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If it was a complete set of rules, it would by necessity be even more arbitrary.
But I don't know what is arbitrary in this book.

I feel the information is presented clearly and systematically, but I think you are responding to the temporary gaps where he tells the student about something but doesn't explain why because it is too soon to understand.

Well, yes the harmonic concepts are not exactly what we have today, but it is the basis for it.

As far as Bach not teaching from Fux; he didn't have to.

The point is CPE said it was an advantage NOT to start with Fux - get straight into the meat, so to speak.

Fux's cantus firmi are written for the specific purpose of exercise. They are composed to illuminate the rules and, at the same time, present difficulties for the student. I would hold off on composing your own cantus firmi until you've gone through all the exercises in the book.

Yes, this is cadential. Notice that the required intervals render a leading tone and a major 2nd to the tonic (except for the Phrygian mode).


Keep in mind that Fux's use of the modes here are for pedagogical purposes and do not necessarily represent actual practice (notice the requirement of the leading tone in most of the exercises), especially in regards to ecclesiastical modes. Fux's book is more about counterpoint and treatment of dissonances than modes.

That's part of the rationale behind the rule. But, you can think of it the same way as parallel 5ths - it's a matter of texture and line independence.

I don't know why anyone here is referring to any of these rules as arbitrary - none of these rules are arbitrary. When you are learning a style of music, you must learn the "rules" of that music. As Fux himself writes, "...the lawgivers of an art have set down nothing pointlessly and without deliberation." That is a true statement.

"What was agreed upon hundreds of years ago
is that the way to measure the distance
between two pitches would be by "intervals,"
and these "intervals" would be based
on the MAJOR scale ONLY."

Gyro- just for clarification. Rarely have any two theorists ever agreed on anything, much less a community of theorists agreeing on some universal language for measuring pitch distance. Also, intervals were discussed waaaay before the "Major scale" was even used.

BTW- keyboardklutz, you shouldn't have any unisons except on the first or last note, especially one approached in similar motion (m.4). Also, this is not a cadence. A cadence in 16C terms is defined by Zarlino as a Major 6th moving to an octave (or its inversion, a m3 to unison.) Always do the cadence first and then go back. This M6-P8 formula is a result of a compositional preference for leading tones moving to octaves in the upper ("cantizans") voice while the lower ("tenorizans") voice moved down from scale degree 2 to 1. That's why the Phrygian mode requires no leading tone, the Major 6th interval is "built in."

So, jumping in and responding to your reply to KBKlutz - trying to decipher your reply...
FUx sees a cadence in terms of a move from a major sixth to the 1, (only?) but where does the leading tone stuff come in?
A leading tone in my language is a major 7th tone - which is not in the phrygian mode - which sports a minor second???
If I sm right Fux is thinking of church modes or somthing similar, and using these so that the tonic or root is the first note of the mode?

Well, thanks so much for that. My examples from Swindale (you may know it?) has unisons but as you say they're approached contrary. I thought my cadence came too easy!

The cadence is M6 to 8. In phrygian (in E as an ex.) it is D and F to E and octave E. Instead of a leading tone you have a minor second (F - E).

Zero, for the most part, the church modes are the same as the Jazz modes (well, not really, but alot of it is the same.) Take a D Dorian scale for example. If you were working with two voices only, the bottom voice would go from scale degree 2-1 at the cadence (E-D), while the top voice would move from scale degree 7-8 (C-D). If those notes were not altered, the penultimate vertical interval would be a minor 6th and the final interval would be an octave. In order to get a Major 6th, one must raise the C to C#, resulting in the leading tone. In the Phrygian mode, the penultimate interval (using the same scale degrees as in the Dorian example) is already a Major 6th.

Now it becomes a chicken/egg argument. Zarlino was the Theorist that established this "rule," but he was really simply articulating what was already being done by the composers of his time. This is the way Theories usually are introduced. Generally theory follows practice and the "rules" clarify what the acknowledged masters of a generation were already doing.

It seems as if I am at a cadence myself in this explanation, so at the risk of eliding into another thought, I will end here.

got that Super

I'm jumping in from the Adult Beginner forum where Keyboardklutz's example here was posted so I tried to do the exercise. I probably shouldn't be doing this: I started rudimentary theory this year starting with note names but moved rather fast, and am at the very beginning of harmony - just piecing my chords together in combination in root position: smidgin of an understanding of cadences and that there is such a thing as movement.

So this is my version, strictly following the rules Keyboardklutz posted. (I've fixed the tritone, KbK). Now I am reading here that there is such a thing as a cadence, but it's a movement from 6 to 1? Wasn't there a time when there was no 7th note, so no leading note? So that would explain the 6 to 1.

So this is my first attempt, before:

Hi keystring,
It's great that you're learning this stuff!

Now, for the fun part:

1) You've got parallel octaves at the end - that penultimate interval is an octave, not a major 6th (See below for more on this).

2) You've got two unison's in the body of the exercise (mm 2, 4). As this is First Species counterpoint in two parts, the unison may only be used at the beginning or end of the piece.

