An Apologia for Motivic Analysis

Art is the imposition of pattern on experience, and our aesthetic enjoyment is recognition of this pattern. —Alfred North Whitehead

Although [episodic developments] may be motivically related to earlier themes, one should not overplay this hand. Within a style grounded in scales, triads, and neighbor-note relations, it is usually an easy matter to “derive” one theme from another. —Elements of Sonata Theory, p.212.

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If you can be charitable about the crudeness of my sketch above, hopefully you’ll recognize it as an image of Orion, the greatest of the constellations in our night sky. In identifying Orion as “a thing” that’s there in the sky (as a Gestalt, a more psychologically-minded writer would say), you belong to a multitude of like-minded people that spans huge temporal and geographical distances. In fact, Wikipedia informs me that Orion formed as a constellation about 1.5 million years ago—about the age of Homo erectus—so it’s entirely possible that singling out Orion from the surrounding starscape is an act as old as humanity itself.

That would make it one of the earliest aesthetic acts of our species. (I’m playing fast and loose with all sorts of details in that statement, but…) I’m serious about calling it an aesthetic act, because that’s exactly the experience I have when I’m stargazing: looking at the night sky, and seeing constellations in it, is a source of profound beauty for me—and, presumably, for many others too. (As a pointless aside, a few weekends ago I was taking a late-evening flight back from a conference, and got to witness, midair, a spectacular meteor breaking up into a shower of green fire and littler pieces… for which the four-hour delay at O’Hare was not too great a price to pay.)

Plenty of other thinkers have tried to grapple with what goes on when we sense beauty in nature, and I think that there are probably many separate causes and effects that get lumped together in that philosophical conundrum, but one strong sense I have is that at least part of nature’s beauty lies in the fact that, out of an essentially random distribution of objects in the sky, we can extract perceptually stable arrangements. That is, we can find apparent order in randomness. I was tempted to write that “we can extract meaningful arrangements,” which is actually the whole point: we assume that there’s meaning—i.e. a cause—behind any patterns that we find, even when there isn’t.

Let’s replay that argument: I find stargazing beautiful because I recognize/discover constellations. In doing so, I’m finding a pattern in perceptual chaos, and it is that pattern-recognition (or pattern-imposition) that constitutes aesthetic experience (or at least the relevant form of aesthetic experience). Note that at no point in the process of enjoying the stars do I have to appeal to the intention (or even existence!) of the stars’ creator. That is: I can enjoy the night sky as a beautiful canvas without worrying about who painted it or why. (On the other hand, behind the scenes knowledge—knowing about Betelgeuse the supergiant, e.g.—can indeed enrich that enjoyment, but the crucial point is that it need not.)

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As you might suspect, this post has to do with the intentional fallacy. While I stand firmly by the claim that artistic interpretation and aesthetic appreciation need not appeal to an author’s intentions (i.e. I believe that the “intentional fallacy” is indeed a fallacy), the main thrust of my post is not merely about buttressing that argument. Rather, I take that argument for granted in order to assert that gazing at Orion can be a model for an approach to artworks generally.

In particular, I want to talk about musical artworks and a mode of analysis that’s heavily deprecated today: motivic analysis. The figurehead/scapegoat/punching-bag for motivic analysis is Rudolph Réti, who was a disciple of Schoenberg, and who advanced (in The Thematic Process in Music) a particularly intricate form of it. He, like motivic analysts everywhere, sought to show how seemingly disparate musical elements were actually related to one another as varied realizations of some underlying basic musical idea. That is, his attempt was to demonstrate that specific patterns underlay the chaotic activity of any given piece of actual music.

Rather than use an analysis of his as an example—poor Réti has taken plenty of beatings already—I’ll dish up a small morsel of motivic correspondence that I’ve tried to present in my own work. The example we’ll be looking at comes from Steve Reich’s piece for string quartet & tape, Different Trains. If you’re not familiar with the piece, I encourage you to become so: programmatically it can be heavy-handed (although it redeems itself in that regard with a twist ending), but from a purely sonic/musical perspective it will explode your mind. (In a sort of literal sense—ask me about it sometime.)

First a crash-course in the piece. More or less throughout it consists of three independent textural layers. The layer that first strikes you is what I call the “paradiddle” layer, which consists of the strings repeating (over and over) this pattern in stacked fourths and fifths:


(If you’re curious, this ostinato reproduces a standard drumming pattern called the paradiddle, in which the drummer alternates left- and right-handed strokes in the same pattern that this ostinato alternates high and low notes.)

The ostinato evokes the aural image of the work’s titular trains chugging along. The programmatic imagery is enhanced by the second musical layer, which consists of train-related recorded sounds played by the tape: train whistles, clanking crossing guards, etc. The final layer is really the heart of the piece: snippets of recorded human speech, played over and over, and transcribed into musical notation so that it can be doubled by the live instruments. The movements of Different Trains are divided up into subsections during each of which only one snippet gets repeated and developed. (Development occurs essentially through repetition… it’s Steve Reich, after all.)

