Counterpoint

Counterpoint

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In music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

, counterpoint is the relationship between two or more voices
Register (music)
In music, a register is the relative "height" or range of a note, set of pitches or pitch classes, melody, part, instrument or group of instruments...

 that are independent in contour and rhythm
Rhythm
Rhythm may be generally defined as a "movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions." This general meaning of regular recurrence or pattern in time may be applied to a wide variety of cyclical natural phenomena having a periodicity or...

 and are harmonically
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...

 interdependent (polyphony
Polyphony
In music, polyphony is a texture consisting of two or more independent melodic voices, as opposed to music with just one voice or music with one dominant melodic voice accompanied by chords ....

). It has been most commonly identified in classical music
Classical music
Classical music is the art music produced in, or rooted in, the traditions of Western liturgical and secular music, encompassing a broad period from roughly the 11th century to present times...

, developing strongly during the Renaissance
Renaissance music
Renaissance music is European music written during the Renaissance. Defining the beginning of the musical era is difficult, given that its defining characteristics were adopted only gradually; musicologists have placed its beginnings from as early as 1300 to as late as the 1470s.Literally meaning...

 and in much of the common practice period
Common practice period
The common practice period, in the history of Western art music , spanning the Baroque, Classical, and Romantic periods, lasted from c. 1600 to c. 1900.-General characteristics:...

, especially in Baroque music
Baroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...

. The term originates from the Latin
Latin
Latin is an Italic language originally spoken in Latium and Ancient Rome. It, along with most European languages, is a descendant of the ancient Proto-Indo-European language. Although it is considered a dead language, a number of scholars and members of the Christian clergy speak it fluently, and...

 punctus contra punctum meaning "point against point".

General principles


In its most general aspect, counterpoint involves the writing of musical lines that sound very different and move independently from each other but sound harmonious when played simultaneously. In each era, contrapuntally organized music writing has been subject to rules, sometimes strict. By definition, chords
Chord (music)
A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...

 occur when multiple notes sound simultaneously; however, harmonic, "vertical" features are considered secondary and almost incidental when counterpoint is the predominant textural element. Counterpoint focuses on melodic interaction—only secondarily on the harmonies produced by that interaction. In the words of John Rahn:
The separation of harmony and counterpoint is not absolute. It is impossible to write simultaneous lines without producing harmony, and impossible to write harmony without linear activity. The composer who chooses to ignore one aspect in favour of the other still must face the fact that the listener cannot simply turn off harmonic or linear hearing at will; thus the composer risks creating annoying distractions unintentionally. Bach
Johann Sebastian Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...

's counterpoint—often considered the most profound synthesis of the two dimensions ever achieved—is extremely rich harmonically and always clearly directed tonally, while the individual lines remain fascinating.

Development


Counterpoint was elaborated extensively in the Renaissance
Renaissance music
Renaissance music is European music written during the Renaissance. Defining the beginning of the musical era is difficult, given that its defining characteristics were adopted only gradually; musicologists have placed its beginnings from as early as 1300 to as late as the 1470s.Literally meaning...

 period, but composers of the Baroque
Baroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...

 period brought counterpoint to a culmination of sorts, and it may be said that, broadly speaking, harmony
Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...

 then took over as the predominant organizing principle in musical composition. The Baroque composer Johann Sebastian Bach
Johann Sebastian Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...

 wrote most of his music incorporating counterpoint, and explicitly and systematically explored the full range of contrapuntal possibilities in such works as The Art of Fugue
The Art of Fugue
The Art of Fugue , BWV 1080, is an incomplete work by Johann Sebastian Bach . It was most likely started at the beginning of the 1740s, if not earlier. The first known surviving version, which contained 12 fugues and 2 canons, was copied by the composer in 1745...

.

Given the way terminology in music history has evolved, such music created from the Baroque
Baroque music
Baroque music describes a style of Western Classical music approximately extending from 1600 to 1760. This era follows the Renaissance and was followed in turn by the Classical era...

 period on is described as contrapuntal, while music from before Baroque times is called polyphonic
Polyphony
In music, polyphony is a texture consisting of two or more independent melodic voices, as opposed to music with just one voice or music with one dominant melodic voice accompanied by chords ....

