Editing Counterpoint (section)

==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}}</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>