Schoenberg op. 19 no. 2

Score here (p.2).

Analysis here.

Read it and weep. 🙂

Update (8/11): A couple of minor errata in the analysis: in m.6, the G in the bottom staff should be parenthesized; likewise for the half-note G-B dyad in m.7. About the parenthesized notes in general, I should add that their purpose is to clarify the function (or “meaning”) of the surrounding notes in the same line; they are not meant to be understood literally as “hallucinated” pitches sounding at the same time as the other notes. (Of course, since all the notes in the analysis are conceptual anyway, the distinction may not be all that important — especially in view of the fact that every parenthesized note is doubled,  up to pitch-class,  by a “real” conceptual note, which is one of the things that makes this piece so easy to understand.)

For those who are wondering how this analysis fits in with other recent posts (not that it necessarily has to, of course!), the point is the following: the traditional classification of op.19 no 2 (and many other 20th century works) as “atonal” depends upon a bad theory of “tonality”; that, indeed, was the main point of my Chomsky post. After all, how was it originally decided that this piece wasn’t “tonal”? Presumably, someone looked at the score, saw the final sonority, or the one in m.6, and said “What chord is that?” After looking around further, they proclaimed, “I don’t see a coherent harmonic progression anywhere in here.” Perhaps they even asked, in desperation, “Where’s the V-I cadence?”  

If, however, we take the Westergaardian view  as our point of departure, such questions never get asked. Our theoretical vocabulary does not refer to chords and progressions, but rather to lines and elaborations. Consequently, the fact that a particular coincidence of notes is “unusual” is never an issue, so long as the notes are individually comprehensible as elements of lines, any more than the fact that 3574.37562 is an “unusual” number poses problems for arithmetic. (I suspect most musicians intuitively realize that this should be the case, but attribute their analytical difficulties to the inadequacy of music theory in general, rather than to the true culprit, which is the particular music theory they have been taught.) 

The above Schoenberg analysis is, I hope, a dramatic illustration of the power of this type of theoretical framework — dramatic because it shows how easy it is to hear a so-called “atonal” composition as “tonal” once we start thinking about “tonal” music in the right way. Contributing to the drama is the fact that Westergaard himself never intended his “tonal theory” to apply to the middle-period music of the Second Viennese School, but yet it does apply, simply because it was the right way to approach music in the first place.  

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10 Responses to Schoenberg op. 19 no. 2

  1. Eric says:

    I’m rather new to this sort of analysis (my school basically spent a day on Schenker) but I don’t understand E-B dyad in m. 5. Is there some way in which the Bb implies B in that harmony? For that matter, why indicate the E-B-F# triad at all and not the C-Eb dyad in measures 4-5? I don’t mean this as a criticism, I think your point that this piece could easily be understood to be in G is a good one, I’d just like to know more about how the analysis comes about.

  2. komponisto says:

    Eric,

    You’ve caught another typo! Yes, the E-B in m. 5 should be E-Bb. I’m not sure how I missed this, but thanks! (Update: now corrected.)

    Regarding the C-Eb dyad: notice that it didn’t “make the cut” in m.4 either. In both cases, I understand it as subordinate to the G-B. There are at least a couple of specific ways one could derive it (such is the richness of Westergaardian theory!), but in any case the point is that the C is a neighbor to the B, and the Eb is a borrowing from another line (in my hearing its source is the “D#-line”, represented in the fourth staff). Together, the subordinate status of these notes allows the dyad itself to be heard as a “neighbor” to the G-B in m.4, and as an “appogiatura” in m.5.

