I am grateful to Reiko Füting for sharing both articles with me.
I: Link to heading
I had never heard the F Major Duet up until encountering Siegele, which made me seek it out. It has a sonic timbre and form that, despite its balance, struck my ear as truly bizarre—a symmetry that is so symmetric that it’s almost off-putting. Siegele is correct to feel that there is a distinct, deliberate message Bach is communicating. Also, unlike in say the great B minor fugue from Book I of the WTK, here the kernel appears not at the beginning (it only appears so), but rather in the middle, as a dissonant middle section, the first non-trivially prime Fibonacci number (I say “non-trivially” because 5 bars or less is too small a number for an actual section of music).
I am not entirely convinced by Siegele’s arguments regarding proportionality, depending on how we divide the piece. Or, phrased differently, I would say that the deep inner structure (in terms of proportionality, regardless of how we split the sections and then compare them to each other as ratios of a whole) comes inherently from its Fibonacci structure: On page 251, if we consider O as 13+24, and I as 10+21, and re-sum, we obtain
13:34:34:13:34:34:13
Or we can recombine in a different way to obtain
13:21:13:13:21:13:13:21:13
which is palindromic, and so on. The key is that the average of the original O and I sections that Siegele outlines is a Fibonacci number; the inner kernel is wrapped in a sequence of increasing Fibonacci numbers, making the proportionality inherently recursive. All other patterns and internal structure that is intrinsic to the piece are born of this. I think here in terms of partial differential equations: observing phenomena in nature somewhat simply, and notating speeds and their relations to each other, we end up with equations that are extremely difficult to solve mathematically, and exhibit enormous amounts of emergent structure.
More interesting to me in Siegele here is that he formalizes what I have felt about how Bach composed for a very long time, and is indeed precisely the way I compose:
“Yet it is never possible to go back behind the stage of concretion and individuation reached at the point of branching out…At the most an earlier stage serves as a new point of departure…For the process of increasing concretion and individuation can take place in the imagination, or at least without staves and notes, until that stage of elaboration is reached which requires paper, pen and conventional notation”. Compositions, at their best, where there are sinews or sutures, where all feels fully formed from the very outset, as they are in Bach, and the best of Mozart and Chopin and Shostakovich, emerge suddenly seemingly, but are the result of a mysterious internal formulation that is the accretion of a variety of emotions and intellectual ideas that are hardly quantifiable—but where one has felt so much, thought so much, and composed so much, in one way or another, that the sequences mapping to emotions and narratives become easier and easier to conjure, indeed nodes in graphs from the past begin to connect to new nodes in the present, and one’s harmonic language and notion of structure grows.
The best structured pieces come at once, fully complete, or one can improvise until one loses the thread, chop, learn what one has written up to the chop, and then hope to continue from there. Otherwise, the piece will be more episodic, like Rachmaninoff, which can also work excellently, though not as well: write a beautiful thirty seconds, and you can surround it with just about anything.
Siegele understands all of this natively; I would be shocked to hear that he was not a composer. Perhaps it is precisely this view of organic generation that puts me at odds at times with Beethoven. I can sense the sinews everywhere—in the Große Fuge, there comes a moment where he uses a simple rising isolated chromatic pattern in the cellos to return to a previous theme, and then: boom! We are back. Too easy, clearly manufactured. I enjoyed the final F major quartet much more (so far, I have only listened to the B-flat major and the final F major of the late quartets), in particular the third movement, a sort of goodbye-letter to life, and then the fourth movement, oscillating between parallel minors and majors, a clear retrospective on his own life, ending triumphantly, with such good humor throughout. But often, while listening to both quartets, I could hear myself telling myself “I wish I were listening to the Brandenburg Concerto No. 6”, easily the best quartet of all time (I take poetic license here, it’s not a quartet per se.).
I came away from listening to the Große Fuge still thinking Beethoven couldn’t really write a fugue. He quotes the B Minor Fugue of Bach; Beethoven, for all his greatness, is modest, which makes me admire him greatly. He is a mortal, revering the gods: he knows he could never write a symphony like the Jupiter, and stated as much, and could never write a fugue like the B minor. I admit in all humility that aside from fugues I’ve composed via personal explosions whose narrative I would explain if they were not private, I cannot conjure a good fugue at will (bad ones, yes). I am blocked, and know the kernel of why, but wish somehow to expedite the process. Siegele communicates very clearly that he has a narrative when he listens to Bach, and whether there are necessarily crosses in Bach repeatedly (I do think to some extent that is true) or Bach inscribing his name (definitely in certain pieces) is not the most important thing. The important thing is the narrative, emanating from the graph-forward-and-backward-linked form, which is essentially various narratives in the mind of Bach linking with one another—these narratives will vary for each listener, because we may label the nodes differently due to our own inner lives and experiences, but the manner and rapidity in which they are linked we all share (though this too our private lives alter somewhat, but in essence, when listening to Bach we are all riding around in Ferraris).
