text: Johann Joseph Fux Explained
  Johann Joseph Fux (in German ˈfʊks/; c. 1660 – 13 February 1741) was an Austrian composer, music theorist and pedagogue of the late Baroque era. He is most famous as the author of Gradus ad Parnassum, a treatise on counterpoint, which has become the single most influential book on the Palestrinian style of Renaissance polyphony. Almost all modern courses on Renaissance counterpoint, a mainstay of college music curricula, are indebted in some degree to this work by Fux.
  The work is divided into two major parts. In the first part, Fux presents a summary of the theory on Musica Speculativa, or the analysis of intervals as proportions between numbers. This section is in a simple lecture style, and looks at music from a purely mathematical angle, in a theoretical tradition that goes back, through the works of Renaissance theoreticians, to the Ancient Greeks. Fux explains that intervals in exact mathematical proportions result in larger and smaller half tones, and he also mentions that some organists added extra keys (split halves to use smaller and bigger half tones), but that adding extra keys on a keyboard was problematic and for this reason they divided every note in "German: zwei gleiche Theile" (two equal parts), resulting in equal temperament. He continues: The works of Mersenne, Cicero and Aristotle are among the references quoted by Fux in this section.
  Fux's compositions were catalogued by Ludwig Ritter von Köchel.[3]
  Concentus musico instrumentalis...1701. Concentus musicus Wien, Nikolaus Harnoncourt (Teldec 8.42171 XH, 244 690 2)[4]
  Kaiserrequiem K51-53. Clemencic Consort, René Clemencic (Arte Nova 74321 27777 2)[5]
  Book: Johann Joseph . Fux. Alfred Mann (musicologist). Mann . Alfred . Edmunds. John . 1965. The Study of Counterpoint from Johann Joseph Fux's Gradus ad parnassum . W.W. Norton & Co. . New York . 0-393-00277-2 . 494781 . harv.
  Book: Fux, Johann Joseph . Gradus Ad Parnassum . Broude Brothers . New York . 1966 . Monuments of Music and Music Literature . Facsimile of the 1725 Vienna edition.
  Book: Jeppesen, Knud . Knud Jeppesen
  . Knud Jeppesen . Haydon. Glen. Glen Haydon. . Counterpoint: the polyphonic vocal style of the sixteenth century . registration . 1992 . Dover . New York . 0-486-27036-X . 1939 .
  Web site: Kroesbergen . Willem . Cruickshank . Andrew . 18th century quotations relating to J.S. Bach's temperament . Cape Town . October 2015 . 2nd . 15 November 2015 .
  Web site: Lorenz . Michael . Michael Lorenz (musicologist) . Fux Documents . September 8, 2016 . Vienna . 15 November 2017 .
  Book: White . Harry . Hochradner . Thomas . Johann Joseph Fux . Text and bibliography by HW, work-list by TH.
  Web site: The Editors of Encyclopædia Britannica . Johann Joseph Fux . Encyclopædia Britannica . Encyclopædia Britannica, inc . March 18, 2016 . November 15, 2017.
  Book: Watchorn, Peter. Isolde Ahlgrimm, Vienna and the Early Music Revival . 2017-07-05. Routledge. 9781351561976. en.
  This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Johann Joseph Fux".