One of those subsections in the first movement sets the text “different trains every time,” which is marked for importance by being the text of the piece’s title. Here’s the musical transcription of the speech melody:

If you attend just to the contour of the melody, the similarities between it and the ubiquitous paradiddle are quite suggestive:
That is, basically I’m trying to argue that the melody of “different trains every time” and the paradiddle are motivically related. If you buy the argument, it makes this subsection a cool lynchpin of the piece: the titular phrase, “different trains,” describes trains lexically, while at the same time its acoustic form sounds like trains. It also means that, in this section, the voice and paradiddle are in canon with each other—a notable state of affairs, given the centrality of canon to Reich’s compositional practice.

But to get to the point of buying that argument, you have to accept many arbitrary reductive steps. You have to agree to pay attention only to contour, rather than to literal pitches. You have to make the huge imaginative leap of filling in the eighth-note rest of the speech melody with (basically arbitrary) notes—the two notes that are, in fact, the most salient part of the paradiddle. So it’s entirely fair to be uneasy about a claim that these two things are motivically related.

Indeed, if I were to claim that it’s a fact about the piece that the two are both versions of the same motive, I’d be on shaky metaphysical footing. That’s indeed the sort of claim that Réti’s (and others’) language forces him into, and it’s hard to ground that claim in reality without appealing either to a composer’s intentions or to some notion of Truth that’s not accessible to modern audiences. Instead, I want to argue that my motivic relationship—and motivic relationships in general—can be defended as constellations (i.e. like Orion): the aesthetic beauty of a motivic discovery is not that it tells us something about the “truth behind the piece” but that the act of finding patterns is itself a valid mode of aesthetic experience. Orion’s meaningfulness as a constellation is only tangentially related to what it tells us about the actual spatial relationships between Rigel, Betelgeuse, Alnitak, and so on.

Put more concisely: motivic analysis is not a science of musical construction, but a form of interaction with an artwork. When we think of consuming (or appreciating, or whatever) a piece of music, we tend to think of sitting in a concert hall enthralled by gorgeous melodies and striking harmonic progressions. That is incontestably one significant aesthetic mode of experiencing a musical artwork. I’m arguing that it’s not the only mode, that musical works (by being garments woven out of such complex fabrics) present a profusion of detail in which it can be edifying to search for patterns. (Motivic) analysis, then, is itself like an artwork—it’s about aesthetic enjoyment, not facts.

I’m sure that there are many analysts who would balk at this characterization of what we do. I’m happy to temper it with the disclaimer that analysis can certainly work towards other (more fact-oriented) ends, but to do so it does need to make ontological appeals to things like authorial intention. (I opened this post with a quotation from Elements of Sonata Theory that cautions against overzealous motivic analysis: within their larger project, an analysis grounded on my argument here would absolutely be out of place.) I merely want to suggest that there’s a way to reclaim the value that theorists like Réti found in their work, a value that’s hard to deny if you’re willing to grant the (hopefully self-evident) notion that pieces of music exist to be appreciated aesthetically. I suspect that it’s the primary value that analysts have found in the work they do, but that in general we’ve been too intellectually insecure to be upfront about that fact. (Incidentally, I also suspect that the beauty we find in analyzing pieces of music is exactly the same sort of beauty that mathematicians speak of when they weigh the aesthetic merits of different proofs of Euler’s identity.)

In a sentence: analysis can be about participation in art, rather than excavation of artifacts.

A little bit of fun (although it has basically nothing to do with cogsci):





Ok, so, to be fair, it does actually have a bit to do with music cognition, although not in the way intended. The widespread cross-cultural prevalence of the pentatonic scale is a pretty-well documented fact, but this isn't exactly evidence for it.

The interesting thing, as I see it, is the ease with which Bobby McFerrin turns the stage into a virtual keyboard. The audience has no trouble at all figuring out how to relate a spatial layout with the arrangement of notes within a scale. If you think about it for a second, it tells us something pretty cool about how our brains work: we make mappings between different dimensions (like space and sound) without any trouble at all. Actually, it's a pretty fundamental part of the way we think.

If you think about it for a second more, what Bobby McFerrin is really doing is a little bit of music theory. He's pointing out that there's a pretty fundamental and powerful metaphor that one can make between the positions on a straight line and the varieties of musical sounds (pitches) that we appreciate. Sure, it's the same metaphor made by a piano keyboard (more or less), but that just means that the keyboard itself is ultimately a really clever arrangement.

That is the essence of music theory: understanding something about music through comparison to something else.

(Sorry to have dropped off the face of the earth!)

The Dialogic Form of Knock Knock Jokes

Here’s one of my favorite knock-knock jokes:

Knock knock.
-Who’s there?
Knock knock.
-Who’s there?
Knock knock.
-Who’s there?
[…
repeat ad nauseam
…]
Knock knock.
-Who’s there?
Philip Glass.

If you get that joke, then you already understand one of the most important principles of James Hepokoski and Warren Darcy’s Sonata Theory. We’ll talk more about that later; for now, let’s analyze the joke I just told.

Central to appreciating my joke is the recognition that it’s very atypical for a knock-knock joke. A really standard, banal KKJ has five lines and goes like this:

Knock Knock
-Who’s there?
Bacon.
-Bacon who?
Bacon a cake for your birthday!

