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:
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:
There are also some general rules governing the combination of the two parts; these rules are common to all five species.
In addition to the general rules listed above, the rules specific to the first species are:
Points to note in this example:
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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
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:
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.
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.