteenth centuries, such as [[Mozart]], [[Beethoven]], and [[Robert Schumann|Schumann]], were still educated in the style of "strict" counterpoint, but in practice, they would look for ways to expand on the traditional concepts of the subject.{{Citation needed|date=August 2018}}

Main features of free counterpoint:
# All forbidden chords, such as second-inversion, seventh, ninth etc., can be used freely as long as they resolve to a consonant triad
# Chromaticism is allowed
# The restrictions about rhythmic-placement of dissonance are removed. It is possible to use passing tones on the accented beat
# Appoggiatura is available: dissonance tones can be approached by leaps.

==Linear counterpoint==
{{Example needed|date=April 2018}}

'''Linear counterpoint''' is "a purely horizontal technique in which the integrity of the individual melodic lines is not sacrificed to harmonic considerations. "Its distinctive feature is rather the concept of melody, which served as the starting-point for the adherents of the 'new objectivity' when they set up linear counterpoint as an anti-type to the Romantic harmony."{{sfn|Sachs|Dahlhaus|2001}} The voice parts move freely, irrespective of the effects their combined motions may create."<ref name="Katz">Katz, Adele (1946). ''Challenge to Musical Tradition: A New Concept of Tonality'' (New York: A. A. Knopf), p. 340. Reprinted New York: Da Capo Press, 1972; reprinted n.p.: Katz Press, 2007, {{ISBN|1-4067-5761-6}}.</ref> In other words, either "the domination of the horizontal (linear) aspects over the vertical"<ref name="Ulrich">Ulrich, Homer (1962). ''Music: a Design for Listening'', second edition (New York: Harcourt, Brace & World), p. 438.</ref> is featured or the "harmonic control of lines is rejected."<ref name="Cunningham"/>

Associated with [[neoclassicism (music)|neoclassicism]],<ref name="Ulrich"/> the technique was first used in [[Igor Stravinsky]]'s ''[[Octet (Stravinsky)|Octet]]'' (1923),<ref name="Katz"/> inspired by [[J. S. Bach]] and [[Giovanni Pierluigi da Palestrina|Giovanni Palestrina]]. However, according to [[Knud Jeppesen]]: "Bach's and Palestrina's points of departure are antipodal. Palestrina starts out from lines and arrives at chords; Bach's music grows out of an ideally harmonic background, against which the voices develop with a bold independence that is often breath-taking."<ref name="Katz"/>

According to Cunningham, linear harmony is "a frequent approach in the 20th century...[in which lines] are combined with almost careless abandon in the hopes that new 'chords' and 'progressions'...will result." It is possible with "any kind of line, diatonic or [[Twelve-tone technique|duodecuple]]".<ref name="Cunningham">Cunningham, Michael (2007). ''Technique for Composers'', p. 144. {{ISBN|1-4259-9618-3}}.</ref>

==Dissonant counterpoint==
{{Example needed|date=April 2018}}

'''Dissonant counterpoint''' was originally theorized by [[Charles Seeger]] as "at first purely a school-room discipline," consisting of species counterpoint but with all the traditional rules reversed. First species counterpoint must be all dissonances, establishing "dissonance, rather than consonance, as the rule," and consonances are "resolved" through a skip, not step. He wrote that "the effect of this discipline" was "one of purification". Other [[aspects of music|aspects of composition]], such as rhythm, could be "dissonated" by applying the same principle.<ref>[[Charles Seeger]], "On Dissonant Counterpoint," ''Modern Music'' 7, no. 4 (June–July 1930): 25–26.</ref>

Seeger was not the first to employ dissonant counterpoint, but was the first to theorize and promote it. Other composers who have used dissonant counterpoint, if not in the exact manner prescribed by Charles Seeger, include [[Johanna Beyer]], [[John Cage]], [[Ruth Crawford Seeger|Ruth Crawford-Seeger]], [[Vivian Fine]], [[Carl Ruggles]], [[Henry Cowell]], [[Carlos Chávez]], [[John J. Becker]], [[Henry Brant]], [[Lou Harrison]], [[Wallingford Riegger]], and [[Frank Wigglesworth]].<ref>Spilker, John D., [http://etd.lib.fsu.edu/theses/available/etd-04032010-120836/unrestricted/Spilker_J_Dissertation_2010.pdf ''"Substituting a New Order": Dissonant Counterpoint, Henry Cowell, and the network of ultra-modern composers''] {{webarchive|url=https://web.archive.org/web/20110815203847/http://etd.lib.fsu.edu/theses/available/etd-04032010-120836/unrestricted/Spilker_J_Dissertation_2010.pdf |date=2011-08-15 }}, Ph.D. dissertation, [[Florida State University College of Music]], 2010.</ref>

==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.&nbsp;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://wwjjkg/ hjgw.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
* [https://counterpointbot.com Counterpoint Bot: An app that generates music using species counterpoint]
{{Counterpoint & polyphony}}
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[[Category:Counterpoint| ]]