  3. It doesn’t take an analytical graph to see that the G-B sonority functions as a pitch center for this piece – I’m no student of the Second Viennese School, but I’m pretty sure this ostinato focus on two pitches (a consonant major 3rd, at that!) is quite unusual for most music that would be called atonal. However, it still fits somewhere along that spectrum because it lacks the sort of familiar harmonic progressions that show up in what most people call tonal music. Again, I don’t think it’s news to anyone that Schoenberg maintained a strong interest in counterpoint and voice-leading principles, but what makes this music different than what might be called “common practice,” even when we hear the G-B reinforced by frequent repetition, is the lack of such progressions. We also don’t generally refer to medieval polyphony as tonal, even though the modes tend to reinforce certain home pitches as well. Still, in my experience, Op.19/2 is often used as an example of a transitional piece, so it’s odd that you should choose this to make your point. I’d be interested to see you take on something more obviously atonal. (I understand that you don’t see “atonal” as a useful word, but you know what I mean.)

  4. […] green music theory makes me a furious insomniac Commenting on my Schoenberg analysis, Michael Monroe writes: It doesn’t take an analytical graph to see that […]

  5. Tortoise says:

    I’ve been intrigued enough by your writings to purchase ITT, and now that I’ve more or less finished it, (I glossed over the latter half of the section on species counterpoint, because it was just getting tedious) I feel like I can begin to offer an informed response. While I do find the underlying theory to be both cool and useful, I still have some issues with your stance, which I hope to discuss with you. I figure that this analysis is a good starting point, as it help me to see whether I understand the mechanics of Westergaardian theory accurately. So, without further ado, here are my thoughts on your analysis:

    First of all, I have a couple of minor issues with your graphs. I find your assignment of the low C natural in measure 6, beat 3 to the given line(s) confusing and poorly motivated. This suggests that you conceive of the C-Eb dyad on the preceing 8th note to be an anticipatory borrowing, while it seems quite strongly to me to be an incomplete neighbor to the B-D on beat 3. I guess that this sort of incomplete neighbor figure, which interrupts the preceding stepwise motion of the line, is not a structure which can be generated from the operations that Westergaard sets forth, but I prefer such a melodic impulse to the borrowing which you seem to imply. (Even in ITT, I am sometimes troubled by the borrowing operation. I suspect I am troubled by it in the way that some mathematicians are troubled by the axiom of choice.)

    One additional quibble about your reduction: I feel that the C-E dyad in the final measure is, in itself, the goal of the descending step motion from the preceding measures, and rather than proceeding further via octave transfer to Eb-A#, I hear it as being left hanging at the end — even though it does not sound in the final simultaneity, I still hear it as part of that “chord”. On second thought, I would make a case for this line to culminate on either A#-D or B-D, rather than A#-Eb, which would in fact strengthen your case for the piece being in G major.

    Now, as for your contention that the piece is actually in G major, I feel that you are not being fully clear about your evidence. In order to say that the piece is in G major, it seems to me that you would have to establish that a) G, B, and D are stable pitches, and b) the other pitches are less stable, and dependent on their relationships to G, B, or D. At first, when I stared at your graphs, I couldn’t even figure out why D was stable, until I noticed the neighbor motion in the uppermost line — I’ll grant that this was my oversight. But your graphs do not make it clear why, say, F# and D#/Eb are not stable. I mean, each gets its own line, which is as static (if less present) as the G-B ostinato. Your parenthesized notes suggest that F# and D# are subsidiary to G and D, but, frankly, you could slap a parenthesized note in front of any pitch you want; that doesn’t make it conceptually prior. Schoenberg sees nothing wrong with combining G, F#, D, Eb, and other pitches in an sonority which receives no resolution, so why can’t the F# and D# lines simply be lines representing stable pitches on their own? The answer, in my mind, depends on information I feel you left out of your graph. The F# and D# are both repeated neighbor notes — ultimately incomplete neighbors, as they persist in the final sonority. There is certainly an oscillation between G and F#, which always comes out in favor of the G. Although D and D# have a similar oscillation, it’s not as clear-cut which note is prior. D does demonstrate itself to be stable from the large-scale neighbor motion in the top voice, as I said before, but this doesn’t automatically preclude D# from being stable as well. In the end, I think it’s the incomplete neighbor-note motion in measure 6 which gives the edge to D over D#, but it’s hardly a landslide. Now, this may in fact be what you meant when you added the parenthesized notes at the beginning of each line, but if so, I think it is a shorthand that leaves much to be desired. (As an aside, this reminds me of a moment from my second semester of Real Analysis. There were three students in the class: two math majors and myself, a music major. The presence of a music major in various upper-level math and physics classes was often seen as unusual by my professors, and given the small class size, we frequently joked about it. I think the professor may have been lecturing on the Riemann zeta function, and at one point he took a blackboard full of equations and said, “But this is cumbersome, so we’re going to use this one symbol to denote all of that. Is that clear?” With a grin on my face, I said, “That seems incredibly lazy. You’d never see a composer writing a single symbol to stand for 50 measures of music.” The professor’s deadpan response: “That’s because musicians don’t have anything to say.”)