. Hence, earlier composers such as Guillaume de Machaut
Guillaume de Machaut
Guillaume de Machaut was a Medieval French poet and composer. He is one of the earliest composers on whom significant biographical information is available....

 and Josquin des Prez
Josquin Des Prez
Josquin des Prez [Josquin Lebloitte dit Desprez] , often referred to simply as Josquin, was a Franco-Flemish composer of the Renaissance...

 are said to have written polyphonic music.

Homophony
Homophony
In music, homophony is a texture in which two or more parts move together in harmony, the relationship between them creating chords. This is distinct from polyphony, in which parts move with rhythmic independence, and monophony, in which all parts move in parallel rhythm and pitch. A homophonic...

, by contrast with polyphony, features music in which chords
Chord (music)
A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...

 or vertical intervals
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

 work with a single melody without much consideration of the melodic character of the added accompanying elements, or of their melodic interactions with the melody they accompany. As suggested above, most popular music written today is predominantly homophonic, its composition governed mainly by considerations of chord and harmony; but, while general tendencies can often be fairly strong one way or another, rather than describing a musical work in absolute terms as either polyphonic or homophonic, it is a question of degree.

The form or compositional genre known as fugue
Fugue
In music, a fugue is a compositional technique in two or more voices, built on a subject that is introduced at the beginning in imitation and recurs frequently in the course of the composition....

 is perhaps the most complex contrapuntal convention. Other examples include the round
Round (music)
A round is a musical composition in which two or more voices sing exactly the same melody , but with each voice beginning at different times so that different parts of the melody coincide in the different voices, but nevertheless fit harmoniously together...

 (familiar in folk traditions) and the canon
Canon (music)
In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...

.

In musical composition, contrapuntal techniques are important for enabling composers to generate musical ironies that serve not only to intrigue listeners into listening more intently to the spinning out of complexities found within the texture
Texture (music)
In music, texture is the way the melodic, rhythmic, and harmonic materials are combined in a composition , thus determining the overall quality of sound of a piece...

 of a polyphonic composition, but also to draw them all the more into hearing the working out of these figures and interactions of musical dialogue. A melodic fragment, heard alone, makes a particular impression; but when the fragment is heard simultaneously with other melodic ideas, or combined in unexpected ways with itself (as in a canon or fugue), greater depths of affective meaning are revealed. Through development
Musical development
In European classical music, musical development is a process by which a musical idea is communicated in the course of a composition. It refers to the transformation and restatement of initial material, and is often contrasted with musical variation, which is a slightly different means to the same...

of a musical idea, the fragments undergo a working out into something musically greater than the sum of the parts, something conceptually more profound than a single pleasing melody.

Species counterpoint


Species counterpoint is a type of so-called strict counterpoint, developed as a pedagogical tool, in which a student progresses through several "species" of increasing complexity, always working with a very plain given part in the cantus firmus
Cantus firmus
In music, a cantus firmus is a pre-existing melody forming the basis of a polyphonic composition.The plural of this Latin term is , though the corrupt form canti firmi is also attested...

 (Latin for "fixed melody"). The student gradually attains the ability to write free counterpoint (that is, less rigorously constrained counterpoint, usually without a cantus firmus) according to the rules at the given 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 late 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
Lodovico Zacconi
Lodovico Zacconi was an Italian-Austrian composer and musical theorist of the late Renaissance and early Baroque eras...

 in his Prattica di musica. Zacconi, unlike later theorists, included a few extra contrapuntal techniques as species, for example invertible counterpoint
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...

.

By far the most famous pedagogue to use the term, and the one who made it famous, was Johann Joseph Fux. In 1725 he published Gradus ad Parnassum (Steps to Parnassus), a work intended to help teach students how to compose, using counterpoint—specifically, the contrapuntal style as practised by Palestrina
Giovanni Pierluigi da Palestrina
Giovanni Pierluigi da Palestrina was an Italian Renaissance composer of sacred music and the best-known 16th-century representative of the Roman School of musical composition...

 in the late 16th century—as the principal technique. As the basis for his simplified and often over-restrictive codification of Palestrina's practice (see General notes, below), Fux described five species:
  1. Note against note;
  2. Two notes against one;
  3. Four (extended by others to include three, or six, etc.) notes against one;
  4. Notes offset against each other (as suspensions
    Nonchord tone
    A nonchord tone, nonharmonic tone, or non-harmony note is a note in a piece of music which is not a part of the implied harmony that is described by the other notes sounding at the time...

    );
  5. All the first four species together, as "florid" counterpoint.


