In music theory, counterpoint is the relationship of two or more simultaneous musical lines (also called voices) that are harmonically interdependent yet independent in rhythm and melodic contour.[1] The term originates from the Latinpunctus contra punctum meaning "point against point", i.e. "note against note". John Rahn describes counterpoint as follows:
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'.[2]
There are several different forms of counterpoint, including imitative counterpoint and free counterpoint. Imitative counterpoint involves the repetition of a main melodic idea across different vocal parts, with or without variation. Compositions written in free counterpoint often incorporate non-traditional harmonies and chords, chromaticism and dissonance.
General principles
The term "counterpoint" has been used to designate a voice or even an entire composition.[3] Counterpoint focuses on melodic interaction—only secondarily on the harmonies produced by that interaction.
Work initiated by Guerino Mazzola (born 1947) has given counterpoint theory a mathematical foundation. In particular, Mazzola's model gives a structural (and not psychological) foundation of forbidden parallels of fifths and the dissonant fourth. Octavio Agustin has extended the model to microtonal contexts.[4][5] Another theorist who has tried to incorporate mathematical principles in his study of counterpoint is Sergei Taneyev (1856-1915). Inspired by Spinoza,[6] 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.[7]
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.[8][9]
Development
Some examples of related compositional techniques include: the round (familiar in folk traditions), the canon, and perhaps the most complex contrapuntal convention: the fugue. All of these are examples of imitative counterpoint.
Examples from the repertoire
There are many examples of song melodies that are harmonically interdependent yet independent in rhythm and melodic contour. For example, "Frère Jacques" and "Three Blind Mice" combine euphoniously when sung together. A number of popular songs that share the same chord progression can also be sung together as counterpoint. A well-known pair of examples is "My Way" combined with "Life on Mars".[10]
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."[11]:
Bach fugue in G-sharp minor from WTC Book 2Bach fugue in G-sharp minor from WTC Book 2
According to pianist András Schiff, Bach's counterpoint influenced the composing of both Mozart and Beethoven. In the development section of the opening movement of Beethoven's Piano Sonata in E minor, Beethoven demonstrates this influence by adding "a wonderful counterpoint" to one of the main themes.[12]
Beethoven Piano Sonata Op.90, first movement bars 110–113Beethoven 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, bars 116–123. The famous theme is heard on the violas and cellos, while "the basses add a bass-line whose sheer unpredictability gives the impression that it is being spontaneously improvised. Meantime a solo bassoon adds a counterpoint that has a similarly impromptu quality."[13]
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."[14] 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."[15]
One spectacular example of 5-voice counterpoint can be found in the finale to Mozart's Symphony No 41 ("Jupiter" Symphony). Here five tunes combine simultaneously in "a rich tapestry of dialogue":[16]
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.[17] The idea is at least as old as 1532, when Giovanni Maria Lanfranco described a similar concept in his Scintille di musica (Brescia, 1533). The 16th-century Venetian theorist Zarlino elaborated on the idea in his influential Le institutioni harmoniche, and it was first presented in a codified form in 1619 by Lodovico Zacconi in his Prattica di musica. Zacconi, unlike later theorists, included a few extra contrapuntal techniques, such as invertible counterpoint.
Gradus ad Parnassum (1725) by Johann Joseph Fux defines the modern system of teaching counterpoint
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]
Considerations for all species
The following rules apply to melodic writing in each species, for each part:
The final note must be approached by step. If the final is approached from below, then the leading tone must be raised in a minor key (Dorian, Hypodorian, Aeolian, Hypoaeolian), but not in Phrygian or Hypophrygian mode. Thus, in the Dorian mode on D, a C♯ is necessary at the cadence.[18]
Permitted melodic intervals are the perfect unison, fourth, fifth, and octave, as well as the major and minor second, major and minor third, and ascending minor sixth. The ascending minor sixth must be immediately followed by motion downwards.
If writing two skips in the same direction—something that must be only rarely done—the second must be smaller than the first, and the interval between the first and the third note may not be dissonant. The three notes should be from the same triad; if this is impossible, they should not outline more than one octave. In general, do not write more than two skips in the same direction.
If writing a skip in one direction, it is best to proceed after the skip with step-wise motion in the other direction.
The interval of a tritone in three notes should be avoided (for example, an ascending melodic motion F–A–B♮)[19] 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.
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.[20]
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,[21] are as follows.
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.
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.
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 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
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.[18]
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 fifthExample of a descending double neighbor figure against a cantus firmusExample 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 dissonance on the beat, followed by the suspended note then changing (and "catching up") to create a subsequent 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.
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.