    And lastly, (for now) I think there’s one aspect of the prelude that your analysis partly ignores. With the exception of the high E in measure 5, and the F# and F natural in measure 6, every note of the prelude occurs as a part of an aural third (That is, a major or minor third, and their enharmonic equivalents). Also, the F# and F natural in measure 6 both form a major 6th with simultaneously sounding notes, so they could be considered displaced thirds. I think that, in this prelude, Schoenberg treats the third as an atomic unit. Most of the thirds are preserved through parallel lines in your analysis, but sometimes you split them up to make separate lines. This is sometimes understandable — separating the F# from the A# at the beginning of measure 5, for example, makes the uppermost lines work out nicely — but I feel like you lose something sometimes. For instances, in response to a query from Eric above, you say that the C-Eb dyad in measures 4 and 5, which are left out of the reduction, comes from a neighbor to the B and a borrowing from the D# line. But, given that explanation, it seems to be a complete coincidence that the simultaneity itself should be a third (though it really isn’t such a huge coincidence: C is an upper neighbor to B, and D# is an upper neighbor to D, but again this is something that your stated analysis leaves out). In any event, I think it’s a mistake to suggest that the C-Eb dyad is a third because the voice leading makes it so; it’s a third because the whole piece is made up of thirds. Though there are times when these thirds clearly proceed in lines, (like the fifth line in your reduction) elsewhere, I contend that the voice leading is merely in support of the (mostly) simultaneous thirds, and not a prior invention.

    I apologize for saying so much in one go; but you’ve given me a lot to think about.

  6. komponisto says:

    Tortoise:

    Thanks for the great comment! I doubt that I’ll be able to fully address the issues you raise all in one go here, but let’s give it a try and see how far we get.

    First of all, I have a couple of minor issues with your graphs. I find your assignment of the low C natural in measure 6, beat 3 to the given line(s) confusing and poorly motivated. This suggests that you conceive of the C-Eb dyad on the preceing 8th note to be an anticipatory borrowing, while it seems quite strongly to me to be an incomplete neighbor to the B-D on beat 3.

    Actually, my “graph” is ambiguous on this matter: it is entirely consistent with either of the interpretations you mention (and possibly others as well). Some ambiguities are inevitable in this type of illustration, where you’re only showing a single “stage of elaboration”. In order to actually show the function of each note, I would have had to show multiple stages, as in the Chopin analysis.

    As it turns out, my interpretation of the C-Eb dyad on the upbeat is the same as yours — with the caveat that the C (written B#) in the left hand does undermine the “resolution” to a certain extent. The reason I put the low C where I did was to show the relationship between that C and the one in the final measure.

    I guess that this sort of incomplete neighbor figure, which interrupts the preceding stepwise motion of the line, is not a structure which can be generated from the operations that Westergaard sets forth,

    On the contrary; incomplete neighbors are an integral part of the Westergaardian inventory. See pp. 234-235 of ITT.

    but I prefer such a melodic impulse to the borrowing which you seem to imply. (Even in ITT, I am sometimes troubled by the borrowing operation. I suspect I am troubled by it in the way that some mathematicians are troubled by the axiom of choice.)

