Species Counterpoint

An Introduction to Species Counterpoint

figure 1	figure 1a

COUNTERPOINT may be briefly defined as the art of combining independent melodies. In figure 1 the lower melody is harmonized by one a third higher - such an arrangement of the voices could be regarded as counterpoint, but there is little or no independence between the parts; for example there is no dissonance between the voices, and both rise and fall together in parallel. However, the arrangement in figure 1a demonstrates much greater independence between its two voices, with movement in one part while the other halts, divergence in the melodic direction of the parts, and with at least some occurrence of dissonance. In a longer melody the voices could peak at different times - this would also emphasize their independence. Clearly, there are several well-known techniques we can use to manipulate the relationship between the melodies; in the following introduction to counterpoint we will look at an historically important method of examining the use of dissonance, rhythm, and melodic direction in composing music.

J.J.Fux's Gradus Ad Parnassum is the classic text dealing with species counterpoint and fugue; it presents a set of rules for writing in the style of 16th century vocal composition (i.e. Palestrina style). Species counterpoint is dealt with in the first part of the book, where Fux defines five species, each of which is concerned with combining two or more voices subject to a well-defined set of rhythmic and harmonic constraints. For two part exercises, the student is required to invent a melody above or below a cantus firmus (CF); the CF is a fixed, given melody which uses only semibreves (whole notes).

Fux provided a cantus firmus in six of the ecclesiastical modes:

Dorian

Phrygian

Lydian

Mixolydian

Aeolian

Ionian

This tutorial offers a synopsis of Fux's rules relating to two-part exercises in the five species, though only in the case where the melody invented by the reader begins and ends as the upper voice.

Fux provided a cantus firmus in six of the ecclesiastical modes:
Dorian
Phrygian
Lydian
Mixolydian
Aeolian
Ionian

There are several rules governing melodic movement in the counterpoint; these are common to all five species. The main purpose of these rules is to prevent any sequence of notes which may be difficult to sing (or more precisely, to try to prevent a succession of notes which would have been difficult or unstylistic for 16th century singers). These melodic constraints state that:

Augmented or diminished intervals between succeeding notes are not allowed.
Leaps greater than an octave, or leaps of a major sixth or a seventh are prohibited.
An ascending leap of a minor sixth or an octave must be followed by a step back down within the compass of the leap (figure 2). In the same way, a descending leap of an octave must be followed by a step back up within the compass of the leap.
A descending leap of a minor sixth is prohibited.
A sequence of notes forming an 'exposed' tritone is prohibited (figure 3).
Accidentals should generally be avoided since they are not in the character of the ecclesiastical modes. However, the penultimate bar in each species requires a specific sequence which may demand the use of a sharp.

figure 2

melodic direction reverses after the leap

figure 3

this diminished fifth from B to F is 'exposed'

There are also some general rules governing the combination of the two parts; these rules are common to all five species.

Perfect consonant intervals are unisons, fifths, and octaves.
Imperfect consonant intervals are thirds and sixths.
Seconds, fourths, sevenths, and all augmented and diminished intervals are dissonances.

Movement from one interval to the next is governed by the following rules:

When the two voices move in the same direction, such movement is called 'direct' by Fux, 'similar', or 'parallel' motion by others.
When the two voices move in different directions Fux calls it 'contrary' motion, others use the term 'opposite'.
If one voice stays on the same note while the other moves, the movement is called 'oblique' motion.
The two parts may not move in direct motion to a perfect consonance.

figure 4

First Species

In addition to the general rules listed above, the rules specific to the first species are:

The counterpoint consists of a single semibreve against each note of the cantus firmus.
No dissonances are allowed.
In the penultimate bar the counterpoint must be a major sixth above the cantus firmus. This requires an accidental in the Dorian, Mixolydian, and Aeolian modes.
In the final bar the counterpoint must be an octave above the cantus firmus.
Unisons are not allowed, except in the first bar.
The counterpoint in the first bar must be an octave or a fifth above the cantus firmus, or a unison.

An example from Gradus

Points to note in this example:

In the penultimate bar the C has been sharpened in order to form the required major sixth.
All three types of motion have been used.
Melodic movement is mostly by step.

Java Runtime Environment

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How to use the applet

Click in the bar in which you want to place a note. A semibreve (whole note) will appear on the line or space which the mouse points at. The note may be replaced by simply clicking in the same bar, or moved up or down by dragging it. Measures which are not visible initially may be scrolled to by using the scroll bar under the staves. A note may be preceeded by an accidental by selecting one of the buttons labelled 'Sharp' or 'Flat', and then entering the note as just explained. When the counterpoint is complete (that is, there is a note in every bar), the counterpoint may be checked for conformance to the rules for first species by pressing the 'Check Answer' button; this results in a list of comments appearing in the text area below the buttons (the comments generally identify exceptions to the rules). A completed exercise may be played back by pressing the 'Play' button. A different mode may be selected by choosing from the 'Select a mode' choice box.