3) You have a whole note in the counterpoint for two half notes of cantus firmus (m 4). Again, as this is a First Species exercise, you should have 1:1 notes in counterpoint to the cantus firmus.

4) You have a P5 to a unison, a perfect consonance to a perfect consonance, in similar motion (m 4, beats 2-3). A perfect consonance must be approached by contrary or oblique motion.

5) You started the piece with an imperfect consonance - a major 3rd. A perfect consonance must be used at the beginning and the end.

As for the leading tone, these exercises do make use of it. The intervals of the cadence should be:

B-C
D-C

This is a major 6th interval to an octave. Notice that the major 6th contains the leading tone, resolving to the tonic.

Keep up the studies!

Thank you, Harmosis, for all that feedback. I feel like I'm groping in the dark since I barely have my feet wet for the most introductory level of even ordinary harmony theory, where you learn that there is such a thing as a cadence, or such a thing as V - I movement, or there is such a thing as a V.

So I have the rules you have set out, and the ones listed by Keyboardklutz. Is the basic idea that I am moving from a unison at the beginning to a cadence which is VI-octave, where VI is the leading note and those last two intervals create a cadence, meaning that it gives a finality?

Slightly off-topic: last night we were talking about plagal cadences, which in a certain quarter is being argued is not a true cadence because it contains neither the dominant nor the leading note. But it came to me that it is called "church cadence", and the notes include the VIth degree, which is actually the leading note in the present exercise. Historically might the plagal cadence herald back to earlier times?

You're welcome!

The beginning must be a perfect consonance, but not necessarily a unison (it can be an octave or perfect 5th as well).

The cadence is a major 6th interval resolving to an octave, but that is NOT to say it is VI resolving to I. When working through species counterpoint exercises, you don't often get functional harmony, so it is best not to think in terms of it. But if you wanted to look at it that way, then the cadences in Fux's species counterpoint would be V-I (as we are discussing counterpoint in two parts, I have placed a hypothetical third part in parenthesis make the point more clear):

-B - C
-D - C
(G)-(C)

The D to B clearly forms a major 6th interval, but as you can see, it outlines a V, not a VI.

Of course this is not the case in the phrygian mode, where we would use a phrygian cadence:

-D - E
(A)-(G#)
-F - E

I you haven't already done so, you should pick up a copy of The Study of Counterpoint from Fux's Gradus ad Parnassum, translated into English by Alfred Mann. It is a good step-by-step study of the species counterpoint that we are discussing now.

The plagal cadence is absolutely a true cadence. As you pointed out, it is often associated with church music where it was used extensively (and why it is often called the "Amen" cadence). The word, "cadence," comes from the Latin word cadere - "to fall." This stems from the fact that musical passages in general tend to fall in pitch as the phrase closes. It does not mean that the major 7th (leading tone) or the 5th (dominant) must be present.

Even so, there is descending leading-tone resolution in the plagal cadence between the root of the IV chord and the 3rd of the I chord:

D-D
G-F# *
B-A
G-D

Even more so with a minor iv chord (between the 3rd of the iv chord and the 5th of the I chord):

D-D
G-F# *
Bb-A *
G-D

Plagal cadences can be very effective, even though the IV/iv chord does not have the tension of a V7 or viiº.

Now that I have stopped Christmas-hops around the country (I feel like a flea) ... thanks again for the additional explanations. I think I'll try that exercise again.

I've also just looked it up and found this write-up Counterpoint (& Species) Definition
My first thought was that I have no business going any further until I have studied basic harmony, but now I'm reading that harmony theory wasn't even invented yet. I don't think I'll mix myself up through this diversion, what do you think?
I see that Fux's book can be purchased on-line. Was the original in Latin?

Yes, it was originally written in Latin.

Harmony theory was certainly known at the time, as evidenced by Rameau's Traite de l'harmonie of 1722.

In my opinion, it would probably be better not to start Fux's counterpoint and common practice harmony at the same time. Although there is much in common between the two, there are enough differences to cause confusion (for example, crossing voices is allowed in species counterpoint, but your harmony professor will not allow it!).

I'm not that far yet: just moving chords around in root position, but I skipped ahead in the harmony book and soon there will be those kinds of rules. I would like to get this exercise right though since I started it. How about this?

That's much better, except that you have the interval of a 4th (m4, beat 3), which is a dissonance; and dissonances are not allowed in two-part First Species counterpoint. There are a couple places where contrary motion would have been better (as you have a lot of parallel motion). It is also considered bad form to approach or depart from a unison by skip, but, as the cantus firmus is skipping (m1, beats 1-2), it's less of an issue. Overall, this is good work. The only real problem is the 4th in measure four.

Thanks again. I did wonder about the 4th. I was conscious that I instinctively wanted to hop down to the dominant which sounds correct to modern ears.

Are you saying that the top voice can actually cross over and go underneath the cantus? If so, that should open up some more possibilities.