Johann Joseph Fux and Species Counterpoint

Teaching counterpoint by progressively adding more notes to a given part, often labelled species counterpoint, did not begin with Johann Joseph Fux’s, Gradus ad Parnassum, published in 1725, but species counterpoint gained its most enduring champion with its publication.

Used by many as the basis for instruction in composition and counterpoint from the eighteenth century up to the present-day, Fux’s Gradus guides the reader through a systematic method for adding notes to a given part (cantus firmus) in two-, three-, and four-part textures.
Although the major and minor tonal system was established at the time of its publication, Fux chose to give his instruction using the Renaissance modes. It was subsequently adapted to the tonal system by later theorists, such as Beethoven’s teacher, Johann Georg Albrechtsberger, but for this article the examples will be taken from Fux’s Gradus and will, therefore, be modal.

Two-Part Counterpoint.

First Species:

First species, or note against note counterpoint, requires one note for every given note in the cantus firmus. Fux’s Dorian example (below)

1st sp 2part

begins and ends with the required perfect consonance and contains a mixture of contrary, oblique and similar motion; it also uses the obligatory raised leading note in the penultimate bar. Forbidden consecutives are avoided by approaching perfect intervals by contrary motion (bars 3-4, 5-6 and 10-11) while the overuse of the same successive imperfect intervals is avoided by limiting their use to two bars at a time (bars 2-3, 7-8 and 9-10).
In this species, all of the intervals are consonant.

Second Species:

Second species, requires two notes for every given note in the cantus firmus; the second note may be a dissonant passing note.
Notice, in Fux’s Mixolydian example (below)

2nd sp 2part

the first note in every bar of the counterpoint is consonant with the corresponding note of the cantus firmus. The second note of the counterpoint may be consonant (bars 1, 5, 6, 10, 11, 12 and 13) or dissonant (bars 2, 3, 4, 7, 8 and 9) with the corresponding note in the cantus firmus. As mentioned earlier, all dissonance in this species comes from accented passing notes which are approached and left by step. Leaps can only be made between two harmony notes: either within the same bar (bars 5, 10 and 12), or between separate bars (bars 1 and 2).

Third Species:

Third species consists of four notes for every given note in the cantus firmus. Fux states that the first note of each bar must be consonant with the given note of the cantus firmus while the three remaining notes can be a mixture of consonant and dissonant notes, providing the following rules are adhered to: dissonant notes must be approached and left by step, consonant notes my leap between each other. The only exception to these rules is the changing note, or cambiata.
A cambiata consists of a leap from a dissonance to a consonance. In the following example, the dissonant second note (7) leaps to the third note, rather than moving by step.



Fux’s Phrygian example (below)

3rd sp 2part

uses predominantly stepwise motion in the counterpoint melody; when leaps occur they are always between harmony notes (bars 1-2, 4, 8). Dissonance generally occurs on beats two or four but can also occur on beat three (bar 9). All rules which have been introduced for writing first and second species counterpoint also apply for third species: all harmonic perfect consonances are approached by contrary motion (bars 2-3, 6-7, 9-10), harmonically within each bar, there is a mixture of dissonant, perfect and imperfect intervals.

Fourth Species:

Fourth species like second species, requires two notes for every given note in the cantus firmus. In fourth species, however, the notes are connected with ties and suspensions; Fux calls this species ligature. When the ties are consonant, they connect two harmony notes. Notice, the melody leaps from one consonance to the next.

Consonant ligs


Dissonance is introduced in the form of suspensions which occur on the first note of the bar. The suspensions must be prepared correctly, as a consonant on the second note of the bar, they then form the suspension on the first note of the bar, which is dissonant, before resolving downwards to the following second note, which is consonant

Dissonant lig


Upper voice suspensions in two parts consist of the 4-3 and 7-6 suspensions; 9-8 and 2-1 are not as common in two-part counterpoint, while lower voice suspensions consist of the 2-3 (Fux also lists 4-5 and 9-10 but these are less common, especially in tonal music).
Fux’s Lydian example (below)

4sp 2part

is a combination of both consonant ties and dissonant suspensions. Of the five suspensions only one is 9-8 (bar 7), the remaining four include two 7-6 suspensions (bars 2 and 11) and two 4-3 suspensions (bars 6 and 8). As in this example, the penultimate note does not need a tie.
Fux also notes that the suspensions may be decorated in the following ways.

Decorated sus

Note: the suspension is decorated not the resolution.

Fifth Species:

Fifth species is a combination of species one to four and is called florid counterpoint. Before introducing this species Fux states that occasionally two eighth notes may be used on beats two and four of a bar.