A succession of later theorists imitated Fux's seminal work quite closely, but often with some small and idiosyncratic modifications in the rules. A good example is Luigi Cherubini
Luigi Cherubini
Luigi Cherubini was an Italian composer who spent most of his working life in France. His most significant compositions are operas and sacred music. Beethoven regarded Cherubini as the greatest of his contemporaries....

.

Considerations for all species


Students of species counterpoint usually practice writing counterpoint in all the modes
Musical mode
In the theory of Western music since the ninth century, mode generally refers to a type of scale. This usage, still the most common in recent years, reflects a tradition dating to the middle ages, itself inspired by the theory of ancient Greek music.The word encompasses several additional...

 except Locrian
Locrian mode
The Locrian mode is either a musical mode or simply a diatonic scale. Although the term occurs in several classical authors on music theory, including Cleonides and Athenaeus , there is no warrant for the modern usage of Locrian as equivalent to Glarean's Hyperaeolian mode, in either classical,...

 (that is, Ionian
Ionian mode
Ionian mode is the name assigned by Heinrich Glarean in 1547 to his new authentic mode on C , which uses the diatonic octave species from C to the C an octave higher, divided at G into a fourth species of perfect fifth plus a third species of perfect fourth : C D...

, Dorian
Dorian mode
Due to historical confusion, Dorian mode or Doric mode can refer to three very different musical modes or diatonic scales, the Greek, the medieval, and the modern.- Greek Dorian mode :...

, Phrygian
Phrygian mode
The Phrygian mode can refer to three different musical modes: the ancient Greek tonos or harmonia sometimes called Phrygian, formed on a particular set octave species or scales; the Medieval Phrygian mode, and the modern conception of the Phrygian mode as a diatonic scale, based on the latter...

, Lydian
Lydian mode
The Lydian musical scale is a rising pattern of pitches comprising three whole tones, a semitone, two more whole tones, and a final semitone. This sequence of pitches roughly describes the fifth of the eight Gregorian modes, known as Mode V or the authentic mode on F, theoretically using B but in...

, Mixolydian
Mixolydian mode
Mixolydian mode may refer to one of three things: the name applied to one of the ancient Greek harmoniai or tonoi, based on a particular octave species or scale; one of the medieval church modes; a modern musical mode or diatonic scale, related to the medieval mode.-Greek Mixolydian:The idea of a...

 and Aeolian
Aeolian mode
The Aeolian mode is a musical mode or, in modern usage, a diatonic scale called the natural minor scale.The word "Aeolian" in the music theory of ancient Greece was an alternative name for what Aristoxenus called the Low Lydian tonos , nine semitones...

). The following rules apply to melodic writing in each species, for each part:
  1. The final must be approached by step
    Steps and skips
    In music, a step, or conjunct motion, is a linear or successive interval between two pitches which are consecutive scale degrees. Any larger interval is called a skip , or disjunct motion...

    . If the final is approached from below, the leading tone must be raised, except in the case of the Phrygian mode. Thus, in the Dorian mode on D, a C is necessary at the cadence.
  2. Permitted melodic intervals are the perfect fourth, fifth, and octave, as well as the major and minor second, major and minor third, and ascending minor sixth. When the ascending minor sixth is used it must be immediately followed by motion downwards.
  3. If writing two skips
    Steps and skips
    In music, a step, or conjunct motion, is a linear or successive interval between two pitches which are consecutive scale degrees. Any larger interval is called a skip , or disjunct motion...

     in the same direction—something which must be done only rarely—the second must be smaller than the first, and the interval between the first and the third note may not be dissonant.
  4. If writing a skip in one direction, it is best to proceed after the skip with motion in the other direction.
  5. The interval of a tritone
    Tritone
    In classical music from Western culture, the tritone |tone]]) is traditionally defined as a musical interval composed of three whole tones. In a chromatic scale, each whole tone can be further divided into two semitones...

     in three notes is to be avoided (for example, an ascending melodic motion F - A - B natural), as is the interval of a seventh in three notes.


And, in all species, the following rules apply concerning the combination of the parts:
  1. The counterpoint must begin and end on a perfect consonance
    Consonance and dissonance
    In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...

