The Lovely Month of May: Schumann op. 48 no. 1 revisited

By way of saying farewell to the month of May, I decided to take advantage of a certain flexibility in the process of translation from German to revisit and reevaluate my post from a year ago on Schumann’s song “Im wunderschönen Monat Mai”. How much do I agree with myself? How has my theoretical outlook changed?

Interestingly, the answer to both questions seems to be “quite a lot”.


Since last year, I’ve developed a more refined, and, in an important sense, self-aware notion of what it is one is doing when one does a musical analysis. “Structural levels” have been replaced by analytical regimes; pseudo-deductive “reduction” has given way to the artistic construction of models (in effect, the “composition of variations”, which is so much more fun!); and certain remaining traces of the chord-theoretic paradigm have finally been expunged from my thought, in favor of allowing the line-theoretic paradigm and all its implications to propagate fully.

Underlying a number of these developments, and closely related to them, has been an increasing sense of analysis, composition, and performance as being all fundamentally the same abstract psychological activity of interpretation and expression — something I might well have verbally endorsed long before feeling it viscerally the way I do now. The key to “performing” (if I may underscore the unification by using this word) this activity is, on the one hand, approaching music in an abstract (“N”, “intutive” in the Myers-Briggs sense) rather than concrete (“S”, “sensing”) way, and on the other hand, simultaneously staying maximally involved with the technical details of the music, not giving into any temptation to veer off from the internal construction of music into mere external commentary about it (as is the fundamental, and basically defining, error of the field of musicology).

In other words: to do art music right, one has to be a “nerd” about it. The fact that our society has such a ready-made pejorative description of the set of mental behaviors necessary for appreciating art music is a perfect illustration of just how hostile our society is to this sort of music. (Not all societies are the same in this regard: the term “nerd” infamously fails to translate effectively into a number of other languages1.) In such an environment, polemics against “modernism” that focus on its allegedly narrow stratum of popular appeal ring very hollow indeed.


So let’s now take another look at the Schumann song, this time from my current vantage point. We shall naturally see some of these points in action.

Most of my recent analyses have featured a single-line, single-note-per-measure analytical regime. This is, I think, a rather important sort of regime, but in the interest of not focusing so lopsidedly on a single regime that one effectively miscommunicates the generality of the regime concept (it includes at least all possible ways of modeling a piece or passage in terms of the constructs of species counterpoint, the parameters being the number of lines, the durations of “cantus firmus” tones — whether or not there is a cantus firmus — and rhythmic relationships of lines to each other), I decided to choose the regime at random (under certain reasonable constraints).

“Unfortunately”, the number of voices chosen turned out to be 1 — so we will be back in familiar territory from that point of view. “On the bright side” (from the perspective of novelty), the rhythmic setting chosen was that of 3 notes per measure, which I haven’t yet done in a published analysis. We could think of this either as a lone cantus firmus moving at that rate, or as a third-species line suitable for a hypothetical one-note-per-measure cantus firmus — depending on what, if anything, we wished to do with our result in terms of constructing “later” multi-voiced models. (There are also other ways we could think of it — I don’t mean to suggest exhaustiveness.)

Here, then, is the result (larger version here):


(As I did last year, I use repeat signs for purposes of abbreviation, even though the repeat is fully written out in the actual score.)

And here, as in a number of other posts, is a model in a special “background” regime, illustrating the overall structure of our line at a glance (enlarged version here):


Now, in fact, I’m grateful to the forces of randomness for choosing a one-voice regime, because it brings into prominence certain theoretical points related to the matters discussed at the beginning.

Note, in particular, our interpretation of g#” and f#” in m.1. How different our mindset is from a “reductive” one, which would regard the g#” as a “dissonance” to be “reduced away” in favor of the f#”! As a matter of fact, the g#” is dissonant with the d in the bass (and its “image” d’) as well as the inner f#’; while f#” is consonant with both tones. This is the end of the matter if we adhere to conventional theory, or even an overly naïve version of Westergaardian theory.