    Boy, if that isn’t a comparison designed specifically for this blog, I don’t know what is! (In fact I’m planning to do a post on the axiom of choice in the near future…) It’s actually a decent analogy. Like the axiom of choice (or Euclid’s parallel postulate, for that matter), the borrowing operation is usually best reserved for when no other option is available. The exception would be if its use made an analysis significantly simpler (just as I may be perfectly willing to use the axiom of choice/parallel postulate if it yields a shorter proof).

    The reference for issues of this sort is section 4.2 of ITT (I know you said you skimmed the species counterpoint part of the book, but I hope you at least read Chapter 4 thoroughly — it’s perhaps the most important chapter in the book). I would particularly draw your attention to the discussion on p.65 about the concept of explanatory tightness, and the problematic nature of rule B3 (which is the species-counterpoint version of the borrowing operation). Essentially, Westergaard has the same concerns that you seem to.

    (In any case, if you are troubled by the borrowing operation, then you should be utterly scandalized by harmonic theory!)

    One additional quibble about your reduction: I feel that the C-E dyad in the final measure is, in itself, the goal of the descending step motion from the preceding measures, and rather than proceeding further via octave transfer to Eb-A#, I hear it as being left hanging at the end — even though it does not sound in the final simultaneity, I still hear it as part of that “chord”. On second thought, I would make a case for this line to culminate on either A#-D or B-D, rather than A#-Eb, which would in fact strengthen your case for the piece being in G major.

    Well, of course these lines only “culminate” beyond the double bar — the implicit destinations of the A# and Eb being B and D respectively. It’s important to keep in mind that a line may not actually reach its destination during the course of a composition. The distinction between the behavior of notes and their conceptual function is absolutely vital — especially for this kind of music.

    Now, if you want to hear the C-E as left hanging, then you need to account for the A# and the Eb in some other fashion. This isn’t particularly difficult to do, but I find such analyses less satisfactory, because they require more lines (and more stages of elaboration) to be introduced. Either way, the Eb is on its way to a D (I would even say that by the end of the piece, the initial D# is best reinterpreted as Eb), and the A# is on its way to a B. The question is: is this hypothetical B-D dyad the same one as the left-hand line in mm 7-9 was headed for, or are they two distinct B-D dyads whose hierarchical relationship to one another then has to be sorted out? I find it much easier to keep the number of imaginary notes to a minimum — especially imaginary doubled notes! Of course, this does have to be balanced against the difficulty of understanding an octave transfer, which also effectively involves imaginary pitches; however, in the case of a transfer, the imaginary notes at least have the virtue of doubling actual sounding notes.

    Now, as for your contention that the piece is actually in G major, I feel that you are not being fully clear about your evidence. In order to say that the piece is in G major, it seems to me that you would have to establish that a) G, B, and D are stable pitches, and b) the other pitches are less stable, and dependent on their relationships to G, B, or D.

    That isn’t quite right — or, at least, it’s a bit misleading. Remember that we don’t start with a “blank slate” (see my Reger post). The “null hypothesis” here is not the proposition that the piece is not in G major; it’s that it’s in some other key besides G major. In other words, all I have to establish is that a G-major analysis is significantly preferable to a C-major analysis, or an F#-minor analysis, etc.

    Think of all the different analyses as in simultaneous competition, with each tonality using the facts of the piece to make its case for why it is the true key of the piece. In this case, the “contest” is pretty one-sided. The very first event — the G-B dyad — already gives strong presumption to G major, although E minor still has a chance if an E is slid under the dyad. However, when the D arrives on beat 4 of m. 2, the game is basically over. At this point, it would take quite a bit of compositional work to get the listener to retrospectively understand this G major as a local tonicization, subordinate to some other underlying tonality — and there is simply not enough time for that kind of work in this piece. G major in effect “runs out the clock” on its opponents.

    At first, when I stared at your graphs, I couldn’t even figure out why D was stable, until I noticed the neighbor motion in the uppermost line — I’ll grant that this was my oversight.

    The fact that D is scale degree 5 does not follow from the fact that it is elaborated by a neighbor motion. Rather, it follows from the fact that understanding it as scale degree 1, say, would require us to understand the opening dyad as scale degrees 4 and 6 which is more difficult than understanding it as scale degrees 1 and 3; understanding the D as scale degree 7 is even harder, because we would have to understand the B as a chromatic note (a raised 5 or lowered 6). And so on.

