This part of fourscoreandmore provides the full cantus firmus exercises of Johann Joseph Fux’s iconic pedagogical treatise, ‘Gradus ad Parnassum’ in three sections:

  1. Two Voices (46 exercises)
  2. Three Voices (44 exercises)
  3. Four Voices (32 exercises)

For each of these sections, we provide four files:

  1. Exercises: all of the cantus firmus exercises with only the cantus firmus present.
  2. Solutions: all of Fux’s solutions to those exercises – i.e. both the cantus firmus and the additional part(s).
  3. Annotations: Those solutions annotated with the interval that every note in each additional part forms with the cantus firmus.
  4. Distinct: Every distinct cantus firmus in all parts. All of the exercises are based on this format, so these simple files distill all possibilities: you can use this file to do any species exercise, on any cantus firmus, in any part arrangement.

Everything is provided in an editable format for teachers to adjust freely for their own class’ needs and released under a correspondingly open licence.

Each exercise includes the following information:

  • Figure number (in the modern Norton/Mann edition, 1965).
  • Species type,
  • Modal final,
  • Cantus firmus part

Details are provided for each part in html format: click these links to explore:

  1. part I: html,
  2. part II: html,
  3. part III: html,

The html docs can be opened in any web browser and used to search the collection by any of the criteria above (e.g., species type).

Downloads

Whole Part Downloads (Part I, II, III)

You can download a whole part at once directly and in your choice of format: .pdf, .mscz, or .mxl. PDFs are known to most and not the main use case here. The .mscz format is for MuseScore specifically; you can open the .mxl files in any music notation software.

Part Exercises Solutions Annotations Distinct
I .mxl,.mscz,.pdf .mxl,.mscz,.pdf .mxl,.mscz,.pdf .mxl,.mscz,.pdf
II .mxl,.mscz,.pdf .mxl,.mscz,.pdf .mxl,.mscz,.pdf .mxl,.mscz,.pdf
III .mxl,.mscz,.pdf .mxl,.mscz,.pdf .mxl,.mscz,.pdf .mxl,.mscz,.pdf

Individual figures (5, 6, 11, …, 204)

We also provide each figure in a separate files. These can be downloaded or viewed and engaged with directly online. Again, the best way to explore this collection and make choices, is via the html summaries:

  1. part I: html,
  2. part II: html,
  3. part III: html.

Cantus firmus

Fux’s use of cantus firmus broadly centres on one cantus firmus for each modal final that stays broadly constant throughout all exercises and parts.

The note sequences are as follows, along with their usage counts and the minor exceptions.

Modal final Pitches Part I (46) Part II (44) Part III (32)
D D4, F4, E4, D4, G4, F4, A4, G4, F4, E4, D4 10 16 at two octaves (D3 and D4) 21 at two octaves (D3 and D4)
E E4, C4, D4, C4, A3, A4, G4, E4, F4, E4 10 12 at two octaves (E3 and E4) 7, one at E5 (fig.184)
F F3, G3, A3, F3, D3, E3, F3, C4, A3, F3, G3, F3 10 including one at the octave above, (fig.13: starting F4) 9 at two octaves (F3 and F4) 4 at two octaves (F3 and F4)
G G3, C4, B3, G3, C4, E4, D4, G4, E4, C4, D4, B3, A3, G3 6 2 -
A A3, C4, B3, D4, C4, E4, F4, E4, D4, C4, B3, A3 6 including one lacking the first D (fig.42: A3, C4, B3, C4, E4 …) 3 at three octaves (A2, A3 and A4) -
C C4, E4, F4, G4, E4, A4, G4, E4, F4, E4, D4, C4 2 Note the two version for the final on C (this line and below) 2 -
C C4, D4, F4, E4, G4, E4, F4, E4, D4, C4 2 - -

Acknowledgements, Contribution, and Licence

Thanks to Jay Wilson for the initial transcription and permission to use them for this expanded initiative. All subsequent annotation, analysis, code etc. by Mark Gotham.

Contributions are welcome. Please submit a PR or get in touch.

Licence:

  • Code = MIT licence, 2026
  • Rendered scores = CC0 (Public Domain). Mark Gotham and FourScoreAndMore.org waive all rights to those documents.