I suspect part of the kernel of why I am blocked for fugues, why most of us are, and why Bach clearly was not, has to do fundamentally with his spiritual conception of the world. I must study the Shostakovich fugues more; they are uneven, but those that work are marvelous.
I know mentally and in my conception what narratives will be in the collection of fugues I’m planning, and why fugue is necessary: I want a harsh, passionate dissonance to emerge in them, that many false starts have already demonstrated the harmonic language of—and they can only be maximally beautiful by having an encasing that is maximally tonal and structured. This is at the heart of the conception of fugue for me, and the heart of passion—efficiency. Proportional structures of maximal intensity (which I define as notes and emotional content therein, divided by time). Of course, silences can also carry an enormous amount of intensity (something which the players in the ensemble complained about in my piece—they did not like the counting of measures in between notes. Bruckner people. Bruckner. I traveled to hear Thielemann perform it at the Musikverein, and after the glorious, enormous fourth movement, almost right after the last note sounded, audience members began clapping. Thielemann’s deep annoyance emanated from the stage, though he tried to hide it: I could see his deep disappointment. It was then I knew I wanted to meet him—he understands Bruckner.)
I think also in my conception of the B minor, and fugue in general, of Webern, in his variations for piano (recorded by Richter). The last sounding note is pure alien crystal in its brilliance: it has been prepared by everything that has come before, by the deeply thought-out structure of it all. That one note still haunts me—it is Bruckner, who loves to take his time and space and prepare the arrival of his marvelous harmonies at the end of his first movements, taken to an even more extreme level, making it a much colder, austere kind of music. It is equally brilliant.
“Rather, pondering the divine order of the world…he incorporated this insight into his work”. I suppose this is ultimately my other complaint with Beethoven. I hear no spirituality there. He is obsessed largely with himself. The composers I ultimately have always preferred, ever since I was young, were largely the ones with a spiritual harmonic language. Bach, Bruckner, Sibelius, Fauré, Poulenc (more a man finding spirituality late, but at heart, remarkably carnal and lush, what a harmonic language! The Motets for a Time of Penitence and the Organ Concerto are wonders, maybe not in terms of structure, but certain episodes have utter gorgeousness, like in Rachmaninoff). Of course, this is limiting: I also prefer the people I view as the direct descendants of Bach, most of whom compose at their best in precisely the manner Siegele describes: a forward constructed graph network. Shostakovich, Debussy (objectively—his harmonic language does not move me, but his forms are incredible), Schönberg. There are many others (I am leaving out Rachmaninoff, who sometimes doesn’t compose this way—but whose conception of sonata form is very intuitive and integral for me and who is a very important composer for me). I am omitting Brahms, because for me he is a refined Beethoven in many respects, but also because I have already digressed so much and focusing on Brahms is just too dangerous. All I will say is I tried to take a break from learning Bach by heart and went to try to learn the Intermezzo in A, but quickly returned to Bach. It was too simple. I do not mean that it isn’t brilliant, or that something can’t be learned from it. I only mean that I am getting older, and somehow my brain just rejects anything that isn’t compositional gasoline. For me, that is the Bach fugues. Also, currently, the G Major Corrente. The G Major Partita in general (but especially the Corrente and Prelude). I map my life out in key signatures.
II: Link to heading
Bach’s sense of proportion is indeed a compositional technique, particularly in his fugues: but I feel strongly that it comes about naturally, in the same way one tells a story to house guests, and tries to make it interesting: a joke at this point; a rising cascade; the peak of the story; dénouement. This is someone who has read and felt and thought and composed so much that his sense of proportion is intuitive. I have always admired the WTK Fassung editions of Bärenreiter; yes, a note here and there or at most a sequence can be altered without destroying the structure, but any more than that, and we are violating the principles of the graph-network outlined in article I. When Siegele says “On the contrary, it requires a plan, or, to put it with poignancy: it results intentionally”, I need him to be more precise. If he is arguing that Bach somehow mapped out on the page how the form was to be, and then composed it, I strongly disagree. Rather, Bach’s forms were formed in his head, a kind of “cloud”: he could hear the kernel, he could hear the key moments with the key voice leading and harmonies, perhaps he composed a few false starts that gave him an even better idea. But once he put pen to paper, it all came out at once: it was a story he knew he wanted to tell, knew all the major parts (or perhaps, none of them, except latently), and then it just told itself.
