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.

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.

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.

[8][9] Some examples of related compositional techniques include: the round (familiar in folk traditions), the canon, and perhaps the most complex contrapuntal convention: the fugue.

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 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.

[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.

Concerning the common practice era, alterations to the melodic rules were introduced to enable the function of certain harmonic forms.

The technique requires chains of notes sustained across the boundaries determined by beat, and so creates syncopation.

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.

[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.

"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.

"[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.

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."

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, Vivian Fine, Carl Ruggles, Henry Cowell, Carlos Chávez, John J. Becker, Henry Brant, Lou Harrison, Wallingford Riegger, and Frank Wigglesworth.

Bach fugue in G-sharp minor from WTC Book 2
Bach fugue in G-sharp minor from WTC Book 2
Bach 3-part Invention BWV 795, bars 7–9
Bach 3-part Invention BWV 795, bars 7–9
Beethoven Piano Sonata Op. 90, first movement bars 110–113
Beethoven Piano Sonata Op. 90, first movement bars 110–113
Beethoven, Symphony No. 9, finale, bars 116–123
Beethoven, Symphony No. 9, finale, bars 116–123
Wagner Meistersinger Vorspiel bars 158–161
Wagner Meistersinger Vorspiel bars 158–161
Mozart Symphony No. 41 Finale, bars 389–396
Mozart Symphony No. 41 Finale, bars 389–396
Gradus ad Parnassum (1725) by Johann Joseph Fux defines the modern system of teaching counterpoint
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
Example of a descending double neighbor figure against a cantus firmus
Example of an ascending double neighbor figure (with an interesting tritone leap at the end) against a cantus firmus