Schematically, that is, a KKJ is a kind of scripted interaction between two people. The first person (we’ll caller her the “teller” of the joke for short) initiates the interaction by exclaiming “Knock Knock!” That interjection calls the basic script to everyone’s mind; it signals that a KKJ is in progress.

The second person (the “receptor”) responds, “Who’s there?” This has two functions: (1) at the level of communication, the receptor is signaling that he knows the script; and (2) within the joke (‘diegetically’), it helps to set of the scene of someone answering their door.

The teller responds with the name of the person at the door (“X”), and the receptor asks “X who?” The punch line then recontextualizes the name X by making it part of a pun. (In a para-generic sixth line to the script, everybody in the audience groans.)

Now, that’s the basic script, but note that there are lots of different ways in which it can be realized. First of all, in the example above, X was just some random word (‘bacon’), but quite often it’s a plausible name:

Knock Knock
-Who's there?
Ahmed.
-Ahmed who?
Ahmedeus Mozart!

In theory, a KKJ researcher could gather statistics on whether or not it’s more common for X to be a common name. A “Knock Knock Joke Theory” would then be able to specify a kind of default value for X (either as a name or not).

The fifth line of the script offers a more complicated set of variations. In my ‘bacon’ joke, the pun was about as simplistic as possible, and most of the line wasn’t actually relevant to the pun. (The fictional knocker-on-doors could in theory have been ‘bacon’ any sort of food.)

A more sophisticated option is for the fifth line to allude to some already-known name or phrase, as in the ‘Ahmed’ joke. Two examples that allude to pop-cultural references:

Knock Knock
-Who's there?
Dwayne.
-Dwayne who?
Dwayne in Spain falls mainly on the plain!

and

Knock Knock
-Who's there?
Toby!
-Toby who?
Toby or not Toby, that is the question!

The ‘Toby’ joke is in another way more interesting, because it blends into a third sort of fifth-line category. In all of our previous jokes, the fifth line pops outside of the joke’s own fictional world: it’s a punch line for the teller and receptor, but not something that a diegetic knocker-on-doors might say. In the ‘Toby’ joke, however, one can almost imagine the K-O-D responding, “Yes, indeed… am I or am I not Toby? That is the question!”

A clearer example of this category would be:

Knock Knock
-Who's there?
Yacht!
-Yacht who?
Yacht a know me by know!

in which the KOD character is clearly responding diegetically to the door-answerer.


Another fifth-line variant occurs when the teller uses the joke as a set up to a fifth line that conveys some actual meaning within the larger discourse between teller and receptor. For example, if a father wanted to tell his daughter to go to bed:

Knock Knock
-Who's there?
Pasture.
-Pasture who?
Pasture bedtime isn't it!

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All the jokes thus far fall into a larger category, which I might call ‘Fifth-Line Puns.’ I think that the Fifth-Line Pun is probably the default (i.e. more common, unmarked) type. Another type of KKJ uses a ‘second level default,’ the ‘Fourth-Line Pun.’ In this type, the teller puns somehow on the receptor’s usage of the word ‘who’ in the fourth line. A classic example is this:

Knock Knock
-Who's there?
Boo!
-Boo who?
Don't cry; it's only a joke!

Another example:

Knock Knock
-Who’s there?
The current leader of China is President…
-The current leader of China is President who?
That’s right: the current leader of China is President Hu (Jintao)!

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So, we’ve seen that although all KKJ’s refer to more or less the same basic script, they can realize that script in slightly different ways. Some jokes go for the most basic, default options, whereas others take a slightly different approach. Some of those alternate approaches, like the 4LP (‘Fourth Line Pun’), can become so common that they turn into a sort of second option, a second-level default.

Other jokes can refer to the same basic script, but stretch it even farther or place it in a new context. Consider this next joke, whose punch line is in white text, which you’ll need to highlight to read:

Knock Knock
-Who's there?
Theresa.
-Theresa who?
Theresa fly in my soup!

Clearly this joke doesn’t work in an aural medium, since it relies on an orthographic (i.e. writing-based) pun. Part of the humor lies in the way the fifth line forces you to reinterpret the sounds that you thought had been implied by the letters of ‘Theresa.’ What this means is that the ‘Theresa’ joke can’t work as a conversational script for two people, but instead needs to be presented as I’ve done here, as a single block of text. (I guess you could pull this joke off in online chat, though.)

For a more extreme variation on the script, consider this one, which clearly alludes to the ‘Boo’ joke from above:

Knock Knock
-Who's there?
Boo!
-I do not know anyone by that name. Perhaps you meant to startle me with the word ‘Boo,’ in which case you were unsuccessful. I see no reason to open the door in either case.

Notice how different this joke actually is from the norm: no fifth line at all, because the receptor takes control of the exchange instead of providing the conventional fourth line. Nevertheless, we still recognize the joke as being related to the garden variety KKJ, largely because the first two lines, which set up the script, are still present.

In a related case, a puckish way of rejecting a KKJ exchange:

Knock Knock
-No one’s home!