    But your graphs do not make it clear why, say, F# and D#/Eb are not stable.

    First, remember that “stable” is not an absolute property; one can only speak of notes being more or less stable than other notes. (It may help to keep in mind that a synonym for “stable” in this context is “superordinate”. Another is “conceptually prior”.)

    It should be clear from the above considerations that there is no ambiguity whatsoever about the relative hierarchical status of, say, G and F#. If we wanted to understand F# as the tonic, we would for instance have to think of G as a lowered scale degree 2. But why would we want to do that? Isn’t it much simpler, given the context, to think of G as tonic and F# as scale degree 7?

    Theoretically, we could think of G and F# as simultaneous tonics, each with their own sphere of subordinate notes, but whose hierarchical status with respect to each other is indeterminate (at least at levels near the surface). But that strikes me as an incredibly complicated way of understanding things. It’s hard enough to think in terms of multiple simultaneous lines; thinking in terms of multiple simultaneous tonal systems requires a very sophisticated listener indeed! That level of sophistication is necessary for some pieces, but it is far beyond what is required for this one.

    I think the professor may have been lecturing on the Riemann zeta function, and at one point he took a blackboard full of equations and said, “But this is cumbersome, so we’re going to use this one symbol to denote all of that. Is that clear?” With a grin on my face, I said, “That seems incredibly lazy. You’d never see a composer writing a single symbol to stand for 50 measures of music.” )

    Actually, you do quite frequently: it’s called a repeat sign!

    in response to a query from Eric above, you say that the C-Eb dyad in measures 4 and 5, which are left out of the reduction, comes from a neighbor to the B and a borrowing from the D# line. But, given that explanation, it seems to be a complete coincidence that the simultaneity itself should be a third (though it really isn’t such a huge coincidence: C is an upper neighbor to B, and D# is an upper neighbor to D, but again this is something that your stated analysis leaves out).

    Because it follows at once by logical entailment. You simply can’t elaborate both members of a third with simultaneous upper neighbors and produce anything other than a third between the subordinate notes. To say that a certain simultaneity is the result of such an elaboration is to give strictly more information than to say that it is a third. After all, there are any number of different ways to end up with a third.

    In any event, I think it’s a mistake to suggest that the C-Eb dyad is a third because the voice leading makes it so; it’s a third because the whole piece is made up of thirds. Though there are times when these thirds clearly proceed in lines, (like the fifth line in your reduction) elsewhere, I contend that the voice leading is merely in support of the (mostly) simultaneous thirds, and not a prior invention.

    Let me point out that this same issue arises even in “traditional” analysis. There’s a difference between the tonal-syntactic features of a work and the motivic features of the same work. The latter, however, necessarily operate upon the former. I agree that there’s a good case to be made that the interval of a third is motivic in this piece — that is, that there is a sort of “rule” in effect that says something like “apply the tonal operations in such a way as to produce lots of thirds”. But that doesn’t change the nature of the operations themselves.

  7. Tortoise says:

    On the contrary; incomplete neighbors are an integral part of the Westergaardian inventory. See pp. 234-235 of ITT.

    Fair enough. I was going by the list of operations described in 3.3; although I had seen Westergaard refer to incomplete neighbors in other places, I hadn’t seem him formally describe them. One issue I have with Westergaard’s characterization, though, is that he only specifies neighbors which are incomplete on the left. I would also like to be able to describe neighbors which are incomplete on the right — figures that might be described as “escape tones” in other characterizations. Now, I realize there’s nothing stopping me from adding my own linear operations to the basic Westergaardian inventory, but it does still feel like a shortcoming to me.

    It’s actually a decent analogy. Like the axiom of choice (or Euclid’s parallel postulate, for that matter), the borrowing operation is usually best reserved for when no other option is available.