But, if we understand that (1) music is made of individual lines with internal structures that do not depend on other lines (even if we have the option of taking other lines into account to resolve ambiguities) and (2) our task in analysis is not to mechanically “reduce” the passage but to compose an aesthetically pleasing model within the constraints of our analytical regime, which will serve to interpret (not “reflect”!) the original passage, then we realize that the two-note-per-measure model implied by our graphic notation, in which m.1 has b’-g#”, is superior to that in which it has b’-f#”:


The background model illustrates an important part of the reason: the connection between the final g#”, the subsequent g#’, and the later g#” at the top of the “hill” (sixth-progression). More locally than that, of course, we also have the arpeggio g#”-e#”-c#” instead of f#”-e#”-c#”, in which f#” is a purposeless note that lacks connection to the c#”.

But what “theory class” would allow one to express these compositional beauties, instead of being forced to say that “the chord” of m.1 is “IV6“?

It’s sort of true that, having realized this, we can retrospectively cobble together a chord-theoretic rationalization of our reading: we can say that, after all, the notes of the “B-minor chord” in m.1 — d, b, d, d’, f#’, b’, and f#” — are not “really” “chord tones”, but are rather “non-harmonic” tones elaborating the “C# major chord” (V) of mm. 1-2. But this has no legitimacy: it is cheating, by peeking at your opponent’s answers. Besides: what kind of “non-chord tone” is the a#? It’s not like we can say it elaborates the b as a neighbor, because chord theory knows only two types of tones: those that are “part of the chord”, and those that aren’t. If a# is a neighbor to b, then b must be “part of the chord”!

Now there is a more interesting objection to the approach taken here that someone might raise: the argument I gave above about g#” being aesthetically preferable to f#”in our model would seem to apply even if Schumann had written no g#” in m/1 of the actual score — if, say, the last two sixteenths consisted of two successive f#”s.:


This is a bullet that I unapologetically bite! For if Schumann had written two successive f#”s, he would be faced here with an argument that he ought to have written g#”-f#” instead. Which, one cannot help noticing, is what he actually wrote. Thus do we learn about composition by the process of analysis!

If our two-note-per-measure model showed f#” instead of g#”, we would be at a loss to “explain why” Schumann chose to elaborate this f#” with g#”; it would appear to be a considerably more arbitrary decision, one of the grand (or possibly less grand) mysteries of artistic genius.

If we used no simpler model at all, we could possibly make what amounts to the same aesthetic argument for g#”, in terms of the actual score; but to do so would be to rely on the reader’s ability to see through a considerable amount of distracting detail to the essential relationships involved — in effect, to construct, implicitly, something equivalent to our simplified model, for themselves. (Otherwise, it would look like we were “arbitrarily connecting notes together”.)

Creative interaction with the piece is how “musical epistemology” works. Our noticing that, in the context of this piece (as represented in our simplified model), b’-g#” is prettier than b’-f#” is the musical equivalent of a “prediction” that Schumann should have written g#”-f#” rather than f#”-f#” on the last two sixteenths. We are manipulating and reacting; we are certainly not taking statistical surveys of “19th-century style”. (Not that there could never be any purpose in the latter; but when we do it, we are not acting as humans being musicians.)

It is this epistemology which provides the correct foundation for musical criticism. If Schumann had written f#”-f#”, this — i.e., the above analysis — would be our way of “noticing our confusion”; if he were a composition student of ours, this would be the argument we would use to persuade him to change it to g#”-f#”.


Now to some points related to the theory implicit in our graphs. Previous versions of myself would have stared, arms folded, at m.5 (for example) and demanded to know what operation generated the f#’. The correct answer, of course, is “Schenker’s generalized passing motion, you fool; go back and re-read Counterpoint, since it apparently didn’t stick.” However, my previous selves probably wouldn’t have found that maximally convincing; they would at least have wanted to know how to understand it in terms of Westergaard’s system, which they believed to be the “right” version of Schenker’s. And the way it is notated — under a single slur connecting b’ to g#’, without any additional slur attacking it more directly to either — does not seem compatible with that. Surely it must be either an incomplete neighbor to g#’, or an arpeggiation (borrowing) occupying a portion of the timespan of b’; in either case, another slur connecting f#’ to the appropriate note would seem called for.

