Need help with Fux

[Sirion]

I've just started to work on Joseph Fux' The Study of Counterpoint (unfortunately without a teacher. There's no one around here, but that'll hopefully change when I move this autumn!). I enjoy it a lot, but the a lot of the music theory in it is alien to me.

I may make this a returning thread, where I ask questions as I encounter them, but for now, there's only two things I'm wondering about:

1. Why both a g and c clef? (obviously, the c clef is the valid one)

2. I don't understand the error made on page 31 (Alfred Mann edition). At the risk of breaking copyright laws, I'll include a small quote:

"...the cantus firmus is in D (la, sol, re), as the beginning and conclusion show, and you started with G (sol, re, ut), you have obviously forced the the beginning out of the mode".

What exactly does mode mean here? I know THE modes, but it must have some other meaning in this example?

[Daniel]

1. Why both? If I remember correctly, it's because they were originally written (say) in soprano clef, which has been updated to (in this case) treble clef.

2. I'd have to read it in context, but the pupil (Josephus?) has obviously used notes not from the correct mode, in which the cantus firmus is written, and the counterpoint should be in.

[Sirion]

Here is a transcription of the musical example (for simplicity, I notates it as quarter note). The first G in the Josephus voice was the wrong note, the the D the corrected note. I've looked over it, and I still don't "get" why the perfect fifth interval don't fit here.

fux1.pdf

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• fux1

[Daniel]

If it's Dorian, which it looks like, how could it start on a G and a D? If you follow through the rest of the cantus, it doesn't make sense to start on a "G chord". Examples like that pretty much always start and end in the same 'key'.

[Sirion]

Of course! Since Josephus' counterpoint voice is the lowest one this time, it is the one who establishes the mode, right? If the voiced switched places, so that the D would be the deeper note, and G the higher, there wouldn't be a problem, right?

[Daniel]

In Dorian D and D or D and A would work. Not D and G or G and D.

[Sirion]

Now I think I get it: A D is the fifth of a G, which would imply that G would be the mode (or the tonic of the chord if we were talking about harmony). On the other hand, A is the fifth of D, making D the mode. Is this the reason?

[Lord Skye]

Need help with Fux

Sounds like a personal problem.

[Sirion]

Apparently, Fux is very popular in school choires because his name often is mispronounced.

[Sirion]

Okay, I've gotten to part two of the book (three voice counterpoint), but I'm still a bit uncertain about things. On page 35, it is explained why mi (F or B) against fa (G or C) is not allowed to use. That's fair enough, because these are small seconds that weren't percieved as good sounding. However, it is also explained how you can use sharps or flats to avoid this. But wouldn't this just move the problem? If you look at the example I included, it's true, mi and fa is not used against each other, but you still have a minor second in there, this time between A and Bb. Is there any specific reason why it is these exact minor seconds that aren't allowed, while others are fine?

Secondly, I've just started out on the second part, where you use the first species of counterpoint in three voices It is explained how the standard triad is considered the ideal, and why other combinations may have to be used (perfect intervals != direct motion). The book suggests that 1 3 6, 1 3 8 and 1 6 8 are accepted substitutes. However, I would presume that when writing in three parts, you have to look at the relationship between each of the voices. In this case then, 1 3 6 would contain a third and a fourth, a dissonant interval not to be used. How come it is accepted here? And why wouldn't 1 5 8, containing a fifth and a fourth be accepted then?

[Sirion]

[Forgot to add attachment to last post]

Sibelius.pdf

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• Sibelius

[Chris]

1. If you are in D Dorian, you need to start the progression with a D chord - either D and D, or D and A. As the cantus firmus is in the upper voice, you can't use the note A in the counterpoint, as this would give a perfect 4th (dissonant). Using G and D (as a perfect 5th) is not allowed as it essentially establishes a G mode. Therefore, the only possible note is D.

 

2. In the example, mi is F and fa is B. They represent a tritone, i.e. there are three tones (six semitones) between them. In the major scale, i.e. C Ionian, it's the 4th note against the 7th note. In D Dorian, it's the 3rd note against the 6th note, etc.

 

I was disappointed that the book didn't go into more detail about this. In the example, it's an upward skip from F to B that is marked as incorrect, however, what about going down from B to F? And what about going up from B to F (it's still a tritone, but in a different context), or down from F to B? I chose to avoid them all, although some clarity would have been nice.

 

3. The upper voices are only reckoned with the bass, but not with each other, so you're essentially looking, with 1-3-6, at a 3rd and a 6th; 1-5-8 is a 5th and an octave, etc. However, in my understanding the rules for voice leading are still to be observed between all voices, no fifths or octaves by direct motion, no "battuta", etc.

 

Chris

[Monojin]

Fux is good for learning counterpoint in general, but for renaissance music, you're barking up the wrong tree. I'll try and pitch in some things I learned from Peter Schubert's Modal Counterpoint: Renaissance Style.

