Regerian “harmony” and the tonal system

More than one websurfer has happened upon this blog recently by putting the phrase “reger chord progressions” into a search engine. (Evidently they were led to my Chopin post, where Max is given a brief mention.) You have to be kidding me, folks.

There is perhaps no corpus of music that more effectively demonstrates the futility of the Rameau-Riemann-Piston conception of music theory (“chord progressions”, “functional harmony” and the like) than the oeuvre of Max Reger. That is despite the fact — and how’s this for irony — that Riemann had been Reger’s teacher, while Schenker (who actually did have something close to the right theoretical idea) couldn’t stand Reger’s music.

I know whereof I speak: as an undergraduate, I spent an entire semester (and the summer afterward) racking my brains in an attempt to “analyze” the first movement of Reger’s clarinet sonata, op. 107, using a version of harmonic theory. Suffice it to say that the results of that effort were nowhere near as beautiful as the music itself.

Even to attempt to describe — let alone analyze — Reger’s music in terms of “chords” and “progressions” is sheer madness. I can’t locate my score for op. 107 (which, thanks to me, is a mess anyway), and there isn’t one online, so we’ll have to “make do” with another of my favorite Reger works, the Piano Concerto in F minor, op. 114 (which is online, in both full score and two-piano reduction). Let’s start right at the beginning (click for larger version):

Well, I’ll grant that the first measure isn’t terribly problematic, even for harmonic theorists. But take a look at the second measure! What the heck is that chord on beat 3?! F-G-C: does this have a name besides [027]? The first chord, a [036], we can at least call “viio7 of V without the D” (though that raises the question of why Max would gratuitously choose to omit the D that “belongs” there — a question to which harmonic theory provides no answer); but what Roman numeral goes under F-G-C?

A solution can be cobbled together, but it requires a bit of clever cheating. A viio7 of V, you see, is a chord of “dominant function” with respect to V, and is required to resolve to its tonic, namely V = {C, E, G}. Well, if we ignore the F in our sonority and declare that an E has been omitted, we can interpret it as the “resolution” of the preceding chord, and put a “V” under it. To appease our guilty consciences, and make ourselves feel better about this theoretical patch-up job, we can remind everyone that, after all, F is the tonic of the piece, and it’s stuck way down there in the bass as a sustained tone or “pedal”.

Unfortunately, to do this is already to give the game away to the other side. For as soon as we allow ourselves to “ignore” notes, we have left Rameau-Riemann territory and entered Schenker-Westergaard territory. Once we admit that a line in a texture does not necessarily have to “conspire with” or “ask permission from” other lines in order to move where it wants, we have ceased to conceive of music in terms of a sequential “progression” of predetermined “chords”, and have begun instead of think in terms of a simultaneous superposition of melodic lines — a superposition that may or may not be tightly coordinated at any given time. And, once we have admitted this way of thinking into our theoretical repertory, there is no excuse (other than intellectual cowardice) for failing to follow it to its logical conclusion — which happens to be the complete and total abolishment of harmonic theory.

In this post-harmonic conception of music theory, each line has an agenda over a given timespan; these local agendas may reinforce each other to a large extent, a small extent, or hardly at all. Let’s look again at the second measure of the above excerpt:

Over the timespan of this measure, there are basically three distinct lines:

1. A descent from the stable A-flat to the (even more) stable F;
2. An ascent from the unstable B-natural to the (slightly less) unstable D-flat, which wants to continue upward;
3. A static and stable F.

(Notice that, once a diatonic collection and tonic note have been established, the various degrees of “stable” and “unstable” are fundamentally properties of scale degrees, and thus only incidentally apply to simultaneities.) Line 1, which reinforces Line 3 to a great extent, completes its task (to get from A-flat down to F) over the timespan under discussion. Line 2, however, though it goes along for the rhythmic ride with Line 1, is on a fundamentally different tonal mission, one which is not yet accomplished at the end of m.2. Its job is to introduce us to the unstable B-natural that will form part of a larger-scale structural line (it is picked up again in m.2, where it then resolves very temporarily to C) and then to ascend to…well, we have to keep listening to find out! (Exercise for the reader: see if you can follow this line to its “destination”, and describe the function of its “journey” within the structure of the orchestral introduction (mm.1-24). What, indeed, is the structure of the orchestral introduction, and what role does it play within the larger context of the movement? Answers will be given in a future post.)

