The
Gradus ad Parnassum (Steps or Ascent to Mount Parnassus) is a theoretical and pedagogical work written by Fux in Latin in 1725, and translated into German by
Lorenz Christoph Mizler in 1742. Fux dedicated it to Emperor Charles VI. 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 "" (two equal parts), resulting in equal temperament. He continues: The works of
Mersenne,
Cicero and
Aristotle are among the several references quoted by Fux in this section. The second part, on
Musica Pratica, is the section of this treatise where the author presents his instruction on
counterpoint,
fugue, double counterpoint, a brief essay on musical taste, and his ideas on composing
sacred music, writing in the
a cappella and in the
recitativo style. This part is in the form of a dialog, between a master (Aloysius, Latin for Luigi, who is meant to represent Palestrina's ideas) and a student, Josephus, who represents Fux himself, a self-admitted admirer of Palestrina. At the outset, Fux states his purpose: "to invent a simple method by which a novice can progress, step by step, to attain mastery in this art." and gives his opinion of contemporary practice: "I shall not be deterred by the most ardent haters of school, nor by the corruptness of the times." He also states that theory without practice is useless, thus stressing practice over theory in his book. While
Gradus ad Parnassum is famous as the origin of the term "
species counterpoint", Fux was not the first one to invent the idea. In 1610,
Girolamo Diruta, a composer of the
Venetian school, published
Il Transilvano, which presented the Renaissance polyphonic style as a series of types: one note against one note, two notes against one note,
suspensions, and so forth. Fux's work repeated some of Diruta's, possibly coincidentally, since he is not known to have had a copy. In species counterpoint, as given in Fux, the student is to master writing counterpoint in each species before moving on to the next. The species are, in order, note against note; two notes against one; four notes against one; ligature or suspensions (one note against one, but offset by half of the note value); and florid counterpoint, in which the other species are combined freely. Once all the species are mastered in two voices, the species are gone through again in three voices, and then in four voices. (Occasionally, in modern counterpoint textbooks, the third and fourth species are reversed with suspensions being taught before four notes against one.) Fux expressed the intention of adding sections on how to write counterpoint for more than four parts, indicating that rules in this area were to be "less rigorously observed". However, citing his poor health as a result of gout and age, he chose to conclude the book as it stood. Modern counterpoint education is greatly indebted to
Gradus ad Parnassum, and Fux presented the ideas with such clarity and focus that both subsequent and modern counterpoint texts continue to cite his work, from the book by
Albrechtsberger (
Gründliche Anweisung zur Komposition) to 20th century examples such as the book by
Knud Jeppesen (
Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century). Furthermore,
Gradus ad Parnassum is a noteworthy historical document in that it clearly delineates the stylistic distinction of the entire baroque era between an antique and sacred style and a more modern and largely secular style. As Mizler was a student of J.S. Bach, musicologist Christoph Wolff has suggested that Bach may have played some part in persuading Mizler to translate the treatise. ==Works==