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I've gone through all five species of Fuxian counterpoint, and I'm moving into combined species. I remember hearing that one of the most important forms of combined species is the combination of fourth (suspensions) and second (2 against 1) species. My confusion comes with the concept. The C.F. is the middle voice, the 2nd species in the lower voice, and the 4th in the upper voice. Assuming duple meter for simplicity's sake, the 2nd species voice would have to move at the upbeat, with the 4th species (dissonant) suspension resolving at the same time. This seems to violate the idea that a dissonant suspension is a non-chord tone that resolves to a chord tone, as the chord itself has likely already changed by the time it resolves.

How is 2nd species counterpoint combined with 4th species counterpoint?

2 Answers 2

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Fux goes into more detail on this in four-voice counterpoint ligatures (page 125 in the Alfred Mann English translation). Recall that ligatures simply delay the following chordal tone. Thus, in strict counterpoint, the second half of the measure (upbeat) should contain notes consonant to the the cantus firmi and the delayed note:

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What about the downbeat?

In Louis Van Beethoven's Studies in Thorough-bass, Counterpoint and the Art of Scientific Composition, Beethoven corroborates the observation that the second half should contain consonant notes while teaching 4-part ligatures. He also lists some acceptable combinations of ligatures and half notes above a cantus firmi. I would recommend memorizing them.

From this we can gather that:

  • Any types of consonances with the cantus firmi can be used on the downbeat.
  • Dissonances can be used on the downbeat if the dissonance resolves (by step) downwards. Note that this is what ligatures already accomplish.

enter image description here Arsi = upbeat; Thesi = downbeat; Discords = dissonances

  • An exception to this is the tritone on the downbeat, which can resolve in contrary motion: one voice moves up by step, and the other moves down by step. Fux uses this in one of his examples (F-B tritone):

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Another important lesson is from Fux on pages 132-134:

As a complete harmonic chord consists of a combination of third, fifth, and octave, whereas in the example mentioned there is a doubled fifth instead of the octave, it is evident that the harmony is not perfect.

  • On the downbeat a complete harmony is oftentimes not possible due to a dissonant ligature. Even so, a triad is always preferred to a dyad.
  • We should try to use a complete harmony on the upbeat.

As always, keep the motion of the voices smooth and singable. It's okay to double notes to do so.

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I hope this helped you!

These rules concern strict counterpoint; past this it is acceptable to have dissonances on every beat if you properly prepare a discord to resolve into another discord. That said, having most, if not all, of the half notes as consonances to the cantus firmi isn't bad either. Fux rarely uses half note dissonances on the first beat, even in his final example (pg 137, fig 204).

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This is one of the reasons I recommend abandoning Fux and picking up a copy of Jeppesen's 16th Century Counterpoint book. Fux simply isn't in-depth enough to explain the rules.

To answer the question, I would begin with "it depends." For a fuller answer, there are a surprising amount of angles to consider.

  1. Recall that the CF is constant for two full beats. The chord is quite often the same for both beats. (This is because a limited nubmer of chords are possible that are consonant with the CF.) So whatever you do in this situation, you likely are only working with one or two chords at a time.

  2. As the number of parts increases, it becomes harder and harder to find [lega] dissonant suspensions and passing tones. I would guess that less than half of your second-species notes on the second beat will be dissonant. Suspension rules are restrictive also; probably less than half of the suspensions will be dissonant. So it is often the case that a measure will have only one dissonance in either part - seldom can you make two legal dissonances.

  3. Depending on your suspension, recall that no other voice may contain the suspension's resolution during the suspension. This really limits the notes you can choose in your second-species voice.

Here is an example. Suppose your CF does this, a C followed by an A. (Let's assume C Ionian mode for simplicity, and let's assume we're in the middle of an exercise and not near the beginning or the cadence.)

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Let's say that whatever CF note came before will allow you to prepare a 4-3 suspension over the C. Whatever note comes after the A does not allow a dissonant suspension, so you leap up to an A to form a consonant suspension here. You now have:

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What chords could we use? Well, the first measure has a C and an E already. So the only likely choices for chords in this whole measure are Am and C. The second measure has an A and an E. This could only begin with an A minor chord. On the second beat we have only A's, so the chord might be Am or F.

With these limitations, there aren't many choices for the lower part at all. On the first beat, it could be C or A. It cannot be E, as that would duplicate the resolution tone of the suspension. If we chose A, this part could use a dissonant passing tone rising A-B-C to the next measure. This is a decent idea, because it supplies the third to the Am chord in the second measure. On the last beat, F is a good idea. It gives us a new chord. C is also a possibility, but we want this voice to keep moving and it just played a C.

enter image description here

All this is to say, the way to combine 4th and 2nd species is to work slowly and carefully. Your dissonant notes will be rarer than you think. As long is it is clear to you what the salient chord is on every beat, your dissonances can be fairly strong.

But really, pick up a copy of Jeppesen. It's reasonably priced and goes into much more detail than JJF. It is also full of many examples of combined species writing.

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