By the way, if there are any Roman numeral enthusiasts left out there, I have a question for you: Consider the third chord of m.2 (on the second half of beat 4); I assume you would label this “VI without the A-flat”. But what about the F? Is it part of the “chord”, or is it the same “pedal tone” it was during the previous three eighth-notes? Or is the low F a pedal tone, while the other F’s are part of the chord? Think carefully about your answer, because I am entirely serious about the question.

Now, at this point someone is bound to object that no sophisticated theorist (and certainly, no one of the caliber of, say, David Lewin, whom I respect enormously, but who happens to have instigated the current revival of Riemann’s ideas) would ever approach this passage in such an idiotic way as reflected in my “Roman numeral analysis”. Agreed, but I must point out, to use an analogy, that this is like responding to Richard Dawkins’ The God Delusion by pointing out that no sophisticated theologian (and certainly, no Oxford don such as Alister McGrath) would ever seek to undermine evolutionary biology. Perhaps not, but by clinging to a superfluous concept such as God, they are helping to prevent the spread of a rational understanding of the world, and thus indirectly lending support not only to the battles of some people against modern science, but to other negative effects of religion as well. Likewise, by continuing to invoke unnecessary and, frankly, deleterious theoretical concepts such as “harmonic progression”, even in conjunction with better ideas such as those of Schenker, music theorists and pedagogues are preventing their students from gaining an honest, explicit understanding of what music is actually made of — and in the process they are lending undeserved legitimacy to all sorts of bad analyses (such as my Roman numeral analysis above).

Those readers who teach freshman theory know perfectly well that the thought process I mocked above is exactly the sort of thought process that many of their students use on their analysis assignments. You can urge them all you like to look at the horizontal dimension, at the phrase structure; you can implore them to (God forbid) play or listen to the passage and use their musical common sense to arrive at an analysis. But, at least for many students, it is all for nought — simply because, while your mind, your soul, and your lips all say one thing, your theoretical vocabulary says something different.

Another possible objection (closely related to the previous one) is that this discussion is old hat, and that passages like the above are common, nothing particular to Reger, and readily tractable within a theoretical framework that includes both “harmony” and “voice-leading” considerations. For example, a Schenkerian theorist might (especially if he or she is familiar with Westergaard) agree entirely with my analysis of m. 2, but simply maintain that mm.1-4 as a whole represent a “I” chord (or Stufe).

My first response to this is to ask, “Why bother?” There is no explanatory work being done by such a concept; to invoke it anyway is to patently violate Occam’s razor. (Again, imagine a theologian agreeing that Darwinian evolution explains life but also holding that life was designed by God.) However, I suspect that a reply might be offered along the following lines: Stufen do in fact perform explanatory work, in that the presence of “coherent progressions” of Stufen (particularly V-I) is a necessary condition for a piece to be “tonal”, 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. 2.)

At first glance, this seems like a vicious circle: how does the listener know to listen for Stufen if he or she is not already using Schenkerian theory? But perhaps what is really going on is that my imaginary interlocutor is imagining a sort of “blank slate” model of musical perception, in which the listener starts off having no idea what system to use to interpret the notes, and is subsequently “cued in” by observing certain musical behaviors. This is where things start to get interesting, and where the example of Reger becomes especially pertinent. For I must now ask: where are the “familiar harmonic progressions” in the op. 114 Concerto? (Or the op. 107 Sonata? Or…?) Reger clearly thought of the piece as tonal (specifically in the key of F minor) — but if you do a Roman numeral analysis of, say, the first movement, you won’t find “f: V I” appearing very often. Indeed, you will probably end up with more colons than “I”’s! Here, for instance, is an entirely typical passage:

Yet, despite the proliferation of such “unfamiliar” progressions, the movement does, in fact, sound “tonal” — it sounds very F-minory to my ears — so what accounts for this?