    .
  2. Contrary motion
    Contrary motion
    In music theory, contrapuntal motion is the general movement of two melodic lines with respect to each other. In traditional four-part harmony, it is important that lines maintain their independence, an effect which can be achieved by the judicious use of the four types of contrapuntal motion:...

     should predominate.
  3. Perfect consonances must be approached by oblique or contrary motion
  4. Imperfect consonances may be approached by any type of motion
  5. The interval of a tenth should not be exceeded between two adjacent parts, unless by necessity.
  6. Build from the bass, upward.


Finally, in species counterpoint it is important to remember that the interval of the perfect fourth is usually considered a dissonance.

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. The species is said to be expanded if any of the added notes are broken up (simply repeated).

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
Steps and skips
In music, a step, or conjunct motion, is a linear or successive interval between two pitches which are consecutive scale degrees. Any larger interval is called a skip , or disjunct motion...

.) 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. Some are vague, and since good judgement and taste have been regarded by contrapuntists as more important than strict observance of mechanical rules, there are many more cautions than prohibitions. But some are closer to being mandatory, and are accepted by most authorities.
  1. 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.
  2. Use no unisons except at the beginning or end.
  3. Avoid parallel fifths or octaves
    Consecutive fifths
    In music, consecutive fifths are progressions in which a perfect fifth is followed by a different perfect fifth between the same two musical parts : for example, from C to D in one part along with G to A in a higher part...

     between any two parts; and avoid "hidden" parallel fifths or octaves: that is, movement by similar motion
    Contrary motion
    In music theory, contrapuntal motion is the general movement of two melodic lines with respect to each other. In traditional four-part harmony, it is important that lines maintain their independence, an effect which can be achieved by the judicious use of the four types of contrapuntal motion:...

     to a perfect fifth or octave, unless one part (sometimes restricted to the higher of the parts) moves by step.
  4. 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.)
  5. Avoid moving in parallel thirds or sixths for very long.
  6. Attempt to keep any two adjacent parts within a tenth of each other, unless an exceptionally pleasing line can be written by moving outside of that range.
  7. Avoid having any two parts move in the same direction by skip.
  8. Attempt to have as much contrary motion as possible.
  9. Avoid dissonant intervals between any two parts: major or minor 2nd, major or minor 7th, any augmented or diminished interval, and perfect fourth (in many contexts).


In the following example in two parts, the cantus firmus
Cantus firmus
In music, a cantus firmus is a pre-existing melody forming the basis of a polyphonic composition.The plural of this Latin term is , though the corrupt form canti firmi is also attested...

 is the lower part. (The same cantus firmus is used for later examples also. Each is in the Dorian mode
Dorian mode
Due to historical confusion, Dorian mode or Doric mode can refer to three very different musical modes or diatonic scales, the Greek, the medieval, and the modern.- Greek 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. The species is said to be expanded if one of these two shorter notes differs in length from the other.

Additional considerations in second species counterpoint are as follows, and are in addition to the considerations for first species:
  1. It is permissible to begin on an upbeat, leaving a half-rest in the added voice.
  2. 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.
  3. 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.
  4. Use caution with successive accented perfect fifths or octaves. They must not be used as part of a sequential pattern.


Third species


In third species counterpoint, four (or three, etc.) notes move against each longer note in the given part. As with second species, it is called expanded if the shorter notes vary in length among themselves.

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 dissonance
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...

 on the beat, followed by the suspended note then changing (and "catching up") to create a subsequent consonance
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...

 with the note in the given part as it continues to sound. As before, fourth species counterpoint is said to be 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
Syncopation
In music, syncopation includes a variety of rhythms which are in some way unexpected in that they deviate from the strict succession of regularly spaced strong and weak but also powerful beats in a meter . These include a stress on a normally unstressed beat or a rest where one would normally be...

.

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.

General notes


It is a common and pedantic misconception that counterpoint is defined by these five species, and therefore anything that does not follow the strict rules of the five species is not "proper" counterpoint. This is not true; although much contrapuntal music of the common practice period
Common practice period
The common practice period, in the history of Western art music , spanning the Baroque, Classical, and Romantic periods, lasted from c. 1600 to c. 1900.-General characteristics:...

 adheres to the spirit of the rules, and often to the letter of them, the exceptions are many. Fux's book and its concept of "species" was purely a method of teaching counterpoint, not a definitive or rigidly prescriptive set of rules for it. He arrived at his method of teaching by examining the works of Palestrina, an important late 16th-century composer who in Fux's time was held in the highest esteem as a contrapuntist. Works in the contrapuntal style of the 16th century—the "prima pratica
Prima pratica
Prima pratica refers to early Baroque music which looks more to the style of Palestrina, or the style codified by Gioseffo Zarlino, than to more "modern" styles. It is contrasted with seconda pratica music...