Eighth notes


Note: this rule is relaxed in tonal music and adheres to Renaissance theory.
Fux gives several examples of this species, many with counterpoint above and below the cantus firmus

Florid 1st species

His examples for this species incorporate all of the previously given rules as well as using decorated suspensions and eighth notes on beat two (bar 6, upper part). This example also uses a cambiata (bar 2, lower part).
As a combination of all previous species and rules, fifth species counterpoint requires the composer to create effective melodies while correctly handling dissonance and avoiding forbidden consecutives.
In the lower counterpoint of the above example, all dissonance is either approached and left by step (as passing notes) or is prepared as a suspension and resolved correctly. The only exception is the cambiata in bar 2, where the dissonant G note leaps to the E on beat three; the dissonance is still treated correctly, however.
It must be remembered that the previous examples, and the rules governing them, may be written using smaller note values. In this way, the note values of the lower counterpoint in the above example could be halved

Notes halved once

and halved again.

Notes halved twice

In this way, Fux’s instruction may be adapted to a number of compositional situations and styles while always maintaining the five species as its basis.

Three-Part Counterpoint.

First Species:

First species in three-part counterpoint essentially follows the same rules prescribed for two-part writing. With an extra part, however, comes the necessity to construct parts which satisfy the harmonic and melodic aspect while avoiding forbidden consecutives. Fux states that the composer should endeavour to use complete triads whenever possible but they may be incomplete for the sake of better melodic writing. In the following example

3part 1st sp

the triads in bars 2 and 3 are both incomplete so that the descending melodic lines in both upper parts is maintained.
Rules regarding hidden fifths and octaves may also occasionally be relaxed in three-part writing if, as Fux states, ‘…there is no other possibility…in order to avoid a worse awkwardness’. Bars 7 and 8 of the following is an example of this.

Relax hidden

Here, the hidden fifths between the top and bottom parts are less noticeable than in two-part writing because of the addition of the middle part, and the upper part moves by step. Consecutive fifths, octaves and unisons are still forbidden, however.

Second species:

Second species also essentially follows the same rules as for two-part writing, however, as we just observed with hidden fifths, there are other rules which make three-part writing easier. For example, in three-part writing a leap between two notes of a triad may occasionally avoid consecutives, an option which is typically not available in two-part textures. Fux gives the following example

Ok 5ths


but cautions that the same example would not be allowed in two-part writing.
As you can see in Fux’s Phrygian example (below)

3 pt 2nd sp

the middle part follows the same rules prescribed for second species two-part writing: if the second note of the bar is dissonant (not part of the triad) it must be approached and left by step, if it is consonant (part of the triad) it may leap.

Third Species:

Third Species again follows the rules prescribed for two-part writing. Fux’s Dorian example (below) illustrates.

3 pt 3rd sp

Fux also gives the following example where second and third species are combined.

2nd & 3rd sp

Fourth Species:

Fourth species follows all rules for two-part writing, however, in three-part writing Fux states that ‘…the ligature is nothing but a delaying of the note following’, and we must therefore use ‘…the same consonance in the third voice that [we] would have used if the ligature had been omitted.’ In other words, the third part must use a note which is part of the triad; it is this note which is displaced by the tie or suspension. Fux’s examples should clarify.

4th sp ex

In this example (above), the third part (middle) either doubles existing notes of the triad (bar 2), or adds another note from the triad (bars 3 and 4).
Fux’s second example (below)

4th sp ex2


introduces suspensions which simply ‘delay the note following’.
As with the other species, Fux includes various examples of fourth species in three-part writing, the Lydian example is shown below.

4sp 3pt

The inclusion of the B flat accidental in bar 5 corrects the tritone (B – F).

Fifth Species:

As with two-part writing, fifth species in three parts combines all of the previous species and rules. One of Fux’s Dorian examples illustrates

Florid 3pt

Four-Part Counterpoint.

First Species:

As would be expected, first species in four parts essentially follows the rules prescribed for first species in two- and three-part writing, one notable point, however, is the relaxation of hidden fifths as the number of parts increases. One of Fux’s Phrygian examples illustrates

1st sp 4 pt

Here, in bars 5-6 and 8-9 the soprano and bass parts move by direct motion to perfect consonances; a move, which in two-part writing, would be forbidden.
As all of the remaining species in four parts essentially follow the rules already given for fewer parts, examples will be given for each species.

Second Species:

One of Fux’s Dorian examples illustrates

2nd sp 4pt

Third Species:

One of Fux’s Phrygian examples illustrates

3rd sp 4pt

Fourth Species:

One of Fux’s Dorian examples illustrates

4th sp 4pt

Fifth Species:

One of Fux’s Dorian examples illustrates

5th sp 4 pt


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