The most famous counterpoint treatise in history - Fux’s Gradus ad Parnassum (1725)

HISTORICAL TRANSLATIONS:

• Lorenz Christoph Mizler, Gradus ad Parnassum … von Johannes Joseph Fux (Leipzig, 1742) [MDZ] [imslp]

• Alessandro Manfredi, Salita al parnasso … da Giovanni Giuseppe Fux (Carpi, 1761) [Google books] [LOG]

• Anonymous, Practical Rules for learning composition translated from a work intitleld Gradus ad Parnassum (ca. 1768 and ca. 1778) [imslp] [Google books]

• Pierre Denis, Traité de composition musicale fait par le Célèbre Fux (Paris, 1773) [Gallica] [imslp]

MODERN ENGLISH TRANSLATIONS:

Sadly, there is no complete English translation, but almost everything can be collectively found in the following four publications:

• Alfred Mann, The Study of Counterpoint from Johann Joseph Fux's Gradus ad parnassum (1965, New York: Norton).

• Alfred Mann, The Study of Fugue (1986, New York: Norton)

• Susan Wollenberg, ‘Gradus ad Parnassum (1725): Concluding Chapters’, in: Music Analysis (Jul. - Oct., 1992, Vol. 11, No. 2/3), pp. 209–243 [Jstor].

• Joel Lester, Between modes and keys: German theory, 1592-1802 (1989, New York: Pendragon Press) [archive.org], see Appendix 3: Translations from Gradus ad parnassum.
  
  

RECOMMENDED MODERN COUNTERPOINT TEXTBOOK:

• Peter Schubert, Modal Counterpoint: Renaissance style (1999, Oxford University Press) [2nd ed. 2008]

FOOTNOTES

1. [03:15] Ian Bent has shown how almost all of the features of Fux’s treatise, including the five species, are based in one way or another on earlier treatises. Ian Bent, ‘Steps to Parnassus: Contrapuntal Theory in 1725, Precursors and Successors’, in: Thomas Christensen (ed.), The Cambridge History of Western Music Theory (Cambridge Uni press, 2002) [cambridge.org], pp. 554-602.

2. [05:24] The treatise shown in the video is: Adrianus Petit Coclico, Compendium musices (1552) [MDZ], p. 37v-38. Coclico used cantus firmus melodies to demonstrate different counterpoint additions. 

3. [05:52] It should be noted that there were some places that still practiced improvisation over a plainchant, both in Fux’s lifetime as well as after. Additionally, there is a genre of composition based on a cantus firmus, though it was not common by the 18th century. However, neither of these practices are present in Fux's treatise; according to him the exercises are to be written, not improvised, and the compositions are free of any cantus firmus.

4. [06:58] Examples of earlier authors that used similar labeling of the motions include Girolamo Diruta (Il Transilvano, part II, 1609 [imslp], libro 2, p. 2), Bartolomeo Bismantova (Compendio musicale, 1677, p. 42), and Angelo Berrardi (Miscellanea musicale, 1689 [archive.org], pp. 103-4. 

5. [07:03] Fux's “direct motion” includes what is today often divided into two subcategories: parallel motion, in which the voices move in the same direction while producing the same interval (as in a series of parallel 3rds or 6ths); and similar motion, in which the voices move in the same direction but produce different intervals. See, for example, Schubert, Modal Counterpoint, pp. 19–20. 

6. [08:56] Gioseffo Zarlino, Le Istitutioni Harmoniche (Venice, 1558) [imslp], part III, chapter 36. English translation in Claude Palisca, The Art of counterpoint: Gioseffo Zarlino - Part three of Le Istitutioni Harmoniche 1558 (Yale Uni Press, 1968), p. 75. 

7. [12:34] See our episode Modes in the 16th and 17th centuries [YouTube]. 

8. [13:02] In the German translation of the book from 1742 this is expressed in the form of a footnote that undermines Fux, saying that in fact the modes are not used anymore: ”…Itzo haben wir gar nicht mehr nöthig uns mit den verkehrten Tonarten, noch viel weniger mit den authentischen und plagalen zu schleppen, als welche bey der heutigen deutlichen Lehre von Tonarten ohnehin nichts helfen. [Nowadays, we no longer need to concern ourselves with the confused modes, and even less with the so-called authentic and plagal ones, since they are of no help in the clear modern theory of tonalities.] Lorenz Christoph Mizler, Gradus ad Parnassum … von Johannes Joseph Fux (Leipzig, 1742) [imslp], p. 165. More about the Fux-Mattheson discussion over mode see Joel Lester, 'The Fux-Mattheson Correspondence: An Annotated Translation', in: Current Musicology, no. 24 (January 1977), pp. 37-62. 

9. [18:28] “Tolerable”, of course, is subjective. For some Renaissance writers, such passing dissonant half-notes were considered too long. Morley, for example, shows how passing dissonances in half-notes can become more “tolerable” if altered by a dot – by making the consonances longer and the dissonances shorter. See Thomas Morley, A Plaine and Easie Introduction to Practical Musicke (London, 1597) [imslp], p. 82 [first ed.]. 

