The professor was Hugo Norden, and at the time he took over my counterpoint class in 1976, he was a venerable professor Emeritus and the author of a number of important books on the topics he taught. The books did not enter my library until years after having already internalized and practiced their contents. I had the living, stuttering exemplar of counterpoint, canon, and fugue before me in the classroom weekly. Someone more simpatico had walked us through the rudiments of the first four species. A quick rip through these for the laymen: the fist species is note against note. The same rules hold as held for Harmony One. Beware the parallel fifth or octave. A few more considerations apply in all species of counterpoint: begin and end on a perfect consonance, cultivate contrary motion, don't exceed a spread of more than a tenth between parts, and the interval of a fourth is treated as dissonant. (We had that problem in Harmony. Refer back to my bit on the origins of the ostinato piece in '74.) The rubric remained as it had been for Harmony. Each mistake cost 10 points. It was treacherous, but I managed to pass without a warning notice for three semesters. Hugo took over the class in the Fall semester of my Junior year. He was tasked with getting across the fifth species in that semester, and fugue in the Spring. He was a marvelous teacher, one of the best I ever had. This was despite his physical infirmities, the chief of which was that he had a terrible stutter. His verbal stutter was coupled to his physical stutter and tremors so that his work on the blackboard (and he did a lot of it) featured machine gun repetitions of syllables and much shrapnel and dust from flying chalk.
Hugo referred freely to his various books, some of which were out of print even at that time. I wonder now if he had taken on this classroom work because he was short of money. I also speculated about the source of his impairment. Had he had a stroke? The obvious sources for the topics at hand would have been his books on canon and fugue. At this moment, "Fundamental Counterpoint" and "The Technique of Canon" are available used for a pretty penny. The fifth species of counterpoint, florid counterpoint, combines the first four species. It is the goal of the entire enterprise in which the art reaches its full complexity. I was looking forward to it. It was, as Goode would have said, a chance at last to let the doggie out to pee. Hugo's teaching drifted from the strict examination of the topic at hand. That was what was so engaging about him. He'd approach the blackboard with his hobbled frame and raise the chalk before he'd said so much as hello.
Whap! The chalk would fly across the board, making note heads as a series of unadorned dots. He went along like this well enough, so long as he didn't try to speak at the same time. As he warmed up to his subject and to us, it became more the norm that he would keep up a running dialogue with chalk in hand. Those near him in the room would be showered in chalk dust. We learned to give him some space. As soon as he'd finished the note heads, he'd go back and fill in stems, dots, ties and beams as needed. He wrote as the classical masters wrote; having formed the piece in his mind complete in all its parts, he then wrote it out in the most efficient way. I appreciated this on the first day of his class, and I was awestruck. Then he began to speak.
"You are looking at an example of fifth species counter-p-p-p-p-p-oint!"
He looked around at all of us.
"It combines the lessons you have already learned into a complete musical whole. To learn to do it well, you will have to follow a few simple rules."
I filled up two black notebooks in my studies with Hugo Norden. The pages are somewhat disordered now. There is some evidence of struggle on my part. I tried taking furious notes, but he moved very fast. I caught a few of his remarks as he spoke and battered the blackboard.
"The fifth species uses eighth notes, and, as you see, mixes other types. There are a series of ornamental resolutions. There are four of these."
He writes them on the board, whappity, whappity, pop, pop, pop, and I dutifully write them down. His commentary refers to the examples that have sprung to life before our eyes.
"You see in number one, the tie over the bar from fourth species. The eighth notes form passing tones to the resolution. In number two, the passing notes come down from above. Number three features a leap down and a step up. The leading t-t-t-t-t-tone. Number four is no good in a four-three suspension, as it features both a leap down and a leap up to the resolution. You will use no two in a row alike. You must tie the half note over the bar."
He took the eraser and wiped the board. Some of us were not finished copying, but luckily I was. He bashed out a fresh cantus firmus, and drew for us a model. On another sheet, I find my working out of this problem adorned with his red ballpoint rubric. Looking at my work, I see hints of the trouble to come. He is very pedantic in his grading. He writes "no second species" when I introduce a bar of that texture in an attempt to break the monotony of the continual ornamental resolutions. He was concerned about fidelity to the letter of his assignment, and I was concerned about the effect and sound of the music. If I were just doing exercises, I had a hard time staying engaged. In reality, I was almost incapable of repressing my creativity. I see these students nowadays as an academic, and I have a great empathy for them. I see myself looking out at them as my spirit in a different body. I've risen up in faculty meetings and gone to bat for them. I bristle when they are treated as Hugo treated me at first. He was human, all too human. Other marks in his red ink call out violations. This is what I had to learn, and I make no excuse. In a pair of parallel thirds with the leading tone on top (sopra), descending, the tritone arises in cross relation between the sopra and the contra. Got me! The dreaded 'devil in music' has claimed another victim and I'm down another ten points.
