II. Counterpoint and Galant Schemas

Gradus ad Parnassum Exercises

Mark Gotham

The previous chapters have introduced species counterpoint and the iconic pedagogical treatise on cantus firmus composition, Johann Joseph Fux’s Gradus ad Parnassum (1725). This page provides the full cantus firmus exercises of that treatise so you can try your hand at species counterpoint à la Fux.

Gradus ad Parnassum is 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 and the other part(s) left blank for you to complete.
  2. Solutions: all of Fux’s solutions to those exercises—i.e., both the cantus firmus and the additional part(s) that Fux wrote as answers.
  3. Annotations: Those solutions annotated with the interval that every note in each additional part forms with the cantus firmus part.
  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 so teachers can adjust and combine exercises freely for their own classes’ needs.

Downloads

These files are provided in several formats:

  • .mxl: open these in any music notation package like MuseScore, Sibelius, or Finale
  • .mscz: for MuseScore specifically, preserving all original formatting
  • .pdf

Click on the links to download any particular type. Please note that the .mxl files are hosted externally on http://fourscoreandmore.org/species/, so you will be redirected and may prefer to open in a new tab.

Part Exercises Solutions Annotated 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

Gradus ad Parnassum Data

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 subsections and tables set out that information in full.

Finally, a note on clefs. These files use the clefs in 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 8vb, bass). Teachers may wish to choose their own clefs as part of adapting these files for class.

Part I (Two Voices)

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 Number of times used, 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 (Three Voices)

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

The table below summarizes the cantus firmi used in Part II:

Modal final Pitches Number of times used, 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 (Four Voices)

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

The table below summarizes the cantus firmi used in Part III:

Modal final Pitches Number of times used, 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)
Further Reading
  • Fux, Johann Joseph. (1725) 1965. Gradus ad Parnassum. Translated and edited by Alfred Mann. New York: W. W. Norton.

License

Icon for the Creative Commons Attribution-ShareAlike 4.0 International License

OPEN MUSIC THEORY by Mark Gotham is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

Share This Book