" or "stile antico
Stile antico
Stile antico, literally "ancient style", is a term describing music from the sixteenth through the twentieth centuries. It refers to a manner of composition which is historically conscious, as opposed to stile moderno...

", as it was called by later composers—were often said by Fux's contemporaries to be in "Palestrina style." Indeed, Fux's treatise is a compendium of Palestrina's actual techniques, simplified and regularised for pedagogical use (and so permitting fewer liberties than occurred in actual practice).

Contrapuntal derivations


Since the Renaissance
Renaissance music
Renaissance music is European music written during the Renaissance. Defining the beginning of the musical era is difficult, given that its defining characteristics were adopted only gradually; musicologists have placed its beginnings from as early as 1300 to as late as the 1470s.Literally meaning...

 period in European music, much music which is considered contrapuntal 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
Fantasia (music)
The fantasia is a musical composition with its roots in the art of improvisation. Because of this, it seldom approximates the textbook rules of any strict musical form ....

, the ricercar
Ricercar
A ricercar is a type of late Renaissance and mostly early Baroque instrumental composition. The term means to search out, and many ricercars serve a preludial function to "search out" the key or mode of a following piece...

, and later, the canon
Canon (music)
In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...

 and fugue
Fugue
In music, a fugue is a compositional technique in two or more voices, built on a subject that is introduced at the beginning in imitation and recurs frequently in the course of the composition....

 (the contrapuntal form par excellence) all feature imitative counterpoint, which also frequently appears in choral
Choir
A choir, chorale or chorus is a musical ensemble of singers. Choral music, in turn, is the music written specifically for such an ensemble to perform.A body of singers who perform together as a group is called a choir or chorus...

 works such as motet
Motet
In classical music, motet is a word that is applied to a number of highly varied choral musical compositions.-Etymology:The name comes either from the Latin movere, or a Latinized version of Old French mot, "word" or "verbal utterance." The Medieval Latin for "motet" is motectum, and the Italian...

s and madrigals
Madrigal (music)
A madrigal is a secular vocal music composition, usually a partsong, of the Renaissance and early Baroque eras. Traditionally, polyphonic madrigals are unaccompanied; the number of voices varies from two to eight, and most frequently from three to six....

. Imitative counterpoint has spawned a number of devices that composers have turned to in order to give their works both mathematical rigor and expressive range. Some of these devices include:
  • 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
Interval (music)
In music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...

), 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 in counterpoint; it is not a kind of imitation, but a rearrangement of the parts.)
  • Retrograde
    Permutation (music)
    In music, a permutation of a set is any ordering of the elements of that set. Different permutations may be related by transformation, through the application of zero or more of certain operations, such as transposition, inversion, retrogradation, circular permutation , or multiplicative operations...

whereby notes in an imitative voice sound backwards in relation to their order in the original.
  • Retrograde inversion
    Retrograde inversion
    Retrograde inversion is a musical term that literally means "backwards and upside down": "The inverse of the series is sounded in reverse order." This is a technique used in music, specifically in twelve-tone technique, where the inversion and retrograde techniques are performed on the same tone...

where the imitative voice sounds notes both backwards and upside down.
  • Augmentation
    Augmentation (music)
    In Western music and music theory, the word augmentation has three distinct meanings. Augmentation is a compositional device where a melody, theme or motif is presented in longer note-values than were previously used...

when in one of the parts in imitative counterpoint the notes are extended in duration compared to the rate at which they were sounded when introduced.
  • Diminution
    Diminution
    In Western music and music theory, diminution has four distinct meanings. Diminution may be a form of embellishment in which a long note is divided into a series of shorter, usually melodic, values...

when in one of the parts in imitative counterpoint the notes are reduced in duration compared to the rate at which they were sounded when introduced.

Linear counterpoint


Linear counterpoint is "a purely horizontal technique in which the integrity of the individual melodic lines is not sacrificed to harmonic considerations. The voice parts move freely, irrespective of the effects their combined motions may create." In other words, either "the domination of the horizontal (linear) aspects over the vertical" is featured or the "harmonic control of lines is rejected."