It could have been dry as the chalk dust, but it wasn't. He loved Bach, and in this respect he had my complete respect. He opened my eyes to another way of seeing Bach, and ultimately to another way of thinking about music. He'd write Bach fugues from memory on the board. (!) He'd stand before the example and pound on or circle an area. The little numerals that indicated any number of parameters from proportion schemes to intervalic relationships, with a diabolical mix of cabalistic numerology thrown in for good measure would soon crowd out the notes. Then the connecting lines and marks he made just to underline the beauty on the board would obliterate the rest. I have notebooks full of this sort of thing, and it looks like the ravings of an unhinged mind. I know better: I drank it in! He'd do all of this and then he'd say,
"The old b-b-b-boy really knew his b-b-b-b-business!"
He assigned us to listen to and study the Bach "Passacaglia" in c minor. Also in my notes, he suggests the Reger "Introduction and Passacaglia" in b minor. (We've dropped a half step, like boats in a lock.) It's back to Bach with the "Crucifixus" from the b minor "Mass." We are to read the last chapter of the "Technique of Canon."
 |
| Calbraith Hunter, Counterpoint Notebook Ex. 1 |
Leonardo of Pisa lived roughly from 1170-1250. His dates are sketchy: he, too, was unmoored in time. He was, some say, 'the most talented' white guy to do math in the middle ages. He is known for having disseminated the Hindu-Arabic numeral system in Europe through the publication of a book called the Liber Abaci. He is also known for a numerical sequence which was of Indian origin, appearing as an example in Fibonacci's book. It was this numerical sequence that Norden was going on about. It is expressed in integers as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, etc. It is a recurrence relation. Each term of the sequence is defined as a function of the preceding terms. In this case, we are adding the integers together. In the Liber Abaci, the intitial zero is omitted. Thus we could start with 1 + 1 equalling the number 2. It has an appealing simplicity, does it not? Then we add (the additive function) the 2 to the previous term, the 1 and come up with 3. 3 + 2 = 5. 5 + 3 = 8. It's turtles all the way out. The wiki (our oracle these days) says that the Fibbonaci numbers are closely related to Lucas numbers. That's good, because Lucas is another word that appears in the counterpoint notes.
I'd like to point out that many of the more narrow minded members of the music student population would have rebelled at the disconnect between this numerical knowledge and practical musicianship. I might have agreed early on, though I quickly became enchanted and a believer. They were not around to object. The upper reaches of counterpoint was for a handful of composers only, and in the end, it was just me and Hugo.
Back to Lucas for a moment. It is said that the Fibonacci sequence is a complementary (not complimentary) pair of Lucas sequences. "Not to be confused with the sequence of Lucas numbers, which is a particular Lucas sequence." This guy Lucas was a nineteenth century dude. (1842-1891.) François Édouard Anatole Lucas did not last long. He may very well have blown the fuse of his muse. In both the Lucas and Fibonacci numbers, the ratio between two consecutive integers "converge" into the "golden ratio." The difference between the two is that Lucas builds his additive sequence beginning with 2 and then 1. Thus: The sequence of Lucas numbers begins: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, ...etc. Turtles as far out as the reductio ad absurdum will allow. In infinite regression is the cosmological godhead reached by another circuitous route. So what about this 'golden ratio?' In both math and the arts, the golden ratio exists when "the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one." Thank you wiki, thank you Google.
In his stuttering chalk talks (and later, huddled together over a desk), Hugo demonstrated how this sort of proportional ordering existed in Bach. He also advocated using the same methods to make new work. The practical application involved positioning events in a timeline that was ordered by such a 'scheme.' I took to referring to these diagrams of events unthought of in detail but mapped out on graph paper as "proportion schemes." A bunch of these for various of my works fell out when I discovered the warning notices. Imagine the irony of that! The man revolutionizes my method and then finds my methods unsatisfactory. We shall come to that and its aftermath.
 |
| Calbraith Hunter, Counterpoint Notebook Ex. 2 |
"I don't trust my ears, or anyone else's"
He'd been introducing us to his notions about "form the silent language" in the context of a lesson in the canon at the octave.The example I preserved features a canonic interval of three semibreves. It also has a repeat feature, that makes it chase its tail like a round. Otherwise, it lacks, as do almost all of Hugos examples any sort of harmonic tension over the long duration, and very little tension or interest in the short, moment to moment, duration. So, being on the one hand intrigued by the formal aspect of the technique and unimpressed with the expressive content of the workaday examples, I was ready to gripe in crabbed pencil in my margins. I wrote: "A mechanical framework for what? Writing meaningless music? Art is the tension of impulse over larger force."
"If you look in the drawers of many comp-p-p-p-p-posers, you'll find quite a few unfinished works."
In the apartment of Cal Hunter, I was well aware, there were many unfinished works, stumps of manuscript paper that contained good starts but no finish, torsos of great ideas with no working out, workings out that had no purpose, and all manner of bungled attempts. Hugo was in too deep. I began making detailed plans for pieces, promising myself that I would better attend to the details. My detailed plans looked like the diagrams that Hugo drew like a maniac. His mania was now mine.
