This page 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. Full exercises: all of the cantus firmus exercises with only the cantus firmus present. Note that the numbers are not sequential here because the numbering includes all of Fux’s examples, including setting out what oblique motion is, for instance.
  2. Full solutions: all of Fux’s solutions to those exercises – i.e. both cantus firmus and additional part(s).
  3. Those solutions annotated with the interval between every note in each additional part and the cantus firmus.
  4. Distinct: Every distinct cantus firmus in all parts. All of the exercises are based on this, so these simple files distill all possible exercises: use this to do any species exercise, on any cantus firmus, and either above or below.

Downloads

Check out the files here on our MuseScore page where you can play them online and download them in your preferred format (mscz, xml, PDF). NB: you need a (free) account to download files.

Part Exercises Solutions Annotated Distinct
I I-Exercises I-Solutions I-Annotated I-Distinct
II II-Exercises II-Solutions II-Annotated II-Distinct
III III-Exercises III-Solutions III-Annotated III-Distinct

Files for Part I are also hosted locally in .mxl format which you can open in any music notation software:

Download File 1: Exercises

Download File 2: Exercises and Solutions

Download File 3: Solutions Annotated

Download File 4: Distinct Formats

Let us know if you have a strong preference for where we keep files.

For Reference

Each exercise includes the following information:

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

For ease of reference, the following sub-section / tables set out that information in full.

Finally, a note on clefs. Those given also follow the Norton/Mann edition (1965) for parts I and II. Part III keeps the same clefs throughout to be consistent both internally and with the modern choral score layout (treble, treble, treble 8, bass). Teachers may wish to choose their own clefs as part of adapting these files for class.

Part I

Figure Species Mode (final) Cantus Firmus Part
5 1 d Lower
6 1 d Upper
11 1 e Lower
12 1 e Upper
13 1 f Lower
14 1 f Upper
15 1 g Lower
21 1 g Upper
22 1 a Lower
23 1 a Upper
33 2 d Lower
35 2 d Upper
36 2 e Lower
37 2 e Upper
38 2 f Lower
39 2 f Upper
40 2 g Lower
41 2 g Upper
42 2 a Lower
43 2 a Upper
44 2 c Lower
45 2 c Upper
55 3 d Lower
56 3 d Upper
57 3 e Lower
58 3 e Upper
59 3 f Lower
59 3 f Upper
73 4 d Lower
74 4 d Upper
75 4 e Lower
76 4 e Upper
77 4 f Lower
78 4 f Upper
82 5 d Lower
83 5 d Upper
84a 5 e Lower
84b 5 e Upper
85a 5 f Lower
85b 5 f Upper
86a 5 g Lower
86b 5 g Upper
87a 5 a Lower
87a 5 a Upper
88a 5 c Lower
88b 5 c Upper

Fux basically uses one cantus firmus for each modal final throughout. The note sequences are as follows, along with their usage counts (46 total) and the minor exceptions:

Modal final Pitches Counts and exceptions
D D4, F4, E4, D4, G4, F4, A4, G4, F4, E4, D4 10 counts
E E4, C4, D4, C4, A3, A4, G4, E4, F4, E4 10 counts
F F3, G3, A3, F3, D3, E3, F3, C4, A3, F3, G3, F3 10 counts including one at the octave above, (fig.13: starting F4)
G G3, C4, B3, G3, C4, E4, D4, G4, E4, C4, D4, B3, A3, G3 6 counts
A A3, C4, B3, D4, C4, E4, F4, E4, D4, C4, B3, A3 6 counts including one lacking the first D (fig.42: A3, C4, B3, C4, E4 …)
C C4, E4, F4, G4, E4, A4, G4, E4, F4, E4, D4, C4 2 counts. The most anomalous case.
C C4, D4, F4, E4, G4, E4, F4, E4, D4, C4 2 counts. More divergent than for the other modes

Part II

Figure Species Mode (final) Cantus Firmus Part
101 1 d 1
104 1 d 2
105 1 d 3
106 1 e 1
108 1 e 2
109 1 e 3
110 1 f 1
111 1 f 2
112 1 f 3
113 1 g 1
114 1 g 2
115 1 a 1
116 1 a 2
117 1 a 3
118 1 c 1
119 1 c 2
121 2 d 1
122 2 d 2
123 2 d 2
124 2 e 2
125 2 e 3
126 2 e 1
127 2 f 1
128 2 f 2
129 2 f 2
130 3 d 2
131 3 d 3
132 3 d 2
134 2,3 d 3
141 4 d 2
143 4 d 3
144 4 d 1
146 4 e 2
147 4 e 1
148 4 e 2
149 4 f 2
150 4 f 3
151 4 f 1
154 5 d 2
155 5 d 1
156 5 d 2
157 5 e 2
158 5 e 1
159 5 e 2

… and the cantus firmus collection …

Modal final Pitches Counts and exceptions
D D4, F4, E4, D4, G4, F4, A4, G4, F4, E4, D4 16 counts at two octaves (D3 and D4)
E E4, C4, D4, C4, A3, A4, G4, E4, F4, E4 12 counts at two octaves (E3 and E4)
F F3, G3, A3, F3, D3, E3, F3, C4, A3, F3, G3, F3 9 counts at two octaves (F3 and F4)
G G3, C4, B3, G3, C4, E4, D4, G4, E4, C4, D4, B3, A3, G3 2 counts
A A3, C4, B3, D4, C4, E4, F4, E4, D4, C4, B3, A3 3 counts at three octaves (A2, A3 and A4)
C C4, E4, F4, G4, E4, A4, G4, E4, F4, E4, D4, C4 2 counts. Corresponds to the first case for Part I.

Part III

Figure Species Mode (final) Cantus Firmus Part
160 1 d 2
163 1 d 1
164 1 d 3
165 1 d 4
166 1 e 1
167 1 e 2
168 1 e 3
169 1 f 2
170 1 f 1
171 1 f 3
172 1 f 4
173 2 d 1
174 2 d 2
175 2 d 3
176 2 d 4
177 3 d 2
180 3 d 4
181 3 d 2
182 3 d 2
183 3 e 2
184 3 e 1
185 3 e 2
186 3 e 3
193 4 d 2
195 4 d 4
196 4 d 1
197 4 d 2
200 5 d 2
201 5 d 1
202 5 d 4
203 5 d 2
204 2,3,4 d 4

… and the cantus firmus collection …

Modal final Pitches Counts and exceptions
D D4, F4, E4, D4, G4, F4, A4, G4, F4, E4, D4 21 counts at two octaves (D3 and D4)
E E4, C4, D4, C4, A3, A4, G4, E4, F4, E4 7 counts, one at E5 (fig.184)
F F3, G3, A3, F3, D3, E3, F3, C4, A3, F3, G3, F3 4 counts at two octaves (F3 and F4)