    And often it is those cases that I find the most unsatisfying. “What’s that note doing there?” “Oh, it’s borrowed from a note in this other line…that sounded three measures ago [or worse, “will sound next measure”]…two octaves higher.” That seems, to me, even worse than “Oh, it’s in the harmony,” because I (personally; I had a few years of experience playing jazz charts before I ever took a music theory class) generally can “hear” the “harmony,” while I can’t get my ears around (yet, anyway) the stretching of both temporal and pitch space needed to make some borrowings (as in Schoenberg) clear. From there, it’s a short hop to the situation that Westergaard forecasts on p. 294, where “any pitch can happen at any time.” Would that be analogous to, say, the Banach-Tarski paradox?

    But even when I find that borrowing seems entirely within reason, I still feel bothered by it much of the time. Consider the Haydn excerpt on page 294, or your own analysis of a “I-IV-V-I” progression. In both cases, borrowing was required to justify the presence of scale degree 4 in an upper voice, and I can see how it happens. But what if the note to be borrowed wasn’t there? What if the Haydn excerpt didn’t include the viola part? What if your progression took place over a C pedal in the bass, rather than a tonic-dominant arpeggiation? Now where does scale degree 4 come from? (This is just one reason why I’d like to have incomplete neighbors on the right, but even if this is allowed, I could probably come up with other cases where one must seemingly borrow a note that isn’t there.)

    (In any case, if you are troubled by the borrowing operation, then you should be utterly scandalized by harmonic theory!)

    Part of my problem, actually, is that the borrowing operation seems to be designed as a catch-all to account for the notes that other operations can’t — in particular, those notes which one might otherwise justify harmonically.

    To say that a certain simultaneity is the result of such an elaboration is to give strictly more information than to say that it is a third. After all, there are any number of different ways to end up with a third.

    Let me point out that this same issue arises even in “traditional” analysis. There’s a difference between the tonal-syntactic features of a work and the motivic features of the same work. The latter, however, necessarily operate upon the former. I agree that there’s a good case to be made that the interval of a third is motivic in this piece — that is, that there is a sort of “rule” in effect that says something like “apply the tonal operations in such a way as to produce lots of thirds”. But that doesn’t change the nature of the operations themselves.

    I don’t agree that getting strictly more information is necessarily strictly better. There’s lots of information one can get from a piece of music, most of which is probably irrelevant or even misleading. Admittedly, a reduction, whether Westergaardian or harmonic, is only a first step in a full analysis. In a sense, it’s the stage where one is looking for evidence — DNA sample, cloth fragment, fingerprints, anything that might be left behind at the scene of the crime. After that, it is up to the investigators to interpret the evidence and arrive at a conclusion, and in the process, they will weed out the irrelevant bits. Thus, it is natural to suppose that you want to get every possible bit of evidence that you can before you begin to interpret it. But again, I worry about having too much information. When I am (personally) solving a difficult puzzle, I am constantly pruning the information I have to deal with, even before I choose to gather data. “Here’s a list of words; do I want to count letter frequencies? That doesn’t sound relevant; I’ll only try it if other lines of reasoning fail.” Unfortunately, the process of pruning the data is often intuitive, and difficult to define. It can lead to difficulties if you prune the wrong things, but you can always go back and gather more data.

    Let me give you a couple of examples to take it back to the musical domain. Imagine, say, a Debussy piece that features parallel triads, seventh chords, or other sonorities — like the opening to “Canopes” from Preludes, book 2. Do you try to account for every pitch in every chord in its own line? Or do you simply give a reduction for the line(s) drawn out by the uppermost notes, and say that the line is doubled in such-and-such a sonority? Even worse, if you have a piece featuring tone clusters, like Cowell’s The Tides of Manaunaum or Penderecki’s Threnody for the Victims of Hiroshima, do you account for every pitch in the cluster? “At 3’51”, the first viola is borrowing from the 8th violin’s line, the 2nd viola is borrowing from the 9th violin, the 3 viola from the 10th…” This sounds absurd to me. At what point does it become absurd?

