Sunday, June 12, 2005

The Art of Counterpoint, Part Five

When Zarlino goes into what he calls "diminished counterpoint", he basically goes from a loosely defined 1:1 ratio counterpoint where repeated notes are admitted (Versus the strict 1:1 counterpoint I use to teach mechanics that does not allow for repeated notes) to free florid two voice counterpoint with a mixture of ratios. To more precisely address the concept of strong beats versus weak beats, I will make this move progressively using strict versions of 2:1 and 3:1 counterpoint in which there are no repeated notes allowed in either voice.

Objections to my concept of dissonance being allowed in strict 1:1 counterpoint I handle thusly: The duration of the note values in 1:1 counterpoint can vary from an entire measure down to divisions theoretically as small as a 128th note or even smaller if triplets, quintuplets &c. are employed. In that sense, there really are no strong or weak beats in strict 1:1 counterpoint: They can be considered as all strong, all weak, an alternation of the two, or a strong followed by two weak beats in a simple or compound triple meter or even other variations in odd meters. A composer may or may not want to use a progression that goes from a perfect fifth, to a seventh, to a ninth, and then to an eleventh at a slow tempo with a texture of whole notes, but that is simply a matter of taste: The quantum mechanics of counterpoint allow for such progressions regardless. Now, in a simple or compound triple meter where the fifth is on the strong beat and the seventh and the ninth appear on the following two weak beats, and the tempo is moderate and the texture is that of quarter notes or smaller, no objection would be raised even by traditional theorists. My point here is, if it's allowable in one instance, it's allowable in any instance; that's the fact of the matter when you consider it logically and exclude subjective evaluations based on taste or the previous established practices of a certain composer or compositional school.

Lastly concerning two voice 1:1 counterpoint, I have been reminded that I failed to address outright the law of melodic leaps. In strict 1:1 counterpoint if either one or the other voice leaps, the exit and entry intervals must be consonances. So, the irreducible law of leaps in 1:1 counterpoint is that leaps can only occur between two consonant intervals. Keep in mind that I am isolating counterpoint from harmony at this time. Later, when we work with three or more voices and are intentionally putting harmonic considerations back into the mix this law will be subject to variation. But by that time, it will be evident that harmony is influencing the counterpoint and that harmonic laws are being borrowed to make the counterpoint freer in that particular context.

In strict 2:1 ratio counterpoint we must begin to deal with the concept of strong and weak beats. The duration of the notes of the respective voices is irrelevant: Where there are simultaneous attacks by both voices, there is a strong beat, where only the diminished voice moves, the beat is weak. It also does not matter if the diminished voice moves by uneven note values - dotted quarter/eighth in a duple meter or quarter/eighth in a triple meter or whatever variation - the non-simultaneous attack is always considered a weak beat or a weak part of a beat.

Just as the normative concept of strict 1:1 ratio two voice counterpoint is that of an "all consonance" environment with dissonance only allowed when both voices enter and exit the dissonance by stepwise contrary motion or by parallel motion involving unequal fifths, the normative concept of strict 2:1 ratio two voice counterpoint is that of an environment in which strong beats have consonances and weak beats may have dissonances as long as the diminished voice moves into the dissonance by stepwise oblique motion. However, just as in 1:1 counterpoint, if both voices move by stepwise contrary motion this normal state may be reversed and the dissonance may appear on the strong beat and the consonance on the weak beat. For example, in the progressions ||10-9|7-6|| and ||6-7|9-8||, or variations on that theme. Beyond even this though - which is simply using the laws that govern strict 1:1 two voice counterpoint in a strict 2:1 two voice contrapuntal environment - there is a much broader concept of counterpoint available with the strict 2:1 ratio that began with the stylistic affectation known as the nota cambiata or the changing note group.



In the above example at 1 is an example of a nota cambiata figure as employed by Palestrina and others of his era. Here is an example of a changing note group in which the first dissonance is quit by a leap directly into another dissonance before the resolution finally comes. Now, that example is over a single note in the bass, but the instance at 2 has the initial dissonance again quit by leap into another dissonance over a different note in the bass. The delayed resolution principle that the changing note group makes possible remains in effect.