10. [19:30] Adriano Banchieri, Cartella musicale [3rd ed.] (Venice, 1614) [imslp], p. 106. 

11. [21:06] The example shown on the video is the Anonymous duet “Ach Elslein liebes Elselein” from Geord Rhau (ed.), Bicinia gallica, latina, germanica, Tomus 2 (Wittenbergm, 1545) [imslp], no. 99. See similar examples in Pietro Pontio’s treatise, Ragionamento di Music (Parma, 1588) [BSB], p. 26. Lastly, in his textbook, Peter Schubert presents how Diruta uses leaps to “hide” apparent parallels as we have shown. Peter Schubert, Modal Counterpoint: Renaissance Style (1999, Oxford University Press) [2nd ed. 2008], p. 49. 

12. [23:03] See for example Johann David Heinichen, Anweisung zu vollkommener Erlernung des General-Basses (Hamburg, 1711) [imslp], pp. 65-66. Earlier usage can be found also in Christoph Bernhard, Ausführlicher Bericht von Gebrauche der Con- un Dissonantien (ca. 1672), transcribed in: J. M. Müller-Blattau (ed.), Die Kompositionslehre Heinrich Schützens in der Fassung seines Schülers Christoph Bernhard (Kassel, 1926), p. 146. 

13. [23:21] Knud Jeppesen credited Franz Nekes for noting this for the first time in 1892. Knud Jeppesen, Counterpoint: The Polyphonic Vocal Style of the Sixteenth Century (1939, Prentice-Hall [first ed. in Denish, 1931]) [archive.org] p. 124. While it might be true that in Palestrina you will not find four quarters with an accented passing note against one whole note, some 17th-century writers did allow it. For example, as early as 1610 Giovanni Battista Chiodino described such a passage (four quarter notes with an accented passing note against a whole note) as “very graceful”. Giovanni Battista Chiodino, Arte pratica (Venice, 1610) [imslp], p. 17. 

14. [23:51] Fux’s term for this phenomenon – cambiata – was used in countless textbooks and is in use until today. It should be noted that we don’t know of an Italian source from the 16th or 17th centuries that uses the term “cambiata” to refer to what Fux is referring to. However, we do find the term nota cambiata / scambiata in some 17th-century sources to describe an accented passing note. Literally meaning “exchanged note”, it probably refers to the “exchanged” order of consonant and dissonant notes. See for example Angelo Berardi, Miscellanea musicale (Bologna, 1689) [archive.org], p. 142, and the Anonymous Regole di canto figurato, contrappunto, d'accompagnare [I-Bc Ms. E. 25] [imslp], chapter XVII, or p. 51 in the English translation made by Early Music Sources [earlymusicsources]. 

15. [25:54] The example shown in the video is taken from Angelo Berardi, Miscellanea musicale (Bologna, 1689) [archive.org], p. 136. 

16. [27:53] Nowadays, the term "retardation" in English generally refers to a prepared dissonance that resolves by ascending rather than descending step. 

17. [28:34] It should be noted that Fux's logic about the retardation doesn't really hold up: in several examples from that chapter, there are instances where if the retardations are removed parallel octaves or fifths will take place. 

18. [28:50] “...chiamerò quella parte, che stà & riceve la percossa Patiente. Perche patisce quella cosi fatta percossa; & quella parte, che offende l'altra, & è quella, che opera e fa la Dissonanza Agente.” Giovanni Maria Artusi, Seconda parte dell'arte del contraponto (1589), p. 27 [TMI] Artusi’s terms derive from the Aristotelian distinction between acting and being acted upon (ποιεῖν and πάσχειν), a conceptual pair that influenced medieval and Renaissance scholars across a variety of disciplines. See Aristotle, Categories 4, 1b25–27; and Metaphysics IX.1, 1046a9–21. 

19. [29:20] Sources that use the agente / patiente [or paziente] terminology include: Silverio Picerli, Specchio secondo di musica (Napoli 1631) [imslp], p. 32; Giovanni Maria Bononcini, Musico Prattico (Bologna, 1673) [imslp], p. 63; Zaccaria Tevo, Il Musico Testore (Venice, 1706) [Google books], p. 175; Giuseppe Paolucci, Arte pratica di contrappunto dimostrata con esempj di varj autori, vol. 1 (Venice: 1765), p. 221; and Gaspare Vignali, Rudimenti di Musica per Accompagnare del Sig.r Maestro Vignali (MS: Us-Eu MSS 1465), p. 7. Many thanks to Johannes Menke for sharing several of these sources. 

20. [30:14] For example: Jeppesen, Counterpoint, p. 131; Schubert, Modal Counterpoint, p.76. 

