# Questions about Fux's 4th species of counterpoint



## paulc

I have some questions about Fux's 4th species of counterpoint, the ligature. I am still confused as to what constitutes a forbidden parallel in this species. Please see the linked picture.

http://members.ozemail.com.au/~paul.cameron/fux_4th_species.bmp

A. Parallel octaves. Not allowed.

B. Octaves on the upbeat, separated by an oblique tenth. These appear uncorrected in Fux's text. Allowed?

C. Same as (B), except that the octaves occur on the downbeat. Allowed?

Examples with four voices:

D. Fifth (actually a 12th, AE) to octave (AA) by oblique motion. Not a parallel. Allowed.

E. Fifth (DA) to fifth (AE) by oblique motion. There are instances in the text where the ligature permits parallel fifths (with three or more voices). Allowed?

Please list your answers and reasoning. If anyone can give me a concrete rule to follow, that would be appreciated. 

Thanks,
Paul.


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## Ramako

By following the examples in Fux's text we reach the following conclusion.

Parallel Octaves and fifths are fine with ligatures *except* if they are reached by 9-8 resolutions. In other words, if the intervening interval on the up/downbeat is consonant everything should be alright.

This (I assume) is because they aren't really parallel octaves because the notes don't happen at the same time. In the case of being reached by a suspension though they do count as parallel octaves because the dissonance doesn't have a proper identity in and of itself.

Sorry, I don't remember very clearly and can't explain well, but I think that was my solution to the problem you mention which also troubled me.


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## paulc

> "Parallel Octaves and fifths are fine with ligatures except if they are reached by 9-8 resolutions. In other words, if the intervening interval on the up/downbeat is consonant everything should be alright.


Thankyou Ramako.

I am leaning towards the same conclusion, based on Joseph's answers and Aloysius's responses in the text. For example, the first two bars in Fig. 75 and bars nine and ten in Fig. 77.

So, examples B, C, D and E in my diagram DO conform with the rules even as such "direct motion" (in the sense that the voices follow one another without the ligature) should be limited.


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## paulc

Although I do wonder about the unison, fifth and octave occuring repeatedly on the downbeat (Example C). Anyway...


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## wogandmush

While a case might be made for their legality, I would say, upbeat or downbeat, sequences of Octaves and Unisons should be avoided. The counterpoint is simply mirroring the cantus firmus (and thus not really counterpoint at all). 

Sequences of Fifths are fine though because they are reached by oblique motion.

And, of course, beware the 7-8 resolution in a counterpoint below.


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