It is therefore worthwhile to say a few words about the proper meaning of slurs, which is perhaps not as widely understood as it ought to be among Schenkerian theorists (let alone other users of Schenkerian-style notation). The primary, overriding meaning of a slur is that the two notes at the ends of it are to be thought of as connected: some conceptual line moves from the first to the second. According to Schenkerian theory, after all, the data of music consist of lines; the slurs in a Schenkerian graph thus help us to see what the lines are. (Note, however, that the absence of a slur does not necessarily imply that no conceptual line connects the two notes concerned.)

Hence the slur in our model of m.5 connecting b’ to g#’ is to be interpreted as meaning that these tones would occur consecutively within a line, in a two-note-per-measure regime. This does, naturally, imply that the f#’ is in some sense an elaboration or prolongation of the motion from b’ to g#’; but the slur itself does not bear the burden of distinguishing between different types of such elaborations.

What does bear that burden is the underlying theory. I claim that in Westergaardian theory (once it is properly understood), there are really only two operations (that result in motion): step motion, and borrowing from other lines. Given this, a motion by skip is essentially always to be understood as involving a borrowing. (In fact, I even think the apparent exceptions, involving incomplete neighbors, are ultimately best understood that way as well.)

Hence, in particular, the f#’ must represent a distinct line from the b’ — a subordinate one, according to the stemming-and-beaming. However, because f#’ to g#’ is a step rather than a skip, we need not think of these as belonging to distinct lines. We may think of m.5 as switching from a line containing b’ to a line containing the motion f#’-g#’. For this reason, a slur connecting b’ to f#’ would be misleading: it would suggest (even while not logically implying) that an ad-hoc subordinate line was being postulated specifically for the f#’ — a formal possibility, to be sure, but an unnecessary complication in a case like this.

On the other hand, a slur from f#’ to g#’ would suggest (though, once again, this is not a strict logical implication) that f#’ was being interpreted as depending specifically on g#’ — thus, as an incomplete neighbor. Though superficially “parsimonious” and decidedly in the spirit of naïve Westergaardian theory, this interpretation strikes me as less elegant than one in which f# is a passing tone within a line that has something more of a prior history:


In my view the “parsimony” apparently sacrificed by the assumption of imaginary tones (e’ and e”) is regained by the ability to dispense with the “incomplete neighbor” category of operation in favor of ordinary passing motion; if we’re going to postulate imaginary lines anyway, by invoking borrowing, then we might as well do it in as elegant a way as possible.

(Not that the story ends here — form a compositional point of view, it’s particularly nice to be able to think in terms of being able to “press a button” and pop a new line into existence at any moment, without needing to “justify” such a line by fitting it into some kind of more “global” context.)

This, then, is the Westergaardian interpretation of (for example) m.5 that I consider to be implied by the way I have notated it. However, it bears mentioning that — as intimated above — there is also a somewhat distinct Schenkerian interpretation. (Note, of course, that Westergaardian interpretations themselves are nearly always valid as Schenkerian interpretations; but not conversely.) This non-Westergaardian Schenkerian reading would allow us to regard the motion b’-f#’-g#’ as passing within a single line after all; the f#’ would, in effect substitute for the normative a’. The (paradoxical) effect would be that of a passing motion whose direction has been changed, despite taking place between the same two tones.

Schenkerian theory can be viewed as allowing a general operation of consonant substitution, where a tone is replaced by another one consonant with it (or at least not step-related to it). This often comes up in the context of avoiding parallel fifths or octaves, as we saw in a couple instances in the previous Ravel analysis. Most often (as here), the tone is a third removed from the original; in many cases (also as here) this allows it to participate in a step-relation with at least one of the tones that the original would have participated in a step-relation with (e.g. f#’ is still step-related to g#’, just as a’ would have been, though not to b’).


It can hardly be emphasized enough that Schenkerian theory widely generalizes the concept of a passing tone. Another instance of this is the incomplete passing motion in spaces larger than a third, illustrated, for example, in m.6 of the third movement of Beethoven’s Ninth Symphony (context):


which can be considered to stand for one of the “normative” forms:


One thinks of this as the result of accommodating the normative passing motion to the demands of the chosen rhythm, which has room for only a single passing tone; of the two choices, e♭” is better than d” (which would sound less like a passing tone than a repetition of the first quarter).