Associated with neoclassicism
Neoclassicism (music)
Neoclassicism in music was a twentieth-century trend, particularly current in the period between the two World Wars, in which composers sought to return to aesthetic precepts associated with the broadly defined concept of "classicism", namely order, balance, clarity, economy, and emotional restraint...

, the first work to use the technique is Stravinsky's
Igor Stravinsky
Igor Fyodorovich Stravinsky ; 6 April 1971) was a Russian, later naturalized French, and then naturalized American composer, pianist, and conductor....

 Octet for Wind Instruments (1923), inspired by Bach and Palestrina
Palestrina
Palestrina is an ancient city and comune with a population of about 18,000, in Lazio, c. 35 km east of Rome...

. However, according to Knud Jeppesen
Knud Jeppesen
Knud Jeppesen was a Danish musicologist, composer, and writer on the history of music....

: "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."

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 duodecuple."

Further reading: Kurth, Ernst
Ernst Kurth
Ernst Kurth, was a Swiss music theorist.- Career :Kurth studied musicology with Guido Adler in Vienna, and earned his Ph.D with a thesis about Christoph Willibald Gluck's's operatic style...

 (2006). "Foundations of Linear Counterpoint", Ernst Kurth: Selected Writings. ISBN 0521028248.

Dissonant counterpoint


Dissonant counterpoint was first theorized by Charles Seeger
Charles Seeger
Charles Seeger, Jr. was a noted musicologist, composer, and teacher. He was the father of iconic American folk singer Pete Seeger .-Life:...

 as "at first purely a school-room discipline," consisting of species counterpoint but with all the traditional rules reversed. First species counterpoint is required to 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 composition, such as rhythm, could be "dissonated" by applying the same principle (Charles Seeger, "On Dissonant Counterpoint," Modern Music 7, no. 4 (June–July 1930): 25-26).

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 Ruth Crawford-Seeger, Carl Ruggles
Carl Ruggles
Charles "Carl" Sprague Ruggles was an American composer of the American Five group. He wrote finely crafted pieces using "dissonant counterpoint", a term coined by Charles Seeger to describe Ruggles' music...

, Henry Cowell
Henry Cowell
Henry Cowell was an American composer, music theorist, pianist, teacher, publisher, and impresario. His contribution to the world of music was summed up by Virgil Thomson, writing in the early 1950s:...

, Henry Brant
Henry Brant
Henry Dreyfuss Brant was a Canadian-born American composer. An expert orchestrator with a flair for experimentation, many of Brant's works featured spatialization techniques.- Biography :...

, Dane Rudhyar
Dane Rudhyar
Dane Rudhyar , born Daniel Chennevière, was an author, modernist composer and humanistic astrologer. He was the pioneer of modern transpersonal astrology.-Biography:...

, Lou Harrison
Lou Harrison
Lou Silver Harrison was an American composer. He was a student of Henry Cowell, Arnold Schoenberg, and K. P. H. Notoprojo Lou Silver Harrison (May 14, 1917 – February 2, 2003) was an American composer. He was a student of Henry Cowell, Arnold Schoenberg, and K. P. H. Notoprojo Lou Silver Harrison...

, Fartein Valen
Fartein Valen
Olav Fartein Valen was a Norwegian composer and musical theorist, notable for his work within atonal polyphonic music.-Background:...

, and Arnold Schoenberg
Arnold Schoenberg
Arnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...

.

Contrapuntal radio


Glenn Gould
Glenn Gould
Glenn Herbert Gould was a Canadian pianist who became one of the best-known and most celebrated classical pianists of the 20th century. He was particularly renowned as an interpreter of the keyboard music of Johann Sebastian Bach...

 used what he considered a kind of counterpoint in his three radio documentaries: The Idea of North, The Latecomers, and The Quiet in the Land (see The Solitude Trilogy
Solitude Trilogy
The Solitude Trilogy is a collection of three hour-long radio documentaries produced by Canadian pianist Glenn Gould for the Canadian Broadcasting Corporation and a film collaboration between the CBC and PBS...

). Gould called this method "contrapuntal radio." It involves the voices of two or more people simultaneously speaking (or playing against each other), entering and leaving the work as in a fugue
Fugue
In music, a fugue is a compositional technique in two or more voices, built on a subject that is introduced at the beginning in imitation and recurs frequently in the course of the composition....

.

External links