I am presently engaged in a battle to the death with Fux's text!
As some will know I have a reasonable knowledge of harmony (and ability to compose and improvise jazz) using modern harmony concepts, but I am struggling with the historical concepts embedded and assumed in the Gradus.

Question:
I have understood (I think) that Fux bases his harmonic analysis on the church modes (gregorian). I also understand that Fux excludes consideration of the Locrian mode on the grounds that the triad does not have a perfect fifth (Loccrian has a diminished fifth). However, when I learn about the church modes I find that hypophrygian mode appears to have the same tonal relations as the locrian.

What gives?

Zero

Hi Zero,
Again, I must reiterate that Fux's text is not about learning the Ecclesiastical modes, but counterpoint. His presentation is modal, but that is really beside the point.

In any case, I'll try to shed some light on mode 4. Although the ambitus is B-b, the finalis is E. Furthermore, this ambitus is the theoretical one. Oddo of Cluny, in his Dialogus in musica, states the ambitus, in actual practice, as A-c'. Locrian mode, as we think of it today, did not exist.

Hi harmosis and thanks for your help.

As I understand your answer the ambitus is the range of the cantus firmus. Mode 4 is the Hypophrgian mode. B-b means B flat ( I am aware that the modes are not pitch specific but you are assuming that we intepret the stave as if it were)

Your observation that the final is E is revealing and helpful. I suppose now that I cannot consider this mode as being locrian. It's rather a mode of a mode (if you will forgive this thought!)

I do not know what you mean by the term "theoretical one" and I do not understand your remark about A-c' as not existing. I neither understand the abbreviation A-c' nor the assertion that it does not exist. It seems I am getting into very metaphysical territory here. I take your point about Fux's text not being about church modes, I am simply trying to estblish some sufficient principles for the understanding of church modes (as opposed to Jazz modes) to work with the gradus.
At present I am struggling with determining which rules of Fux are related to the musical conventions of Fux's time and which rules are related to modern harmonic concepts of counterpoint. In other words how Fux can be used in modern counterpoint.
As you are no doubt aware I am also struggling with some of the historical terms such as diminution (improvised ornamentation) and the like. I just seek a knowledge of counterpoint which is useable for me. It's difficult to gauge what depth of knowledge of historical concepts I require in this purpose.

I am making copiuos notes! I shall keep trying!

Zero

Hi Zero,
You mistook my meaning: I did not say that that ambitus A-c' did not exist; I said that the Locrian mode, with "B" as the tonal center did not exist. For the sake of clarity, I shall restate my points:

1) There was no such thing as Locrian mode - BCDEFGA with B as the tonal center - in the time of Fux. Nor was this ever an Ecclesiastical mode.

2) The ambitus of mode 4 is theoretically B-b, meaning the note "B" to the note "B" one octave higher. "Theoretical," meaning this is the ambitus that theoreticians recognized, not necessarily reflective of actual practice.

3) In actual practice, the ambitus of mode 4 was A-c', meaning the note "A" to the note "C" a 10th higher (an octave + a 3rd).

4) The finalis of mode 4 is E, not B.

I hope this helps!

Zero- Think of the "Hypo" (plagal) versions of those modes as simply representing melodic material that goes below "tonic" a fifth or so and also goes above "tonic" a fifth or so. It's really the same mode as it's non hypo counterpart, just with the melody in a lower range. And as Harmosis alluded to, these ambitus designations are simply theorists attempts to codify actual musical practice into some theoretical system. In this case, by designating "boundaries" of the octave. The problem was that many composers ignored these boundaries (Josquin for example) and consequently, many compositions really fit neither the authentic or plagal mode ambitus designations. Real music has often messed up a great theory, but we theorists are relentless in the pursuit of codification.

Yes Super and Harmosis this does help. I am clearer now. I made the mistake of thinking of the tone series as if they were scales - which particularly the hypo's are not as the tonal centre is not in their root position - if you get me!
Modes seem to be note ranges rather than scales.
I take on board the caveat that real music did not always fit the theory,and I shall remember point 3 of Harmosis's answer about the actual practice of using moe 4. Its now embedded in my mind that the Lociran mode did not "exist" for theorists. It's becmong clear - gradually.

I am considering getting a program called "Counterpointer" by Ars Nova http://www.ars-nova.com/counterpointer.html to help me in my self studies as I have noone to mark my exercises. Anyone have experience of this software?

Once again thanks for the time and input guys, its appreciated. Dont forget its only the problems that I am posting here, I am enjoying this study and learning!

Zero