21. [39:25] Zarlino and Artusi write that the resolution of dissonant suspension can be made to perfect or imperfect consonances or to another dissonance, and Pontio demonstrates resolving into unisons and octaves. Artusi, Seconda parte dell'arte del contraponto, p. 27; Zarlino, Le Istitutioni Harmoniche, part III, chapter 42 [Eng. tran., p. 97]; Pontio, Raggionamento, e.g. p. 51, 57. Later 17th century authors such as Berardi, Miscellanea musicale, also seemed to allow the resolutions to octaves and unisons but under some conditions, see for example p. 123, where he demonstrates a resolution of 7 to 8 saying that it shouldn’t be done in two voices. Otherwise, resolutions of 9 to 8 and 2 to 1 can be seen in p. 127. 

22. [31:39] It is implied that Fux does not like the melodic repetition in the exercise, but in some treatises such repetitions are considered clever – imitation in a positive sense. Peter Schubert presents such motivic variations by Pontio, Banchieri and Zarlino. Schubert, pp. 120-22. 

23. [37:14] Fux furthermore describes the relationship between a “harmonic triad” (i.e., a 5/3 chord) and a sixth chord in an interesting way, using an example involving a C-major chord. According to him, in a “harmonic triad,” the C is in its “proper place” in the bass; in a sixth chord, however, it “has been moved from its proper place to an unusual one”—an explanation that invokes  the concept of inversion, which was becoming increasingly widespread in his time. 

24. [37:53] In his book Modal Counterpoint, Peter Schubert uses the terminology of hard vs. soft rules: rules that must be observed (such as the absolute avoidance of parallel perfect intervals) as opposed to rules that may be ignored according to different situations (such as hidden parallels, that may take place according to the context). 

25. [39:30] Nicola Vicentino, L'antica musica ridotta alla prattica moderna (Rome, 1555) [link], p. 30. 

26. [41:48] It should be noted that Palestrina’s music, even if not so commonly, was still performed in the 18th century. Bach arranged, for example, Palestrina’s Missa sine nomine for his use [imslp]. But also other old liturgical pieces were performed: in our episode about Bach’s choir [YouTube]  we also mentioned that Bach regularly performed music from a collection of early 17th-century motets: Florilegium Portense (Vol. I: 1618, Vol. II: 1621) [CPDL] [imslp I] [imslp II]. This is just to note that Fux’s focus on an early style wasn’t in a complete vacuum. 

27. [44:07] “Die Gründe der Harmonie, und der reinen Composition sind unveränderlich in der Music; es mag die Mode in der Music werden und sich verändern, wie sie will. Der Verfasser aber hat lauter solche Lehren vorgetragen, welche in der Music allezeit bleiben und seyn müssen, weil sich solche auf die unveränderliche Gesetze der Natur gründen, und wird daher der Fux ein Autor classicus in der Composition bleiben, so lange eine Harmonie ist, und eine regelmäßige Music unter den Menschen gemacht wird.” Lorenz Christoph Mizler, Gradus ad Parnassum … von Johannes Joseph Fux (Leipzig, 1742) [imslp], preface. 

28. [45:00] “I Giovani adunque nati in Italia all' Arte dell' Armonia portati, non si stanchino di rileggere il Fux, e di esercitarsi ne' di Lui precetti.” Alessandro Manfredi, Salita al parnasso … da Giovanni Giuseppe Fux (Carpi, 1761) [Google books], Lettera del Sig. Niccola Piccinni Maestro di musica al traduttore. Other Neapolitan teachers who also made use of Fux’s treatise include Leonardo Leo and Pasquale Cafaro, as well as Giacomo Tritto, who recommended it in his Scuola di contrappunto. See Peter van Tour, Counterpoint and Partimento (Uppsala Universitet, 2015), pp. 193-200; and Giacomo Tritto, Scuola di contrappunto (Milan, 1816) [imslp], p. 44. 

29. [45:21] See Bent, “Steps to Parnassus,” pp. 579–584; and Alfred Mann, "Joseph Fux’s Theoretical Writings: A Classical Legacy," in Johann Joseph Fux and the Music of the Austro-Italian Baroque, ed. Harry White (Aldershot: Scolar Press, 1992), pp. 57–71. 

30. [45:32] See again Bent, “Steps to Parnassus,” pp. 585–591. 

31. [45:39] Luigi Cherubini, Cours de contrepoint et de fugue (Paris, 1832) [gallica]. 

32. [45:51] Hellmut Federhofer, 'Luigi Cherubini: "Cours de Contre-point et de Fugue" in Deutschland und Österreich' (Acta Musicologica, Vol. 74, Fasc. 2, 2002) [Jstor], pp. 129-13. 

33. [46:18] Heinrich Schenker, Kontrapunkt (Stuttgart, 1906) [archive.org]. See also Hellmut Federhofer, 'Fux's "Gradus ad Parnassum" as Viewed by Heinrich Schenker', in: Music Theory Spectrum 4 (1982), pp. 66–75 [Jstor]. 

CREDITS

Created by Elam Rotem, May 2026

Written with the help of Sean Curtice, Iason Marmaras and Tim Braithwaite.

Sung example recorded with Liga Zirina, Doron Schleifer and Korneel Van Neste.

Special thanks to Peter Schubert, Johannes Menke and Anne Smith.