Short example of "Florid" counterpoint
Contrapuntal derivations
Since the 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, the ricercar, and later, the canon and fugue (the contrapuntal form par excellence) all feature imitative counterpoint, which also frequently appears in choral works such as motets and madrigals. Imitative counterpoint spawned a number of devices, including:
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), 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.)
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.
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][22]
Nonetheless, according to Kent Kennan: "....actual teaching in that fashion (free counterpoint) did not become widespread until the late nineteenth century."[23] Young composers of the eighteenth and nineteenth centuries, such as Mozart, Beethoven, and 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]
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 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."[3] The voice parts move freely, irrespective of the effects their combined motions may create."[24] In other words, either "the domination of the horizontal (linear) aspects over the vertical"[25] is featured or the "harmonic control of lines is rejected."[26]
Associated with neoclassicism,[25] the technique was first used in Igor Stravinsky's Octet (1923),[24] inspired by J. S. Bach and 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."[24]
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".[26]
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 composition, such as rhythm, could be "dissonated" by applying the same principle.[27]
In classical music, a fugue is a contrapuntal, polyphonic compositional technique in two or more voices, built on a subject that is introduced at the beginning in imitation, which recurs frequently throughout the course of the composition. It is not to be confused with a fuguing tune, which is a style of song popularized by and mostly limited to early American music and West Gallery music. A fugue usually has three main sections: an exposition, a development, and a final entry that contains the return of the subject in the fugue's tonic key. Fugues can also have episodes, which are parts of the fugue where new material often based on the subject is heard; a stretto, when the fugue's subject overlaps itself in different voices, or a recapitulation. A popular compositional technique in the Baroque era, the fugue was fundamental in showing mastery of harmony and tonality as it presented counterpoint.
Giovanni Pierluigi da Palestrina was an Italian composer of late Renaissance music. The central representative of the Roman School, with Orlande de Lassus and Tomás Luis de Victoria, Palestrina is considered the leading composer of late 16th-century Europe.
Polyphony is a type of musical texture consisting of two or more simultaneous lines of independent melody, as opposed to a musical texture with just one voice (monophony) or a texture with one dominant melodic voice accompanied by chords (homophony).
In music, harmony is the concept of combining different sounds together in order to create new, distinct musical ideas. Theories of harmony seek to describe or explain the effects created by distinct pitches or tones coinciding with one another; harmonic objects such as chords, textures and tonalities are identified, defined, and categorized in the development of these theories. Harmony is broadly understood to involve both a "vertical" dimension (frequency-space) and a "horizontal" dimension (time-space), and often overlaps with related musical concepts such as melody, timbre, and form.
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
A fourth is a musical interval encompassing four staff positions in the music notation of Western culture, and a perfect fourth is the fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, because the note F is the fifth semitone above C, and there are four staff positions between C and F. Diminished and augmented fourths span the same number of staff positions, but consist of a different number of semitones.
A nonchord tone (NCT), nonharmonic tone, or embellishing tone is a note in a piece of music or song that is not part of the implied or expressed chord set out by the harmonic framework. In contrast, a chord tone is a note that is a part of the functional chord. Nonchord tones are most often discussed in the context of the common practice period of classical music, but the term can also be used in the analysis of other types of tonal music, such as Western popular music.
In music, a canon is a contrapuntal (counterpoint-based) compositional technique 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. The follower must imitate the leader, either as an exact replication of its rhythms and intervals or some transformation thereof. Repeating canons in which all voices are musically identical are called rounds—familiar singalong versions of "Row, Row, Row Your Boat" and "Frère Jacques" that call for each successive group of voices to begin the same song a bar or two after the previous group began are popular examples.
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. Diminution may also be the compositional device where a melody, theme or motif is presented in shorter note-values than were previously used. Diminution is also the term for the proportional shortening of the value of individual note-shapes in mensural notation, either by coloration or by a sign of proportion. A minor or perfect interval that is narrowed by a chromatic semitone is a diminished interval, and the process may be referred to as diminution.
Jehan le Taintenier or Jean Teinturier was a Renaissance music theorist and composer from the Low Countries. Up to his time, he is perhaps the most significant European writer on music since Guido of Arezzo.
In music, a cantus firmus is a pre-existing melody forming the basis of a polyphonic composition.
Voice leading is the linear progression of individual melodic lines and their interaction with one another to create harmonies, typically in accordance with the principles of common-practice harmony and counterpoint.
In music, consecutive fifths or parallel fifths are progressions in which the interval of 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. Octave displacement is irrelevant to this aspect of musical grammar; for example, a parallel twelfth is equivalent to a parallel fifth.