  8. komponisto says:

    One issue I have with Westergaard’s characterization, though, is that he only specifies neighbors which are incomplete on the left. I would also like to
    be able to describe neighbors which are incomplete on the right — figures that might be described as “escape tones” in other characterizations.

    Such notes are nearly always anticipatory arpeggiations or borrowings. (See p. 252 for a typical example.)

    “It’s actually a decent analogy. Like the axiom of choice (or Euclid’s parallel postulate, for that matter), the borrowing operation is usually best
    reserved for when no other option is available.”

    And often it is those cases that I find the most unsatisfying. “What’s that note doing there?” “Oh, it’s borrowed from a note in this other line…that sounded three measures ago [or worse, “will sound next measure”]…two octaves higher.

    You might want to carefully reread pp. 291-292. At a sufficiently remote level of structure, the borrowed tone always occurs during the timespan of the source. (If you prefer, you can consider “doubling” as the fundamental operation, with borrowing being a special case, rather than the other way around.)

    That seems, to me, even worse than “Oh, it’s in the harmony,” because I (personally; I had a few years of experience playing jazz charts before I ever
    took a music theory class) generally can “hear” the “harmony,”

    Introspect on what you’re hearing when you hear “the harmony”. You’ll find that you’re hearing collections of notes; the only difference is that you’re not bothering to ask yourself what the sources of those notes are. Appealing to “the harmony” is just analytical laziness, pure and simple.

    while I can’t get my ears around (yet, anyway) the stretching of both temporal and pitch space needed to make some borrowings (as in Schoenberg) clear. From there, it’s a short hop to the situation that Westergaard forecasts on p. 294, where “any pitch can happen at any time.”

    But of course, any pitch can happen at any time. The task of the theorist is not to constrain compositional choices, but to express how the results of those compositional choices are understood by a listener.

    The passage you refer to is an instance where Westergaard falls into the sort of error that is so characteristic of other theorists: confusing behavior with conceptual function. It’s true, as he writes, that “whatever the borrowed pitch does in the line for which it is borrowed, the original pitch must form part of a completed structure in the line from which it was borrowed”. But this is properly a constraint on the listener’s analysis, not on the composer’s score.

    The underlying mistake here is the “blank slate” fallacy: assuming that the listener must be “cued in” by the behavior of notes in order to understand a passage in terms of the tonal system.

    Part of the problem, also, is that throughout ITT Westergaard has conflated two separate tasks: (1) constructing a metalanguage in which analyses can be expressed; and (2) constructing a formal theory that predicts how a listener will analyze passages of music. I am mainly interested in (1) (which is a prerequisite for (2) anyway). Consequently, I am less concerned than Westergaard with resolving analytical ambiguities in advance, as it were; and I’m not particularly bothered by the possibilty that particular works or passages may turn out to be especially tricky to analyze — provided the difficulties in such cases are inherent in the music.

    But even when I find that borrowing seems entirely within reason, I still feel bothered by it much of the time. Consider the Haydn excerpt on page 294,
    or your own analysis of a “I-IV-V-I” progression. In both cases, borrowing was required to justify the presence of scale degree 4 in an upper voice, and I can see how it happens. But what if the note to be borrowed wasn’t there? What if the Haydn excerpt didn’t include the viola part? What if your progression took place over a C pedal in the bass, rather than a tonic-dominant arpeggiation? Now where does scale degree 4 come from?

    One possibility that springs immediately to mind (for my example):

    1. E
    2. E-E (Rearticulation)
    3. E-F-E (Neighbor)
    4. E-F-D-E (Inc. Neighbor)

    As for the Haydn violin line, one might analyze it as in the example on p.294 (upper right side).

    But the more important point is this: my example has simultaneous F’s in both the soprano and the bass. Likewise, the Haydn passage does include the viola part — for a reason. If the passages were different, why shouldn’t we expect the analyses to be different? (Note the irony here: I have been accused of “neglecting the vertical dimension”; yet here I am pointing out just how important it is!)

