# 16th Century-Style Counterpoint



## Mr. Big Noodles (Oct 30, 2016)

AKA: Da modez FO REAL

This isn't the usual fare for this forum, let alone the entirety of SSO, but I figured that somebody might like this information since I see a wide range of interests here. You can skip down to the embedded videos to get to the meat and potatoes of this post. Also, I put the information in this thread onto a PDF, in case you want to download it. Be warned: the bit above canon at the octave is problematic to say the least. Read on to find out why that is.

If you've ever said to yourself, "Hey, I'd like to learn counterpoint," you've probably run across the name Johann Joseph Fux. Fux wrote a treatise titled Gradus ad Parnassum, which is a style guide for "Palestrina-style" counterpoint, broken up into five "species." There is a good breakdown of species counterpoint starting on page 46 of Toby Rush's Music Theory for Musicians and Normal People, and a scholarly translation with great annotations is available to us through Alfred Mann. Unfortunately, Fux omits many crucial elements of sixteenth century style, such as treatment of hexachord mutation and effective rules for fifth species ("florid") counterpoint.

I don't mean to make this post all about Fux's deficiencies, because that is a moot point and it is amazing that he was able to deduce as much as he did from what were probably scant resources (no internet in those days). He was an (early) 18th century man trying to revive the 16th century; back in those days, anything past 100 years ago was ancient history. Nevertheless, I've always had problems getting my species exercises to sound good and be consistent with the style at the same time. I was unable to derive an effective system for myself from Fux. Now I am taking counterpoint classes and am required to compose good, stylistically accurate music. One of my composition projects was a canon, and even the instructions given by my professor were not particularly rigorous. Fux isn't the only guy to write a counterpoint treatise. Hell, there are lots of composition treatises from the 16th century that detail this stuff. If you're like me though, you don't have time to read all that. Imagine my delight when I found these videos from the venerable Peter Schubert:





Oh dear, that intonation. Even so, the improvisation part is impressive.

He is telling you which melodic intervals the dux (leading voice) can do so that the comes (following voice) will not make bad harmonic intervals against it. Now this is just canon at the fifth. He has no corresponding video for canon at the octave, so I went ahead and deduced the rules myself based on acceptable intervals in the style. Essentially, the only harmonic intervals allowed are octave/unison, third, fifth, and sixth. Fourths are no good, as are seconds and sevenths. Additionally, for each mode, there are only a handful of scale degrees that will readily accept an octave or fifth, but I won't get into that just yet.







I did all of these in mode 1. What is mode 1, you ask? We would call it "dorian" in modern terminology, but there are a bunch of melodic practices that go along with each particular mode. For instance, the motion from scale degree 5 to 1 is perfectly fine in dorian, lydian, and mixolydian, but is a huge no-no in phrygian. These are the modes according to their maneriae:






The maneriae use Greek ordinal numbering (protus, deuterus, tritus, tetrardus). Each maneria indicates whether the final (tonic, root, whatever you want to call it) is D, E, F, or G. There is an authentic mode and a plagal (hypo) mode for each maneria.

Maneria protus (D) = modes 1 and 2 (dorian and hypodorian)
Maneria deuterus (E) = modes 3 and 4 (phrygian and hypophrygian)
Maneria tritus (F) = modes 5 and 6 (lydian and hypolydian)
Maneria tetrardus (G) = modes 7 and 8 (mixolydian and hypomixolydian)

Anyway, let's try this out in mode 1. I'm going to split this up into a few posts so that this doesn't get more overwhelming than it already is.


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## Mr. Big Noodles (Oct 30, 2016)

I squeezed these out real quick using nothing but the intervallic rules and some rather formulaic cadences. First I'll do canon at the fifth, both above and below.





Audio for 5th above.





Audio for 5th below.

Those are alright. It works out for the most part, but I find that you can&#8217;t just be putting down these intervals willy-nilly: if you&#8217;re not paying attention, you&#8217;ll end up with octaves and fifths that obscure the mode, and in the case of my fifth below exercise, I even ended up with a diminished fifth (B-F), which is bad for this style. Still, I was able to crank out something that sounds halfway decent in no time at all and with absolutely zero revision compared to the hours of toil that I would normally spend on something like this and still have a garbage piece of music at the end.