Well, let’s ask ourselves when it is that we first “discover” that the piece is tonal and in F minor. Speaking for myself, I am already thinking in terms of F minor when the above-cited chromatic passage is reached — well before the first explicit F-minor “V-I cadence”, which occurs in the first measure of p. 6 in the two-piano score. In fact, I can’t imagine anyone getting past the first four measures with any doubts whatsoever about the tonality. But how can this be the case, when there hasn’t yet been any “harmonic motion” at all (if we’re to believe our imaginary Schenkerian) — when only a single chord has been stated?

Ah, but that’s just it! I don’t know about you, but if I hear an F minor triad in isolation, I’m usually going to think of it as the tonic triad in F minor. Why? Because that’s the simplest way to think of it given the evidence I have available. Thinking of it in any other way would require me to refer to absent entities. For example, I could think of it as the mediant triad in D-flat major if I wished, but that would require me to imagine a hypothetical D-flat. (You might want to object and say that to think of it as the tonic triad — i.e. as scale degrees 1, 3, and 5 — in F minor requires one to imagine the rest of the F-minor scale; but remember that the notes of a diatonic collection are not all equivalent in their conceptual status: there is a natural hierarchy based on the complexity of the various acoustical phenomena. Thus, what we call “scale degree 5″, for instance, is actually conceptually prior to all other scale degrees except 1 and 8. So, when I say “tonic triad in F minor”, I’m actually referring to a slightly more primitive concept than “elements 1, 3, and 5 of the F minor scale”.) In fact, if I hear a single F in isolation, I am going to think of it as the “tonic” — in the precise sense that I will be prejudiced toward hearing any subsequent events (or any simultaneous events that I choose to imagine) as conceptually subordinate to the F, rather than the other way around. So, given these constraints, and given the way the Reger concerto opens, I am going to be hearing F as the tonic from the very beginning.

Furthermore, I will continue hearing it this way until a different analysis is forced upon me by the events of the piece. In order for that to happen, the F-minor analysis has to become excessively complex — not according to some absolute standard of complexity, but only relative to alternative analyses. Thus, for example, if immediately after the initial F a B-flat were to follow, I may be strongly tempted to change my analysis to one with B-flat as tonic, since, all other things being equal, it’s easier to think of F as scale degree 5 and B-flat as scale degree 1 than it is to think of F as scale degree 1 and B-flat as scale degree 4 (“scale degree 5″ is a simpler notion than “scale degree 4″). (Of course, since the F came first, all other things are not equal, so the specific way in which the notes were articulated would play a vital role in my choice of interpretation.)

Thus, at least as far as my own hearing is concerned, the “blank slate” model of musical analysis is totally inaccurate. (I suspect that, if readers are honest with themselves, they will find that the same is true in their own cases.) I do not listen for “cues” to decide which of several possible systems to hear the piece in terms of (even ignoring the problem of how the “cues” themselves might be interpreted before such a system has been chosen!). Rather, the analytical system (“tonality”) is given at the outset, and the events of the composition merely constrain the analyses produced by the system. Tonality is therefore not a property that certain musical compositions have and others don’t; it is a cognitive procedure by means of which I (and, I suspect, you too) attribute structure to all music.

I hope you see where I am going with this. If tonality is what I have said it is, then it necessarily applies just as much to the music of Boulez and Babbitt as it does to that of Bach and Beethoven.

But, regardless of whether or not you accept my definition of “tonality”, you cannot have it both ways. “Tonal” is either a historical/descriptive category that applies to works, or a theoretical/explanatory category that applies to listeners’ analyses. Either you test for “tonality” by looking for paradigmatic musical events (in which case Reger works such as this fail the test), or else you assume it a priori and interpret the events of the piece accordingly (in which case there is no such thing as “atonal music” — it becomes an incoherent concept, constructed out of a category error). What you absolutely may not do, however, is apply different definitions to different composers or works. If Schoenberg’s music is atonal because it lacks “familiar progressions”, then so is Reger’s. On the other hand, if Reger’s music is tonal because its notes can be organized hierarchically according to their level of stability (as determined ultimately by acoustical simplicity), then so is Schoenberg’s (and everyone else’s).