Just when Siegele starts getting going with the Ricercar, he stops. No! I found that fascinating, along with his discussion of the C major and C minor fugues. Again he stops! Not with that C minor fugue!
On page 73, he discusses harmonic disposition of thematic entries. These arguments in music theory drive me bonkers, because of this Schenkerian (perhaps it’s called something else) I/IV/V/III, and so on, designations that completely miss the point of Bach. His music sounds so harmonically brilliant and dense because of the notion of implied harmony, something fundamentally lost with a strictly chordal, vertical music. All those passing tones, as they’re so commonly called, which are so much more than merely passing. Depending on how one emphasizes them, how much pedal one uses, how one sees them in the overall structure, they can be so much more, and imply so much more, even when not overtly emphasized.
The sequence of falling fifths addressed below is something I have discovered independently composing, almost surely because of learning Bach by heart. It’s such a useful modulation (I don’t like this formulation, but can’t think of a more concise phrasing: tools come naturally, they are not forced in the best works, lest they sound manufactured, and different ones come up again and again in different composers’ works). Bach has many such tools. Another one of my favorites is when he modulates upwards, say to the sub-dominant or dominant, and then cascades downwards, via some beautiful sequence back to the tonic or to a new tonic (for example, in the Dis-moll Prelude in Book II, a long time obsession of mine, he holds an E natural in the first section in the right hand, and then cascades down B major, E-flat minor, then D-flat major, and ends up at G-flat major, the relative major). Again, this idea ties in with narrative: a good storyteller or speaker of course raises their voice higher, becomes more animated, during a poignant part of the story, before and leading up to communicating and transporting the listener to the moment Bach had that particular feeling, a feeling I’m sure Bach experienced so often, in so many variations: immense joy and revelation.
“Tempo is not unconditionally submitted to the competence of performance. Rather, it is an indispensable quality of composition…these tempo degrees are related to each other proportionally”. Yes! I want badly to communicate my notion of rubato in my piano works better in my notation, and especially to strings when I orchestrate. It is absolutely essential to the structure. I have heard so many recordings of Bruckner, completely destroyed by the “slow, deep feeling” tempo the conductor has opted for. “How deeply they feel it, they play him so heavily, so slowly!”. Any conductor who doesn’t play Bruckner with a bit of anxiety, or a pianist Bach with romanticism, clarity, and pulse, and of course an innate sense of proportion is missing the point.
I should mention, very important to Bach, and alluded to by Siegele on page 76, is the notion of rubato. In the Bach fugues, I hear micro-rubato everywhere; unfortunately, most professional pianists do not. Most of them play the fugues relatively straight, and destroy them (of course, they still work, just not as well as they could). Until I heard the András Schiff recordings of the WTK, they did not click for me.
“At the same time, it created the indispensable prerequisite for the blending of genres, which is so characteristic for Bach’s work”. Again, spot on. I think immediately of the Fis-Dur Fugue from Book II. What a bizarre, stately, wonderful, unclassifiable court-dance to open with, before moving into suddenly dramatic, upwards cascading material, before returning to the primary subject of the fugue. Only a massive genius could compose something like this, mixing a dictionary of dances together to create something rooted in tradition of love of the masters, while also being wholly original and totally unidentifiable. I feel this is what many contemporary composers are missing: revere the great masters, love their work unequivocally, speak honestly in your own, and it will be original and interesting by definition.
Siegele’s comments about Bach’s notation at times not being mysterious, but rather practical: it was easier or more convenient to notate 2/2 rather than 4/4, due to difficulties in having to beam. This was enlightening and inspiring to me. Bach wanted to get his music out there as quickly as possible, as efficiently as possible. If I could get away with notating as sparsely as he did, and trust tradition and a team of performers and students and colleagues to disseminate appropriately, I absolutely would (though I greatly admire a beautifully complex score as a work of visual art itself, a la George Crumb—how deeply emotionally and spiritually satisfying to look at one’s own score when notated beautifully). That being said, Bach’s scores are beautiful in their seemingly spartan simplicity; he very much had a strategy for his music to live on, while also maximizing his output.
In short, reading the Siegele was a bit like reading Schopenhauer: one doesn’t necessarily need to take all the arguments at face-value. Rather, one enjoys it because it reads like poetry, and because the sensibility and opinions of the author we largely agree with.