A quick note: a canon has to break off at some point to make a cadence. You see that notated in my graphics, along with the text for the cadential melodic motions (clausulae) of the voices: a "cantizans" approaches the cadence by providing a leading tone (7-1), and a "tenorizans" is stepping down to the finalis from above (2-1). In later styles, there is also "bassizans" which is a 5-1 motion, and even "altizans," which is 5-5, or potentially 5-3 or 5-6.

Now the octave imitation. I was suspicious of these because the only melodic intervals allowed (according to my chart) are thirds, fourths, fifths, and staying at the same pitch. In other words, there is no stepwise motion. I didn&#8217;t try to doctor these up, because I want you folks to see and hear the problems. The damn thing sounds like a bunch of arpeggios, which is really not good. If I freehand a canon at the octave, I can set up chains of sixths and thirds with plenty of stepwise motion, so I have no idea why this formulation is no good. Albeit, it is totally contrived, but by the rules of the system, I should at least have some fighting chance by strength of the intervals alone. You see in my canon at the octave above, I ended up with consecutive fifths by contrary motion. That&#8217;s way not good. In my canon at the octave below, I end up with a harmonic fourth. That interval isn&#8217;t even allowed in the style. So, you see that this is far from perfect. I&#8217;m going to keep researching and developing my canonic technique to see if I can find a way to do octave canons better. I&#8217;m guessing that the process that works for canon at the fifth cannot work for canon at the octave, so I&#8217;ll have to devise some other steps.





Audio for 8ve above.





Audio for 8ve below.


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## Explorer (Oct 31, 2016)

Subbed.

Also, this has me now looking at stacking a dry melody signal chain with a wet signal chain containing a harmonizer effect with a delay. That would make it easy to run experimental riffs in the music generation stage, to later be edited into a final form with added cadences.


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## Mr. Big Noodles (Oct 31, 2016)

Explorer said:


> Also, this has me now looking at stacking a dry melody signal chain with a wet signal chain containing a harmonizer effect with a delay. That would make it easy to run experimental riffs in the music generation stage, to later be edited into a final form with added cadences.



Similar to this? (3:23)

Queen - The Prophet's Song


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## Mr. Big Noodles (Nov 3, 2016)

Alright, here's an example of how I might approach a canon at the octave above. Basically, I try to lock into an imperfect consonance (either a sixth or a third) and then proceed with stepwise motion. Note how I only have one high point in my leading voice (dux), which is the D above the staff, and how I stay within the range of an octave. I've delineated the intervals of the dux below the bottom staff with either positive or negative integers, so 3 is an ascending third while -3 is a descending third, 2 is an ascending second while -2 is a descending second, etc.






Audio

You'll notice that my intervals are a little fifthy/thirdy at the beginning, which facilitates good harmony with the following voice (comes), but once I establish sixths or thirds there really is no need to have a dux that leaps around a lot. Also, dat contrary motion.

Here's another short canon at the octave below.






Audio

You see that I use a lot of stepwise motion. Once you arrive at an imperfect consonance, you really have a lot of freedom and should use as much stepwise motion as you can. This canon's weakness is long chain of sixths in the second half, but the harmony is at least correct on a technical level. Interestingly, the only intervals I use in the dux are seconds ascending/descending, and perfect fourths ascending/descending. The first interval I am outlining, however, is a third: by ascending to F, I can guarantee a good entrance on D.

Are these the greatest canons at the octave ever? Certainly not; I threw them together in a little less than a minute, so I'm not expecting them to hold up to the 15th and 16th century Flemish masters or anything. But they are certainly better than the canons I generated from the chart I threw together in the first post. I'm trying to extract a formula from this right now so that I can make these with my eyes/ears closed. Typically I rely on intuition, but it helps to have some rigor involved. I'm trying to work more in that direction.


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## tedtan (Nov 3, 2016)

Interesting. Somehow I missed this Monday.


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## Given To Fly (Nov 11, 2016)

In case people are wondering what we learn in music school, this is week 1 or 2 of 16th Century Counterpoint, usually taken during the third year, and part of the required 8 semesters of Music Theory. 

I'm not sure what the Music Theory majors had to do.


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## LavaScript (Dec 28, 2016)

If anyone here new to counterpoint wants to have a checklist to look over while practicing it I have this page I used for my AP Music Theory class. It's pretty helpful and I wrote down the different types of contrapuntal motion on it.

Also I'm not sure about fourths in counterpoint. If I remember correctly they aren't allowed period in strict counterpoint but in some forms I believe Perfect Fourths are allowed, but obviously not Augmented Fourths (Tritones).


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