The inverted forms of this cambiata figure were not employed by Palestrina, presumably because his hyper-conservative approach to style rejected them as a matter of principle, or taste (Palestrina is one of my favorite composers in all of music history, and is in some ways superior to Bach in my opinion, so please don't take that as a criticism). Nevertheless, they are obviously available and no law of counterpoint would be broken by employing them. In fact, the full quadrant rotation of this figure could be completed and the retrograde variations could be used as well. What does this tell us in the broader view about 2:1 counterpoint? As long as there is a consonance in one or the other positions over the bass note - and no forbidden perfect parallels are implied - leaps into and out of dissonances are restricted only by taste when preceeded and followed by a stepwise departure from and resolution to a consonance. Obviously, this law presents the composer with an apparently vast ammount of potential freedom, and that's true. However, experimentation in this idiom after attaining facility with strict 1:1 counterpoint will shorten this to a finite set of possibilities governed by your individual taste, which is exactly the point of these explorations.

5 Comments:

Blogger Forrest Covington said...

Hello "Hucbald". You have a potentially interesting blog here. I'm not going to make any remarks about the theory stuff, although I have to say I haven't ever seen a 'cosine' of the overtone series before. I don't recall whether Pythagorus ever discussed it.

I agree with one previous commentor that the white on black template, while striking, is hard on the eyes and discourages anyone from reading all of your long and involved posts.

Also, it is considered normative in the blogosphere to have an email contact at least on your profile page, so that people don't have to use your comments section to write to you, as I am doing now. You can set up a free Yahoo or something for this purpose if you are worried about spam on your regular email. A picture isn't a requirement, although the logo you have is pretty good. I assume your real name is Hucbald. Most music bloggers are not afraid of posting their real names, unlike political bloggers where there is the potential for trouble.

What would be most interesting of all is some audio samples of your compositions. If you lack a place to post them, try Soundclick. com, which is what I use, having no web storage available. It would help place your theoretical musings in perspective, and give the rest of us a valuable insight into your artistic nature.

As for your blogroll, Blogger Help has an excellent tutorial on this. It appears you already have a start on that aspect.

Good luck to you, and I will be checking your blog. I will be especially interested to see, over time, what remarks and ideas you have on music in general, aside from music theory per se.

Forrest

11:42 AM  
Blogger Forrest Covington said...

Hello "Hucbald". You have a potentially interesting blog here. I'm not going to make any remarks about the theory stuff, although I have to say I haven't ever seen a 'cosine' of the overtone series before. I don't recall whether Pythagorus ever discussed it.

I agree with one previous commentor that the white on black template, while striking, is hard on the eyes and discourages anyone from reading all of your long and involved posts.

Also, it is considered normative in the blogosphere to have an email contact at least on your profile page, so that people don't have to use your comments section to write to you, as I am doing now. You can set up a free Yahoo or something for this purpose if you are worried about spam on your regular email. A picture isn't a requirement, although the logo you have is pretty good. I assume your real name is Hucbald. Most music bloggers are not afraid of posting their real names, unlike political bloggers where there is the potential for trouble.

What would be most interesting of all is some audio samples of your compositions. If you lack a place to post them, try Soundclick. com, which is what I use, having no web storage available. It would help place your theoretical musings in perspective, and give the rest of us a valuable insight into your artistic nature.

As for your blogroll, Blogger Help has an excellent tutorial on this. It appears you already have a start on that aspect.

Good luck to you, and I will be checking your blog. I will be especially interested to see, over time, what remarks and ideas you have on music in general, aside from music theory per se.

Forrest

11:42 AM

12:10 PM  
Blogger MikeZ said...

Fascinating blog! Picking but one of a thousand questions:

Did the great composers (3 B's &c), when writing, say to themselves things like "OK, now here I need a II-VI-I progression (because the theory calls for it)", or did they think, "This will sound good"?

Or did the notion of a II-VI-I (for example) come about because people who studied their scores found that progression?

12:29 PM  
Blogger MikeZ said...

PS: I just found the Hucbald reference. Eminently appropriate.

12:31 PM  
Blogger Hucbald said...

Crud. I have my settings so that I was not notified of these comments, and I just discovered them. Sorry about that.

Forrest, you are renowned in out field and I've heard about you many times over the years. Thanks for posting, and I will change my settings to display my e-mail address. I'm still trying to figure some of this stuff out, so please bear with me.

Unfortunately, I can't change the template at this point without losing all the changes I've made to this one, so that will have to wait until I get time to copy this one to TextEdit and transfer all the details to a new template. With my ridiculous schedule, it may be a while.

MikeZ. Same thing. I am not being notified of comment posts, so I appologize. It was Rameau who first tried to systematically explain harmony in the 1700's. He was a contemporary of Bach and Bach was critical of his theories, which surprises me since Bach has the most highly organized harmonic progressions of any composer of his era. We'll get to Rameau since I have the English translation of his "Treatise on Harmony" and I want to go through it again.

Sure am glad I decided to go through the old posts before I leave town for a few days. Sheesh.

2:00 PM  

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