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Now, finally, we can get back to talking about the ‘Philip Glass’ joke. First of all, note that it doesn’t (or isn’t supposed to) go like this:

Knock Knock
-Who’s there?
Knock Knock
-Knock Knock who?
…argh.


That is, one aspect of knowing the KKJ script is the fact that the phrase “Knock Knock” always retains its first-line, joke-initiatory power. If the teller responds to “Who’s there?” by saying “Knock Knock” again, she rejects the possibility of a normative third line, and instead reopens the exchange by returning to the first line.

Next, note that the joke never actually gets to the fourth or fifth lines of the script: the punch line comes as a long-delayed third line, at which point the receptor gets the point and the script can be abandoned.

(A possible modification of the joke would let it continue from the third line:

Philip Glass.
-Philip Glass who?
Philip Glass.
-Philip Glass who?
[etc…]

I don’t know how to get this one to end, a problem that minimalist composers actually have to struggle with, I guess.)*

Understanding the ‘Philip Glass’ joke therefore requires recognizing that the basic KKJ script is in play, but also recognizing that the script is being deformed, and that the deformation is actually an essential part of the joke’s meaning. Using the word ‘deformation’ here isn’t meant to imply that the joke is somehow malformed—as I said at the beginning, this is one of my favorite KKJ's. It merely is meant to convey that the joke reshapes the conventions of the basic KKJ script in a creative, non-standard way.

To wrap up this discussion of jokes, I’d like to make one final point. If you’ve followed me so far, then hopefully you see why the question “Is this or that specific joke a Knock Knock Joke?” is actually a pretty meaningless thing to ask. If I asked that question about the ‘Philip Glass’ joke, what would it matter if someone said the answer was ‘yes’ or ‘no’? That question is really only about where you draw boundaries around your words—a fight that like to call lexical gerrymandering.

A more useful question is “Is it useful to interpret this joke with reference to the basic KKJ script?” If you think so, then you can defend why that script ought to be invoked (i.e. what about the joke suggests that the script is in play?) and you can explain how the joke’s deviation from the script is relevant to its meaning.

In other words, a Knock Knock Joke is not some rigid form or mould that one has to cram certain jokes into. Rather, it’s a sort of dynamic process, and we can better understand individual jokes by exploring how they relate to a generic set of expectations (which I’ve been referring to as a ‘script’).

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Understanding “KKJ form” in this way is more or less what Hepokoski and Darcy refer to as ‘dialogic form.’ The individual thing (joke or sonata) is in dialogue with a set of genre-based conventions. In their words: “Sonata Theory starts from the premise that an individual composition is a musical utterance that is set (by the composer) into a dialogue with implied norms. This is an understanding of formal procedures as dynamic, dialogic,” and, “Understanding form as dialogue also helps us to realize that in some cases standard procedures may be locally overridden for certain expressive effects” (pages 10 and 11 of Elements of Sonata Theory).

In fact, many of the terms I’ve used throughout our discussion have been borrowed directly from Hepokoski & Darcy, including: various levels of ‘defaults,’ ‘parageneric’ elements, and ‘deformations.’

Hepokoski and Darcy understand ‘sonata form’ to work very much like the KKJ’s I’ve presented here, except of course for the fact that sonatas are far more complex than the silly five-line script of a knock knock joke. Their attitude, which I’ve tried to convey, is not “How can we cram this sonata into the form?” or “How can we slap labels on all the parts of the sonata?” Instead, Sonata Theory attempts to ask “How does this individual piece interact with our expectations about what sonatas usually do? How does its realization or denial of those expectations contribute to its meaning?”

The first step in answering those questions is to figure out what those expectations might be, and it is that project that Elements spends most of its bulk addressing. I hope to write more in the future about what expectations Sonata Theory identifies, and to show how those expectations are used to cool effect in some real pieces of music.

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In closing, one final joke. I do quite like the ‘Philip Glass’ joke, but in fact my true favorite knock knock joke (another deformation) comes from the lovely Canadian television series Slings and Arrows:

Knock Knock
-Who's there?
Nay, answer me; stand, and unfold yourself!

(As the show’s main character says: “Excellent. First line of the play. The world's longest knock-knock joke. Who's there... indeed!”)



(Please buy, or at least Netflix, the show if it catches your interest!)


*It’s interesting to ask how this continuation of the joke would work: how does the receptor know that the second “Philip Glass” backtracks to the third line, rather than being a fifth-line conclusion to the joke? Well, the receptor isn’t dumb: by this point he gets that the joke is about repetition, and at any rate the regular script calls for the third and fifth lines to be different somehow, so a backtrack is the logical conclusion. But it also draws on a more general principle: if I see that A is followed by B once, then I’m likely to expect A to be followed by B again. This is the basis for another, unrelated aspect of Sonata Theory, which is the notion of ‘rotational form.’

How about a nice game of chess?

(Because it seems my main goal here is to inflate my nerd cred as far as it'll go:)

Today I felt like watching the famous end of the movie WarGames (you know, the one with Matthew Broderick and The only winning move is not to play):




(I've cued it up to more or less the moment I wanted to point out, but of course I encourage you to enjoy the whole clip.)

