Intended tempo of exercises in Fux's Gradus ad Parnassum

Question

Fux uses whole notes for the cantus firmi in his book, so do others influenced by his work. But I find them almost unbearably slow within the usual tempo ranges.

I know that there must have been a note value "inflation" at some point in music history since the quadruple whole note and double whole note, which fell from common usage, were named longa (long) and breve (short) respectively and the whole note, which is the longest note value in current common use, was named semibreve (half of short).

Is it possible that the intended note values of the whole notes in Gradus ad Parnassum would translate better to today's notation as quarter notes?

Answer 1

It is not possible to infer intended performance tempi from the note values used in Gradus ad Parnassum. And there is no reason why we should do so. These exercises are designed primarily for tuition of counterpoint, not for performance. So, clarity of notation is of greater importance than any suggestion of tempo. As @Roland Bouman points out in his comments above, a system based upon division of whole-notes is well suited to this task, as "the beams and stems won't distract you from the exercise."

The wikipedia entry about species counterpoint uses the following musical excerpts to demonstrate first, second and third species counterpoint (before also describing fourth and fifth species); they effectively demonstrate the clarity of notation achieved by using divisions of the whole-note:

First Species:

Second Species:

Third Species:

So, this usage of note-values provides clarity in these counterpoint examples and exercises. But, there is no reason why we can't use different note-values to provide clarity in performance scores, too. After all, note-values are relative; although, shorter and longer note values may seem more suited to faster and slower "real" speeds of played or sung notes, no note-value has an inherent speed, only a relative speed to other note-values.

Your question hints at this, mentioning a presumed "note inflation" during music history. Indeed, if one looks at examples of, say, Palestrina (the composer Fux models in his Gradus ad Parnassum), we see not only similar note-values to those used in Fux's exercises, but longer note-values too. Below is an example from Palestrina's Missa Papae Marcelli:

To the "modern-eye", it may seem easy to subconsciously halve these note-values, to "hear" 4/4 as one reads the score. But, even if we do this, we should be careful not to ascribe undue significance to such a mapping; the score this example is taken from is itself a late 19th-century edition, quite unlike the original manuscript.

We should also be careful not to assume that this process of "note inflation" is absolute, since (for instance) the time of Palestrina. All note values are relative. Any score can be notated in a number of different ways, even if certain note-values seem more or less appropriate in any given situation. After all, 3/2, 3/4 and 3/8 are all valid time-signatures, although in theory a score using any of these could be notated in 3/4; equally it is perfectly possible to find a fast 3/2 score and a slow 3/8.

Let me close my thoughts here with some examples of music using note-values which may be considered "outside the expected range".

This link has a youtube video with a recording and score of Messiaen's Quartet for the End of Time. At 17m57s Movement 5 begins, its metronome marking is 16th-Note = 44 (although the performers on this recording are playing significantly faster!) Why this extreme metronome marking? (I have my own ideas, but would rather leave the question "hanging" here!)

At the other end of the scale consider, for instance, the scherzo movements of Beethoven symphonies. Take Symphony No.1, for example: much of the third movement is written in note-values of a quarter-note or longer (with occasional passages using eighth-notes). The metronome marking is Dotted-Half-Note = 108, and this is certainly not an extreme marking within Beethoven's output. In fact, there is some debate as to whether Beethoven's metronome markings are intentional or possibly even incorrect. (See for instance, here.)

In absolute terms, the Beethoven marking is nearly 30 times as fast as the Bartok.

And this answer hasn't even touched upon the perceived speed of other musical parameters. Just flicking through a book of Charlie Parker transcriptions, I came across Ko-Ko, a chart marked as Quarter-Note = 308, but with a harmonic rate where the chords change only every two bars (or occasionally per bar). Yes this is a transcription, so the metronome marking could have been written differently, but it still seems appropriate as it describes the tempo of the rhythm section. Yet the "speed" of the harmonic changes certainly don't seem to be represented by this metronome marking…

Whether for use for study or as a performance score, choices of note-values are not inherently linked to any particular speed; although some note-values may seem more appropriate than others in any given context, note-values are, in the end, relative.

Answer 2

maybe a setting a specific speed was not his intention. He wrote the Gradus to bring music students back to the right path of composition, and he did it through examples of the different modes of counterpoint, i guess one can play it as a crotchet if need be..