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In the given image below, Fux writes a counterpoint to a cantus firmus given to him as part of his studies by his fictitious teacher Aloysious.

A rule that is often emphasised is that one should remain in the mode (in this case, the mixolydian mode), and there should be NO accidentals, except in the second to last bar where the 7th has to be raised.

Note that the cantus firmus is in the upper stave and the counterpoint in the lower. Also this, if not evident, is Second Species CounterPoint

enter image description here Thus, the question is as follows. In the fourth to last bar Fux raises the 7th - why? By doing so he has exited the mode

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  • Hmmmm, interesting. There's also a conspicuous voice crossing in the 6th bar. The CF itself isn't explicitly in Mixolydian, but it's been too long since I've done species stuff to know if that loosens things up at all. Obviously in some sense the reason is because the note is ultimately leading to the G of the next bar as a sort of pre-cadence, but it does seem like a strange move in modal species terms. Could it have anything to do with the fact that the next CF note would have been a tritone away from an F natural?
    – Pat Muchmore
    Commented Jul 4, 2014 at 15:27
  • The cadence approach and prominent B naturals were what I was thinking of, too...
    – Bob Broadley
    Commented Jul 4, 2014 at 15:39
  • in bar 10 the CF is at C, the very next bar F# (the CP) is the highest tone (a sort of leading up to a tritone), that alone would turn me off. If he were to use F natural the interval would have been a minor 3rd which is a valid (and preferred) imperfect consonance. I too considered the cadence as a possible explanation, however, this is according to Fux, not allowed.
    – Aiden Strydom
    Commented Jul 4, 2014 at 16:09
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    He's just Fuxing with your head, that's all.
    – Kaz
    Commented Jul 4, 2014 at 20:54
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    Looked it up in the original 1725 edition, imslp.org/wiki/Gradus_ad_Parnassum_(Fux,_Johann_Joseph) p. 61 -- it's definitely there in the original. My guess is that since each of the last two Fs move up to G it may have been considered a cross-relation to make the first F-natural and the second F#.
    – Michael Scott Asato Cuthbert
    Commented Jul 8, 2014 at 0:49

3 Answers 3

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First of all, the clefs are not quite right and the bottom part should be an octave lower (this is inferrable from the illegal 4th in the penultimate bar).

Modes in Renaissance style are not the strict collections of 7 notes used in "modal" pop and jazz songs. Instead, a mode tells us where the tonic is located within a field of 11 notes, 7 diatonic and freely used (A,B,C,D,E,F,G) and 4 chromatic (B-flat, F-sharp, C-sharp, and G-sharp).

Flats are used primarily to avoid the tritone; thus if your melody wants to go to B but the cantus firmus is on an F, you can use B-flat instead. (Flats are used for other purposes too, such as the "una nota super la" rule and certain cadences in Dorian, but that's another story.)

Sharps are used primarily in cadences, as you correctly point out, and also in cases which at the time were caused "causa pulchritudinis": using a major third in a triad which would normally be minor for its richness of sound (an epic example is the opening phrase of Palestrina's "Stabat Mater").

It appears that Fux is trying to achieve the latter category of effect but, as is clear from reading an updated counterpoint manual such as Jeppesen or Gauldin, he got a few things slightly wrong. A sharped note should function melodically as a leading tone to the next higher note; in this case, the F-sharp would be correct if followed by G, although that would cause problems in the next bar.

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I know it's an old discussion, but I thought I might add my five cents:

I'm working on the "Gradus" these days (Mann's translation) and have asked myself the same question. Then I remembered that in footnote 9 to Chapter one Mann says that "the tritone is to be avoided even when reached stepwise (f-g-a-b) IF THE LINE IS NOT CONTINUED STEPWISE AND IN THE SAME DIRECTION". Could it be that Fux simply wanted to avoid the melodic tritone in bars 7-9 of the tenor voice (b-a-g-f) by sharpening the f, since he did not continue stepwise to e but skipped to d instead?

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A possible explanation would be that the F# in the fourth bar from the end in the counterpoint is sharped so that there is no tritone with the B in the third bar from the end in the cantus firmus. The unaccented D that follows F# in the counterpoint would not alleviate the formation of the tritone.

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  • not really a valid comment since Fux could have replaced the 'B' with an 'E' such that the passage would be G -> E -> D -> F#. The latter makes more sense since the motion would still be similar, however, the interval would be a minor third (from E to G) - which is an imperfect consonance, thus... better
    – Aiden Strydom
    Commented Jun 2, 2015 at 6:35
  • @AidenStrydom I am speaking of the relation of the quarter note F# in the fourth bar from the end in the counterpoint, with the whole note B in the third bar from the end in the cantus firmus, not the unaccented quarter note in the counterpoint.
    – Chris
    Commented Jun 4, 2015 at 10:06
  • i know... and you're still wrong. had he made the B in the third to last bar an E he wouldn't have needed to raise the fourth to last bar's F to an F#
    – Aiden Strydom
    Commented Jun 4, 2015 at 10:20
  • You seem to find the cause of this F# to be the B in the second quarter of the third bard from the end in the counterpoint while I think that the whole note B in the CF would be the problem, even though it is in another voice. Mostly because it is an accented B and it comes before the B in the CP. Even if, like you propose, he substituted the B with the E (therefore changing a minor 6th with a minor 3rd, both imperfect consonances), a tritone would be sounded in the outer voices. Could you care to define what counterpoint rule/guideline are you following?
    – Chris
    Commented Jun 4, 2015 at 10:59
  • @AidenStrydom but the CF is given. He uses the same CF in the first species eight pages earlier. On top of that, the resulting descending fifth in the CF would be uncharacteristic. Replacing the B in the third to last bar with an E is not an option.
    – phoog
    Commented Apr 16, 2023 at 10:03

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