Anyways, listen to the score here. It struck me as fitting (or something) that the climactic scene to this anti–Cold War film is scored in faux Shostakovich style. Do you think someone planned that?

Ars longa

Speaking of words, one of my many nerdy hobbies is collecting and dissecting the words that we use to talk about space/time/music/rhythm/sight/sound, in a sort of hybrid of ety– and entomology. As many musical thinkers like to point out, we as a literate culture have a tendency to “spatialize” music—to think of it as notes arranged in space (on a page) rather than as sounds arranged in time.

To some extent, I agree that this tendency isn’t always great. As far as we choose one metaphor for structuring our experience, we’re probably marginalizing aspects of the experience not well described by the metaphor. (I’m piggybacking again on the ideas of Metaphors We Live By by Lakoff and Johnson, which I linked to in my last post.) On the other hand, cross-wiring different spatial and sensory domains has allowed us to achieve conceptual heights that might be unscalable otherwise.

Nonetheless, critics who point out this tendency to metaphorize music often fail to question some very closely related conceptual metaphors. For example, I’ve often heard people criticize a sentence like “That piece has a gigantic coda!” on the grounds that using a spatial metaphor like ‘gigantic’ changes musical experience from an aural one to a visual one.

But hold on a second! There’s a huge difference between the spatial and the visual. Although sight is a human’s primary mode of gathering spatial data, we also interact with the space around us through touch* and even, if you think about it, hearing. Usually we use hearing to determine an object’s relative direction and distance from us, rather than its size, which is why ‘gigantic’ is likely to be thought of as a visual description. But it could easily be a kinesthetic one as well.

In fact, consider the word ‘long’ as it describes a temporal experience (say, the Adagio from the end of Mahler 9). In my experience, ‘long’ is used to describe time about as often as it is used to describe the spatial extent of an object. The temporal usage of the word is also old as well as frequent—just think of the longa (as opposed to the brevis) of early musical notation. In fact, I’m not really sure that it is a metaphorical use of the word: no etymology that I’ve seen tells me that the spatial meaning was the original one.

Both uses of the word make a good deal of sense. If you think about the basic equation from physics that speed = distance / time, you realize that our language is pretty fluid in its treatment of all three categories. To express disgust at a particularly egregious performance of the Mahler Adagio, I might say any of the following: “It was just too long!” or “It was abominably slow!” or “It lasted forever!”† As a young child in the back set of a car, I often had conversations similar to the following: “How long till we get there??” »Still 60 miles.« or “How far away are we now?” »About an hour.« So when someone comments that a particular musical experience is ‘long,’ perhaps it’s less explicitly a spatial metaphor than some might assume. (‘Short’ is an interestingly different case, in that it has a purely temporal equivalent—‘brief’—and because ‘short’ is the opposite of ‘tall’ as well as ‘long’.)

Anyway, what prompted this particular ramble was a word I hadn’t considered before: observe.

‘Observe’ has an interesting array of meanings: it can synonyme with ‘pay attention to,’ but it can also mean ‘express verbally the results of one’s observation’ (“Henry observed that they just don’t make music like they used to.”) Etymologically, it derives from the Latin verb servare, which means ‘to serve'. Interestingly, that suggests that its oldest meaning is the one in: “It is a custom / more honour'd in the breach than the observance.” At any rate, the verb’s got a convoluted history and set of uses.

So for some reason, it occurred to me today that you can’t observe a piece of music.‡ At first I thought that was because a core component of ‘observation’ is inspection with the eyes, so of course it would be nonsensical to ‘observe’ music (except, perhaps, by observing the score—but that conveys an altogether different sense). But I’m not sure that that’s the case: neither etymology nor dictionary restricts the word’s meaning to the usage of sight. (Though, of course, etymology and dictionary aren’t the final arbiters of a word’s meaning or grammar.) Moreover, I don’t find a sentence like “He observed the foreman’s tone of voice with great trepidation” to be too offensive, though it does sound a little weird. “She observed a strange smell emanating from the next room”? “Zombo observed that the room was very dry.”§

So I don’t think that sensory modality is the main reason that “Yesterday we observed Beethoven’s Fifth” sounds wonky. I think that the more powerful factor is the sense of clinical (“scientific”) detachment connoted by the word—you can’t ‘observe’ a piece because to sufficiently perceive it, you have to be emotionally (or aesthetically) affected by it in a way that the word ‘observe’ is inappropriate for. You can observe a performance of a piece, but somehow we conceive of ‘the piece itself’ as something that must be experienced rather than observed.

I should clarify that I don’t see this as telling us The Truth about pieces of music; rather, it tells us something about the grammar of our language, and therefore perhaps something about the way we conceptualize musical artworks. (I think, on a different level, it suggests that someone compose something with the intent that it be observed rather than experienced, but perhaps you might say that was the goal of some Stravinsky, Cage, or Reich.)

Anyway, I’m not sure if any of that had a point, but it’s one sort of thing I pay attention to in language. It’d be interesting to coin an entire sublanguage to deal with temporal and aural experiences in a non-metaphorical way, but that sounds like a lot of work if I want to avoid simply relexing that corner of English.