Ensure that your browswer's Zoom setting is at 100%; the applet may not operate at lower zoom settings.

Problems have been reported by users running Java applets on Mac OSX. Apparently the version of Java on the Mac comes from Apple, instead of from Sun, and is well known to be buggy. The most recent help I've found for this problem comes from Michael Horowitz's Java Tester page. Also make sure you have the most recent version of Java for Mac; instructions are at Apple support. If you're still having trouble you can Google "Java applets on Mac". I haven't got a Mac or access to one, sorry I can't help further on this...

On some internet forums users have reported problems with Firefox 3.5, not only in relation to Java applets running in that browser. I have no problems with the applets in Firefox 3.0.1. The Firefox / applet problem may be resolved by disabling the "next-generation Java plugin". This plugin will be disabled by going to Control Panel > Java > Advanced tab > Java Plug-in where 'Enable the next-generation" should be un-checked.

Most of the English translation by Alfred Mann of Gradus Ad Parnassum has been published by Norton in The Study of Counterpoint and by Dover (now) in The Study of Fugue. As far as I am aware there is no English translation of the complete text, but there is a facsimile of the original Latin text published by Broude Brothers. Other noteworthy texts on counterpoint include:

Arnold Schoenberg's Preliminary Exercises in Counterpoint (Faber & Faber Ltd)
Counterpoint, by Gordon Jacob; Part Two from Harmony, Counterpoint & Improvisation Book 1, editor Sir George Dyson (Novello)
Counterpoint by Knud Jeppesen, trans. Glen Haydon (Prentice-Hall Inc.)

Each of these texts differs to a greater or lesser degree from Gradus in its choice and/or implementation of the rules; that is, the other texts have more rules, or less, or variations on the same rules. Fux's dialogue format is very entertaining at times, the other books are quite dry in comparison.

The part of Gradus Ad Parnassum which deals with fugue is in The Study of Fugue. Fux wrote that this was the most important part of his book.

The following excerpt is from the back cover of Norton's edition of The Study of Counterpoint

Composers who have been familiar with Gradus Ad Parnassum include J.S. Bach, who is known to have read the book and praised it; Haydn studied it meticulously for his own training in composition; Leopold Mozart used it for his son's early composition lessons, and Beethoven made a condensed version with annotations, which he used when teaching his students. More recently Richard Strauss and Paul Hindemith used it when teaching.

It should be clear that this method is well tested, and provides some useful insights into fundamental aspects of composition.

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Aside from the obvious prohibitions against parallels, what sorts of errors is the applet looking for? Only asking because I just wrote a rather jumpy first species line in a Phrygian example, with consecutive leaps in the same direction, and the applet seems to think it's fine. Dr. E.K. July 2009

Fux doesn't state a specific rule on how many jumps are acceptable, so I didn't include one in the applet's rule set for melodic movement. What should the rule be? In the second species example from Gradus on the next webpage Fux writes two ascending leaps of a 3rd. Also in the third species example. On the fourth species page Fux's example follows an upward leap of a 4th with another 3rd. Fux's third species examples frequently use root -> fifth -> octave, or root -> fifth -> seventh -> octave melodically. Maybe three consecutive 3rds should be forbidden, or two consecutive 4ths.

A second decision I had to make was in regard to movement back within the compass after a large leap. Fux says the movement should be stepwise (this is noted above) but in many examples, as in the one on the second species webpage, he moves back by a third or more. So I decided that the applet should simply remark on direction of movement in this case, rather than that it must be stepwise.
And although Fux prohibits the descending melodic sixth he uses it in at least one example. The applet remarks on all descending minor sixths.

A third decision should have been in relation to repeated notes. In every one of Fux's first species examples he repeats at least one note, sometimes two, and in the mixolydian example he writes three Gs in a row. He doesn't write repeated notes in the other species, but unfortunately the applet permits it. (There are a number of other improvements I'll hopefully get around to one day - as mentioned on the second species page, although Fux recommends a minim rest at the start for species two through five the applet doesn't allow it, and it would be good to be able to choose the CF as the upper voice.)

So in regard to melodic movement in first species, the applets WILL comment on augmented or diminished melodic leaps, exposed tritones, descending minor 6ths, leaps greater than minor 6ths (excluding octaves), and will remark that minor 6th or octave leaps should be followed by movement back within the compass of the leap. The additional melodic (and harmonic) restrictions for the other species are noted on those pages. G. McC.

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