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I'm going to assume that the question is attempting to write a fugue in the baroque/early classical style. (Fugal works in renaissance style are a different matter, which allow somewhat more leeway in the intervallic construction of a subject, but restrict other elements much more severely.) As an introduction to this topic, I'll defer to Robert Gauldin, ...


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There is absolutely no reason why a fugue subject has to be "unique". The best known counterexample is probably the finale of Mozart's Jupiter symphony, where the principal fugue subject is a commonplace four notes shamelessly stolen from every textbook on elementary counterpoint from Fux onwards: In fact Mozart may have stolen this idea from Haydn (...


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You may be overloading your expectations for the subject to be unique. You can treat the subject to some degree as generic. Minimally it needs to define the tonic/tonality. It's more important how the subject gets treated in the course of the fugue. When looking at subjects in the Well Tempered Clavier, I notice many subjects will start with some ...


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Yes. Elaborating on ttw's to-the-point answer: one of counterpoint's general aims is how to write voices that keep the listener's attention engaged over a sustained passage of time, by avoiding redundancy or "cheating," particularly the redundancy encoded in two-species rules. Those rules apply at all time scales, to all pairs of voices. It's tedious to ...


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I can imagine a tenor derived from e.g. an early invocation that doesn‘t fit to a note-to-note c.p. But such practices are historical nonsense: trying to apply the rules of Fux to music that was not „written“ for polyphony. Because: First step to train the rules of Fux would be to compose a good c,f. The aim of studying c.p. must be to overcome the ...


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Given a cantus firmus, is it always possible to do counterpoint with it? By the time we get to Handel, he says yes, even if his countersubjects are often mostly rests. We'd have to move this question to mathoverflow to find someone dogged enough to find a counterexample, a c.f. so pathological that counterpoint would be impossible. You may have to qualify ...


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I think this question can only be answered if you know not only the constraints on species counterpoint (as the OP clarified to Westergaard's formulation), but also the constraints on what constitutes a "proper" cantus firmus. Westergaard (I'm assuming we're talking about his tonal theory book) is working with a set of rules of species counterpoint that are ...


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There is some mathematical analysis about the subject. There were a few cantus fermi that could be proved not to have a satisfactory counterpoint. Generally, most melodies do admit of some type of counterpoint.


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