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*Actually ‘proprioception,’ the kinesthetic sense that lets you touch your pinky to your thumb without looking. The elementary-school notion of “the five senses” that everyone learns about is problematic in all sorts of ways.

†I should add that I actually do like the piece a lot, and in fact although one might be likely to criticize a performance for taking a bad tempo, it’s probably largely non-temporal factors that would make it feel so interminable.

‡To appropriate Wittgenstein, Philosophical Investigations I §251: “Of course, here ‘I can’t imagine [that]’ doesn’t mean: my powers of imagination are unequal to the task. These words are a defense against something whose form makes it look like an empirical proposition, but which is really a grammatical one.” That is to say: I can’t observe a piece of music simply because the semantics of ‘observe’ don’t easily allow its application here.

§ The ‘that’ in my last sentence makes a huge difference. (“Zombo observed the room’s excessive dryness” sounds lots worse to my ear.) Something that might be worth meditating on further: perhaps we can only ‘observe’ facts—that is, we can only observe something if it can be formulated into a verbal expression. (?)

the Power of Words

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The Frankish mode theory did have a way of accounting for melodies that were wayward by its standards: they were classified as being of “mixed mode” (modus mixtus), meaning that some of their constituent phrases departed from the basic octave species of the melody as a whole. But that is just another effort to dispel an anomaly by giving it a name—something on the order of an exorcism.

(Richard Taruskin’s The Oxford History of Western Music, Vol. 1 Music from the Earliest Notations to the Sixteenth Century on p.80 in the paperback edition.)

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I want to start by saying that I like Taruskin’s choice of metaphor here. It taps into one of the very real mythic functions that words have—as acts of power on a spiritual level, with the ability to conjure, bless, curse, enchant, and so on. It’s a striking dramatization of the faculty language has for shaping our reality. It also suggests a more complicated situation than Taruskin’s cursory ‘exorcism’ might imply.

For one thing, by giving a phantom a name, we’re admitting it to our cosmology; names conjure demons as often as they exorcise them. Coining a name usually does more than inflate our vocabulary; usually the name comes along with a new concept as well. And by invoking a new concept, we sharpen our discrimination and enrich our experience of events.

Consider the ‘hexatonic pole’ relationship of Neo-Riemannian theory, which relates a major triad to the minor triad a major third below it (and vice versa). Although the harmonic distance between the two triads is great, the contrapuntal distance is minimal: no voice need move more than a half step.

It’s distinctively spooky and fairly easy to recognize once you’ve heard it named. After I learned about hexatonic poles as an undergrad, they started popping out to me all over the place in film scores and 19th century music. All it took was a name.

Of course, that goes in the opposite direction that Taruskin means. He brings up exorcism, not conjuring. Like Richard Feynman’s father, he recognizes that there’s a difference between explaining something and merely naming it. And I don’t deny that sometimes people do make that mistake, they confuse the two actions. But Melville Feynman was less glib than Taruskin; Taruskin’s dismissive attitude rankles a little bit.

The former recognized that naming is still a step in the process: you name in order to conjure or exorcise, to explain or dismiss. He didn’t merely tell Feynman “We don’t know why that is.” Rather, he said, “Yes, things don’t ever accelerate unless forced. We don’t know why that is, but we call it inertia.” (Or Newton’s First Law—I dislike the word inertia, but that’s a rant for another day.) If a theorist runs into a wrinkle or gap in the theory, the honest thing to do is to recognize the problem and flag it for later attention. The first step in doing so it naming it. Something about Taruskin’s wording seems to imply that he thinks that the naming itself is the profane act, rather than the lack of follow-through.

This attitude seems to come through more clearly in a later passage that touches back on the same imagery:

Alfonso’s* collection of courtly songs expressed loving devotion to the Virgin Mary, and once again blurred the line we now insist on drawing between the sacred and the secular. (Sometimes the blur is finessed by using the word “paraliturgical”—“outside the liturgy” yet still somehow sacred—to cover it up; the belief that demons and fractious categories can be exorcised by naming them is indeed an old superstition.)

(On page 128, in Chapter 4, “Music of Feudalism and Fin’ Amors”)

Here it seems to me that the proposed term, ‘paraliturgical,’ recognizes exactly the sort of genre-bending that Taruskin’s interested in. Admittedly, I’m unfamiliar with the musicological literature dealing with this sort of music. If there has been a lack of effort to understand the blurring of sacred and secular genres here, that is worth criticizing. But if that’s the case, why not just say so, and avoid the misleading (and condescendingly avuncular) language, evocative though it may be?


*King Alfonso X of Castile, León, and Galicia

Analytic Behaviors, Part II

A couple years ago, during the summer I helped out at a local music shop’s warehouse. It was late July, and they were getting prepared for the annual school’s–in rush on instruments. Most of the job consisted of preparing blocks of instruments to be sent to schools on rent-to-own plans; we had to open up the factory packaging, apply a barcode sticker and the store’s nametag, then put the instrument and case into a new box for delivery. It was more or less assembly-line labor in teams of two, and quite an educational experience. It was fun for the two weeks I was at it (though I can’t imagine how awful it’d be for a lifetime).