In music, consonance and dissonance are categorizations of simultaneous or successive sounds. Within the Western tradition, some listeners associate consonance with sweetness, pleasantness, and acceptability, and dissonance with harshness, unpleasantness, or unacceptability, although there is broad acknowledgement that this depends also on familiarity and musical expertise. The terms form a structural dichotomy in which they define each other by mutual exclusion: a consonance is what is not dissonant, and a dissonance is what is not consonant. However, a finer consideration shows that the distinction forms a gradation, from the most consonant to the most dissonant. In casual discourse, as German composer and music theorist Paul Hindemith stressed, "The two concepts have never been completely explained, and for a thousand years the definitions have varied". The term sonance has been proposed to encompass or refer indistinctly to the terms consonance and dissonance.
The Orgelbüchlein BWV 599−644 is a set of 46 chorale preludes for organ — one of them is given in two versions — by Johann Sebastian Bach. All but three were written between 1708 and 1717 when Bach served as organist to the ducal court in Weimar; the remainder and a short two-bar fragment came no earlier than 1726, after the composer’s appointment as cantor at the Thomasschule in Leipzig.
In music theory, an inversion is a rearrangement of the top-to-bottom elements in an interval, a chord, a melody, or a group of contrapuntal lines of music. In each of these cases, "inversion" has a distinct but related meaning. The concept of inversion also plays an important role in musical set theory.
A part in music refers to a component of a musical composition. Because there are multiple ways to separate these components, there are several contradictory senses in which the word "part" is used:
Cambiata, or nota cambiata, has a number of different and related meanings in music. Generally it refers to a pattern in a homophonic or polyphonic setting of a melody where a note is skipped from in one direction followed by the note skipped to, and then by motion in the opposite direction, and where either the note skipped from is distinguished as a dissonance or the note skipped to is distinguished as a non-harmonic or non-chordal tone. With regards to music pedagogical activities and species counterpoint, it refers to a more specific set of patterns.
The Canonic Variations on "Vom Himmel hoch da komm' ich her", BWV 769, are a set of five variations in canon for organ with two manuals and pedals by Johann Sebastian Bach on the Christmas hymn by Martin Luther of the same name. The variations were prepared as a showpiece for Bach's entry as fourteenth member of Mizler's Music Society in Leipzig in 1747. The original printed edition of 1747, in which only one line of the canon was marked in the first three variations, was published by Balthasar Schmid in Nuremberg. Another version BWV 769a appears in the later autograph manuscript P 271, which also contains the six trio sonatas for organ BWV 525–530 and the Great Eighteen Chorale Preludes BWV 651–668. In this later version Bach modified the order of the variations, moving the fifth variation into a central position, and wrote out all the parts in full, with some minor revisions to the score.
These [variations] are full of passionate vitality and poetical feeling. The heavenly hosts soar up and down, their lovely song sounding out over the cradle of the Infant Christ, while the multitude of the redeemed "join the sweet song with joyful hearts." But the experiences of a fruitful life of sixty years have interwoven themselves with the emotions which possessed him in earlier years ... The work has an element of solemn thankfulness, like the gaze of an old man who watches his grandchildren standing round their Christmas tree, and is reminded of his own childhood.
The brilliant scale passages not only represent the ascending and descending angels, but sound joyous peals from many belfries ringing in the Saviour's birth.
Traditional sub-Saharan African harmony is a music theory of harmony in sub-Saharan African music based on the principles of homophonic parallelism, homophonic polyphony, counter-melody and ostinato-variation. Polyphony is common in African music and heterophony is a common technique as well. Although these principles of traditional African music are of Pan-African validity, the degree to which they are used in one area over another varies. Specific techniques that used to generate harmony in Africa are the "span process", "pedal notes", "rhythmic harmony", "harmony by imitation", and "scalar clusters".
References
↑ Laitz, Steven G. (2008). The Complete Musician (2nded.). New York: Oxford University Press, Inc. p.96. ISBN978-0-19-530108-3.
↑ Mozzalo, Guerino (2017). The Topos of Music I: Theory: Geometric Logic, Classification, Harmony, Counterpoint, Motives, Rhythm. New York: Springer International Publishing.
↑ Anon. "Species Counterpoint"(PDF). Faculty of Fine Arts, University of Victoria, Canada. Archived from the original(PDF) on 23 October 2018. Retrieved 16 May 2020. (archive from 23 October 2018)
1 2 3 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, ISBN1-4067-5761-6.
1 2 Ulrich, Homer (1962). Music: a Design for Listening, second edition (New York: Harcourt, Brace & World), p. 438.
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. ISBN0-521-35522-2 (cloth); ISBN0-521-02824-8 (pbk)
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