(For contrast, the best Westergaardian interpretation, it seems to me, would regard the e♭” as being borrowed from some other line in which an E♭ in some octave moves to the F above.)

This topic is particularly important to me, because, as an adolescent trying vainly to make sense of music in terms of chord theory, I was deeply suspicious of the concepts of “escape” and “reaching tones” (or “échappées” and “cambiatas” — yes, they really called “reaching tones” “cambiatas”!) Their postulation did not strike me as quite sincere — particularly since they were rarely invoked in analytical examples. It was as if you weren’t actually supposed to approach or leave a dissonant tone by leap (save in the special case of an appoggiatura), but we had to invent these categories because the masters very occasionally broke the rules and did that; and what would we do without a label for such cases? So we hastily invented a couple, without thinking too hard. Of course, it’s not like they were even sufficient: to this day, I still don’t know what the e♭” in Beethoven’s Ninth would be, in Walter Piston’s (read: Nadia Boulanger’s) ontology.

If only I could have been exposed that much earlier to the Schenkerian approach, which systematically relates all phenomena to the most paradigmatic cases!


Now, finally: we come to the question of whether I still agree with what I said about the Schumann song last year.

The answer is: partially.

Looking over the text of the post, there is little if anything that I would retract. In particular, I’m still pretty firmly of the opinion that F# minor is the right key in which to interpret the piece. I might insert a caveat to the effect that the analysis presented above (i.e., my current analysis, at least in the single-voice regime) implies that the question itself has somewhat less importance than I would have thought before; what matters more is that the right diatonic collection in which to interpret the c#”-b’ motion prolonged by this piece is that shared by F# minor and A major.

Most especially, I stand by my assertion that this motion (which I consider as \hat{5}-\hat{4}) is only part of an Urlinie, and not some kind of illustration that there are more than the standard three possible forms of the latter. This very question came up recently on Reddit; my stance, as reflected in my comments there, is as emphatic as ever on this point.

I should acknowledge that it doesn’t strictly follow from Schenker’s example in Free Composition that he would necessarily disagree with my overall (F#-minor) analysis, since that example concerns only the first eight bars; nevertheless, I suspect the smart money is still on his disagreeing. I do, of course, stand by my argument.

When it comes to the graphs I presented, the story is, I have to say, somewhat different. Just look, first of all, at how much less pretty they are than the graphs in the present post. This is not, by the way, simply because of all the slurs. I did that very deliberately, in imitation of Schenker, and subsequent to my excited realization concerning their meaning (discussed above). As a matter of fact, when such slurs are handwritten, or engraved in the way they are in The Masterwork in Music, they convey a beautiful suggestion of physicality, resembling wires you could pull on in order to feel what connects to what. Unfortunately, I don’t know how to replicate their appearance in computer programs like Finale; as a result, and somewhat to my regret, I have switched to a style of graphing that uses fewer slurs.

(The problem, of course, isn’t unique either to me or to Schenkerian graphing; just contrast older editions of classic scores with their latest computer-generated counterparts, and you’ll see what a sad visual story it is, notwithstanding the advances in textual scholarship. The Wagner complete edition is particularly appalling: just open up the first page of Tristan und Isolde to see what I mean, with regard to slurs in particular.)

But in any case the content of the graphs leaves so much to be desired! I seem to have utterly failed to pick up on the importance (indeed, the very role) of g#”, or really of the motivic patterns so clearly brought into relief in the graphs above. It’s as if I was still thinking of analysis as being quasi-scientific “reduction” instead of artful modeling. I can at least give myself credit for using musical notation instead of “chord” symbols! Yet I seemed not to have fully grasped the true advantages of doing so.

Now, as you can see, things are different.

1It does, however, map disturbingly well onto certain traditional European stereotypes of Jews — something which will become relevant in a future essay, when I discuss the Nazis’ singularly strange critique of Schenker, as quoted near the bottom of this page.


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