Every day my partner and I would tackle a new stack of instruments—Jupiter trumpets, Vic Firth drum kits, whatever. By the middle of the day, we’d have settled into a steady rhythm: one of us grabs a box off the pallet, knifes the box open, passes the new instrument over, takes back a labeled instrument and shoves it into an outgoing package. Meanwhile the other person industriously slaps labels and barcodes onto the steady stream of new instruments. Depending on the day, the whole cycle would take thirty or sixty seconds; once we got going the timing was pretty reliable and neither of us had to waste time standing around or fight a backlog. What interested me about the whole business was experiencing a relatively slow regular periodicity that wasn’t subdivided into isochronous smaller units. After lots of repetitions, my sense of time would dilate or contract so that each grab/knife/shove cycle felt like the basic unit of time.

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As promised, now follows a post on hypermeter to carry on my discussion of analysis-directed behaviors. Having thought about it for a few days, it strikes me that my own language in the last post was a bit inconsistent. It might be better to use ‘analysis’ (or ‘analytic statement’) to refer to a fact about a piece and to use ‘interpretation’ (or ‘interpretive behavior’) to mean the sorts of actions I talked about before. That’s not a perfect way of surveying the semantic landscape either, though, since even plain analytical statements usually assume some sort of cognitive behavior, and such mental acts on the listener’s part aren’t normally what we’d call interpretations. Well, for now I’m content to leave the language a little fuzzy.

First a quick gloss of the term ‘hypermeter’ (since I’m not really sure who my intended audience here is supposed to be…). “Meter” as we commonly use the word refers to two things: (1) the feeling of “strong-weak-strong-weak” (or “strong-weak-weak-strong-weak-weak,” etc.) that we experience when we listen to music, and (2) the way composers notate that feeling, i.e. with time signatures and bar lines and suchforth. The concept of “hypermeter” recognizes that sometimes the feelings of strong and weak beats alternate at levels slower than the notated measure (i.e. sometimes a slow version of (1) exists even though (2) doesn’t show it).

As a fairly straightforward example, consider the last movement of Dvořák’s New World Symphony. It might be helpful to download a score from here, but then again it might be useful to work your way through without a visual aid.

It starts with nine measures of introduction before the theme comes in. The first two measures (one “yaaaaaah-dum” each, to use the technical notation) are a bit irregular, but after that the piece settles into a reliable hypermeter for a long time.

Let’s start with the notated 4/4 meter. Listen to 20 or 30 seconds of the movement and conduct the usual {down, left, right, up} pattern along with the music. (If you’re not looking at a score, the first four notes after the initial yaaaaaah-dum’s are the four quarter notes making up measure 3; each quarter note should get one handstroke.) Now listen to the same passage but offset your conducting by a beat: on every real downbeat, you should be conducting a “4” instead… your physical downbeats are going to fall on relatively weak points in the music. For me, conducting in this second way feels awful, contrary to the music (whereas conducting with the music is a sort of enjoyable groove). I use conducting like this to check my metric analyses: if the conducting feels good, I’m more confident about my analysis. If you don’t feel a distinction between conducting with and against the meter, you’ll have to find some other way to evaluate the metric claims I’m going to make.

Assuming that conducting with the music feels right, though, let’s proceed. Instead of conducting in 4/4, now conduct in cut-time (2/2)—up and down every half note. This too ought to feel good, although now your hand is moving twice as slowly as before. I imagine most conductors would probably actually conduct the piece this way.

Now we introduce hypermeter. Conduct it again, moving your hand at the same speed as conducting in 2/2, but now conduct the {down, left, right, up} pattern instead of the {down, up} pattern of 2/2. You’ll have to skip the first two bars… it’s probably easiest to start this experiment (and all following ones) with a downbeat at m.10, where the theme starts. In essence, now you’re conducting as if the music were rebarred in 4/2 time. For me, placing a 4/2 downbeat on m.10 feels good, but if I wait until m.11 for the downbeat, things feel backwards.

Conducting this way (“4/2 conducting”) demonstrates the most basic level of hypermeter: every other bar begins with a stronger downbeat (“hyperstrong”… although that isn’t a real Theory™ word). Theorists would say that the movement exhibits a “two-bar hypermeter;” that is, two notated measures fit together to make up one “hypermeasure,” as demonstrated by our conducting.

We can halve the speed of our conducting again to demonstrate that the music exhibits four-bar hypermeter, too. (“4/1” conducting, I guess we’d call it.) Again, for me “4/1 conducting” only feels right when I place a downbeat at the beginning of the theme. In fact, I feel pretty good about halving the speed of my conducting as much as two more times, resulting in “sixteen bar hypermeter.” At these altitudes, it can be hard to move reliably slowly, so I find that it can be helpful to subdivide my conducting pattern ({down, down, left, left, right, right, up, up}) or even to turn my conducting into a dance, letting footwork take over the slowest counts (a footfall ever 8 bars: left foot is the 16-bar downbeat and right foot is the upbeat).