 

The mode is specific to each voice, and is established by nothing more than melodic motions, and cadences (which, in renaissance thinking, also consist of nothing more than melodic motions). The motions in question are skips or outlines between the final (the "root note") and the fifth scale degree, or from final to final. You're supposed to end a piece on the final (hence the name) but as for the rest, it's a lot more free than Fux is making you believe. If your bass starts in G, that doesn't stop your CF from being in the dorian mode, although you will have to bring them both in line for the cadence. No keys, chords or progressions to be found here.

 

A perfect fourth becomes consonant if it is "supported" by a bass note either a third or a fifth below, but that is true for all of common practice.

 

Skips or outlines of a tritone are never allowed in the renaissance style. Pretty much all of the theory is vocal in nature and that stuff's icky to sing. You may use a B-flat (never a F#) in this and other situations. The only other accidentals allowed are historically unwritten sharps ('ficta') to produce leading tones at cadences.

 

I hope you found this helpful. Feel free to PM me if you have questions.

[Chris]

Hi Monojin

 

Thanks for the info. I have some questions if that's ok.

 

The mode is specific to each voice, and is established by nothing more than melodic motions, and cadences (which, in renaissance thinking, also consist of nothing more than melodic motions). The motions in question are skips or outlines between the final (the "root note") and the fifth scale degree, or from final to final. You're supposed to end a piece on the final (hence the name) but as for the rest, it's a lot more free than Fux is making you believe. If your bass starts in G, that doesn't stop your CF from being in the dorian mode, although you will have to bring them both in line for the cadence. No keys, chords or progressions to be found here.

 

Can you give an example, e.g., do you mean to say you could write a bass line in C Ionian and write a contrapuntal line above it in C Dorian?

 

A perfect fourth becomes consonant if it is "supported" by a bass note either a third or a fifth below, but that is true for all of common practice.

 

Could you give an example of this too? If a 4th had a 5th below it, wouldn't that fifth be outside of the triad, e.g., G-F-C, with F being a 5th below C, but outside of the C major triad.

 

Skips or outlines of a tritone are never allowed in the renaissance style. Pretty much all of the theory is vocal in nature and that stuff's icky to sing. You may use a B-flat (never a F#) in this and other situations. The only other accidentals allowed are historically unwritten sharps ('ficta') to produce leading tones at cadences.

 

Thanks for that - it's good to have some clarification.

 

Chris

[Monojin]

Can you give an example, e.g., do you mean to say you could write a bass line in C Ionian and write a contrapuntal line above it in C Dorian?

Rather, C Ionian and D Dorian. Writing two lines whose finals are one step apart is slightly more challenging than if they were a fifth or a fourth apart, but definitely possible. There's even a bunch of canons at the second above/below to be found in treatises.

I should clarify that the early exercises in my textbook do prescribe adding a line in the same mode as the CF (apart from authentic/plagal variants).

A lot of Renaissance repertoire thrives on modal fluidity and ambiguity. For example, this motet was praised by a contemporary theorist for seamlessly combining the dorian and phrygian modes. I don't fully understand what he meant yet, but you may notice that the overall modal character changes constantly without clear cutoff points, and that there are sometimes somber melodies buried under cheerier ones and vice versa.

http://www.youtube.com/watch?v=nfVnqU8hyxU

Could you give an example of this too? If a 4th had a 5th below it, wouldn't that fifth be outside of the triad, e.g., G-F-C, with F being a 5th below C, but outside of the C major triad.

 I meant a 5th below the lower note comprising the 4th, so that would be C-G-C, a standard consonance comprising a fifth and an octave to end a piece with.

A third below would be E-G-C, also known as a first inversion chord in common theory. You can even write such a consonance in parallels. One early renaissance style based on that principle is fauxbourdon. Example: http://www.youtube.com/watch?v=bAQ2pBXZ6GU

[Chris]

Thanks for your responses.

 

The first part is really interesting. Could you give an example of what would define a line above a C Ionian bass line as being in, say, G Mixolydian. To my thinking, if the music began on a C-G, then it would simply be established in C Ionian.

 

As for the second part, I misunderstood and see it now.

 

Chris

[Monojin]

Hello, another belated reply to this topic.

 

I have checked another textbook and it seems that the renaissance theorists themselves were uncertain about which voice was representative of the overall mode of the piece. Initially, it was usually the tenor, as the tenor usually sung the cantus firmus or other recycled material that the piece was based on. As the renaissance went on, the bass became more like a harmonic bassline and began to represent the mode. In any case, it wasn't about "chords" for a very long time, rather melodic lines centered around the final (i.e. the 'root note' that is the goal note at cadences) and the reciting tone (which is sometimes, but not always, a fifth above the final!)

 

To illustrate different simultaneous modes, a canon at any awkward interval will do. This is a puzzle canon by Scipione Cerreto where each voice enters a second higher than the last. Based on the melodic contours, the modes would be ionian, dorian and phyrgian, respectively. If you try to sing or play them in isolation, they will sound very different. As for the combination... you decide.

 

[Chris]

To my ear, the music as a whole is in A minor; and now after hearing that,

all of the other lines sound like they're in A minor, although perhaps they

didn't at first.

 

Modes are fascinating, I need to study them more.

 

Thanks.