    (This is just one reason why I’d like to have incomplete neighbors on the right, but even if this is allowed, I could probably come up with other cases where one must seemingly borrow a note that isn’t there.)

    Feel free to produce an example, so that we can discuss it.

    Part of my problem, actually, is that the borrowing operation seems to be designed as a catch-all to account for the notes that other operations can’t — in particular, those notes which one might otherwise justify harmonically.

    Why on Earth is it a problem that borrowing eliminates the need for “harmonic” justification? That’s the whole point! The replacement of harmony by borrowing is a huge theoretical improvement; this, probably more than anything else, is what got me so excited about Westergaardian theory in the first place.

    I find it astonishing that one could even think of criticizing the borrowing operation as a “catch-all” in this context, given the alternative on the table. With borrowing, you at least have to produce an explicit source pitch that forms part of a completed structure in some line. With harmony, on the other hand, notes are simply pulled out of thin air as “part of the chord”. It’s an excuse for not asking the hard analytical questions about where those notes actually come from. See Fallacy of Limited Depth.

    I don’t agree that getting strictly more information is necessarily strictly better. There’s lots of information one can get from a piece of music, most of which is probably irrelevant or even misleading…I worry about having too much information. When I am (personally) solving a difficult puzzle, I am constantly pruning the information I have to deal with, even before I choose to gather data. “Here’s a list of words; do I want to count letter frequencies? That doesn’t sound relevant; I’ll only try it if other lines of reasoning fail.” Unfortunately, the process of pruning the data is often intuitive, and difficult to define. It can lead to difficulties if you prune the wrong things, but you can always go back and gather more data.

    You are speaking as though the goal of analysis were to uncover a kind of hidden message within the music. But that isn’t it at all. Rather, the goal is to account for the music itself. A more appropriate analogy would be with sentence-diagramming rather than cryptography or detective work,

    Consider a sentence:

    “The cat ate a bird.”

    If I tell you that “cat” is a noun, that doesn’t tell you what role it plays in the sentence; it could be a subject or an object. However, if I tell you that it is the subject of the sentence, then not only have I answered what the real question is anyway, but you know that it must be a noun (or a pronoun–i.e. standing for a noun).

    Let me give you a couple of examples to take it back to the musical domain. Imagine, say, a Debussy piece that features parallel triads, seventh chords, or other sonorities — like the opening to “Canopes” from Preludes, book 2. Do you try to account for every pitch in every chord in its own line?

    Yes — or more accurately, every pitch in every chord is part of some line. Although this is insufficiently emphasized by Westergaard, remember that lines themselves are subject to hierarchical organization (not all lines are equal), and that lines can have diffent lifespans. Theoretically, a line could even have a lifespan of a single note — though of course this is hardly ever the case (at least below the immediate surface).

    Even worse, if you have a piece featuring tone clusters, like Cowell’s The Tides of Manaunaum or Penderecki’s Threnody for the Victims of Hiroshima, do you account for every pitch in the cluster? “At 3’51”, the first viola is borrowing from the 8th violin’s line, the 2nd viola is borrowing from the 9th violin,
    the 3 viola from the 10th…” This sounds absurd to me. At what point does it become absurd?

    It becomes absurd when it doesn’t reflect the conceptual processes going on in the piece (i.e. some other analysis reflects them better). But you have to look at the piece, and compare alternative analyses, in order to decide this; you can’t simply ask, as an abstract rhetorical question, “what if it leads to really complex analyses?” 20th-century music is genuinely complex; we should expect analyses to reflect the complexity of the music.

  9. […] and thus for Schenkerian or Westergaardian theory to be applicable in the first place. (Cf. Michael Monroe’s comment regarding the lack of “familiar harmonic progressions” in Schoenberg’s op. 19 no. […]

  10. walker says:

    If you all are really interested in an analysis of this work I suggest the following:

    Language and Form in An Early Atonal Composition: Schoenberg’s Op 19 no 2
    by T DeLio

    I also highly reccomend any writings of Allen forte or Joseph Straus’ introduction to post-tonal analysis.

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