A traditional analysis (made up of analytic statements) would read something like “The movement begins with purely duple hypermeter, extending up to a 16-bar periodicity; the main phenomenological cues for metric accent include…” A critic might respond with “I just don’t buy that you can hear a hypermeter at background levels like that!” Which is a fair response; music-psychological research does seem to indicate that people generally aren’t very good at discriminating relatively long intervals.

On the other hand, I find our conducting game to be a convincingly meaningful way of (behaving while) listening to the piece. What convinces me is the fact that conducting any other way feels less good. If you don’t agree, I’m interested to have a discussion about your experience. Does the whole conducting project not change your listening experience in a meaningful way, or is it that there’s a certain degree of slowness at which it stops meaning anything?

Anyway, for now I’ll proceed assuming that the physical experience of the above game has convinced you. Maybe I’ll stick to 8-bar hypermeter for now, since at that speed I can get by without bringing in any footwork. I can conduct along with the movement for about a minute before things go awry. If you’re not looking at a score, see if you can feel where the problem happens. If you feel it the same way I do, it’s right before the violins switch to playing in triplets (the first continuous stream of triplets we get in the piece).

If you’re looking at the score, the problem spot for me is at the bottom left corner of page 236, where I ought to feel a 16-hyper-downbeat. So far in the piece, big downbeats have signaled big changes in the music (like the strings taking over for the brass, etc.). Here, though, the violins repeat their figure for two extra bars, and the big change (i.e. the big downbeat) happens at rehearsal 2.

Rehearsal 2 is the beginning of TR, the transition section of sonata form. (Today I’m just going to assert these things…) Lots of things signal the beginning of the new section, perhaps most importantly the absence of the main theme, although the triplets (a change in texture) are another big indicator. From our perspective, the cool thing is that the hypermeter that we’ve been playing with so far also breaks down here. The disruption right before 2 was the first sign of trouble, but at least that didn’t interfere with the 2-bar hypermeter (“4/2 conducting”… try it: that level still works up through 2). During TR itself, even the 2-bar level breaks down, since the piece starts repeating itself in 3-bar units. So this part of the piece, a new formal section, switches over to a different hypermeter.

It’s actually a little more complicated than that: the first 6 measures of TR imply a 3-bar hypermeter, but then the winds take over the triplet motion and fight for the old 2-bar hypermeter instead. Then the strings take over again and go back to 3. Just before S (the second theme; the clarinet solo), the meter gets even more confusing (more complicated than I want to talk about today), but note that this confusing spot coincides with the diminished seventh harmony that Dvořák uses to pivot into G major for the second theme. Again, the metric design of the piece links up with other aspects of the music.

One final cool analytic trinket: we’ve discovered that the primary theme area felt good if conducted with duple hypermeters, whereas triple lengths were more characteristic of TR. Note how Dvořák transitions between the two: the disruption just before rehearsal 2 preserves the 2-bar (i.e. low-level duple) hypermeter but turns a 4-bar hypermeasure into a 6-bar (i.e. partially triple) one. Then TR gets rid of even the 2-bar hypermeter. So the transition from P to TR is smoothed out metrically by introducing triple-ness at a slower level first. Cool stuff!

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So my bloggy analytic sketch has done two different things, I think. First, I’ve suggested a way of getting into the piece by conducting along with it. That alone has some merit since it changes (or enhances) my enjoyment of the music. Second, and more intellectually interesting, I’ve sketched out how our conducting behavior actually gets us to experience part of the movement’s formal construction in a new way. (Or maybe you’d already intuited all this about the piece. At least, in that case, I’m boring but not wrong…)

I really like this conducting business, and I’ll probably come back to it in the future. You can apply it to lots of different repertoires: using it in some later–Steve Reich pieces, for example, you can see (or, actually, feel) how phase-shifting is still a background process in his music even when it isn’t obvious anymore.

Something I find especially cool, though, is that a more sophisticated form of this behavior actually is an integral part of South Indian (Carnatic) classical music. (It probably is in Hindustani—i.e. North Indian—music too, but I’m less familiar with that tradition.) In Carnatic music, pieces and performances are structured around elaborate gestural (“conducting”) cycles called talas; good audience members* conduct the tala during the performance. Since the audience is tracking the tala, the performer can play some extraordinary things that strain against (but ultimately fit back into) the tala. If you merely listen to the performance, you’ll completely miss the feeling of rhythmic tension and release. If you want to learn more—and it’s so awesome that you really ought to—you might start by checking out the work of David Nelson. (His PhD diss, “Mrdangam mind: The tani avartanam in Karnatak music,” Wesleyan University 1991 — or his Solkattu Manual.)

Until later, then:


(Sorry for the annoying watermark that appears on the video… apparently whoever made it didn’t want to pay for a non-demo copy of the software. But it’s a pretty good video in that it’s easy to watch the tala & follow what’s going on. If you see a link to a video titled “Trichy Sankuran,” that’s definitely worth watching, too, although the title spells the performer’s name wrong… it’s Sankaran.)

*Not just ‘listeners,’ as we’re used to saying in our tradition.