Schemata and Categorization

Much ink has been spilt on pitch-based categories in music: pitches within specific tuning systems or absolute pitch classifications, dissonance vs. consonance categories, categorical divisions based on scales or chords, schemata based on pitch and harmony patterns. However, categorical perception is also largely important in our perception of temporal parameters. A crucial example is the perception of microtiming. But, how does formation of categories affect our perception of larger time spans: themes, form, or even meter? Are certain formal spans dependent on a temporal dimension (i.e. does a sentence or period DEPEND on its length or can we define the category without a temporal parameter)? Are these temporal dimensions merely conventions arising from the style or genre (i.e. periods as 8 measures within a classical style) or are they due to underlying psychological causes such as cognitive limits? Why is it that, within a classical period or sentence, we tend to hear symmetrical spans – are asymmetrical spans really that unnatural for perception or was symmetry merely a cultural construct?

While many questions arise from this brainstorming, I am ultimately interested in how these mental precepts arise and how they guide our processing of music (preferably during online listening).

Possible starting point: Using established schemata (Gjerdingen?) as temporal stimuli and investigating perception of said percepts with modulations on the temporal domain. Can we perceive these schemata with metrical/rhythmic disparities? Are the temporal parameters vital in the definition of these schemata? (<—I see this more as a pilot study).

4 thoughts on “Schemata and Categorization

  1. What kind of “modulations in the temporal domain” do you have in mind?

    I would encourage you to work toward a more specific definition of “categorical perception.” As it is here, it is very general.

    One possible intermediary question I see here is: “How stable are our perception of larger temporal units (i.e., units that go over the threshold for pulse attribution)? And, if so, what are the mechanisms that allow for this stability (structural/contextual features and/or cognitive mechanisms)?

    Do you have some specific study in mind? It would be helpful to situate and focus your question.

    You can use this space for work-in-progress toward the formal proposal; I will review it periodically and give feedback as necessary.

  2. I have been speaking with a friend that is doing his dissertation on schemata (he works with Gjerdingen) and he is postulating a theory that schemata are metrically based – this is also alluded to by Gjerdingen himself but not completely hashed out. He is working on this from a computational point of view (seeking schemata based on temporal parameters), but I am interested in actual perception.

    In either case, I think this would be a worthwhile project to undertake as a starting point for temporal parameters of formal issues. I submitted this question as one of my group questions. We decided it may have been too complicated to do a full-blown group project, but I think it is feasible for preliminary testing, and hopefully, in time, some online experimental paradigm.

    Experimental design would follow something like this:
    1) Training phase: Participant learns parameters of schemata through explanation and exposure to real musical examples (with metrical constraints*).
    2) Experimental phase: Participant has a forced-choice task in which he chooses schemata for pre-composed musical examples which contain metrical inconsistencies.*

    *A large part of this, of course, would include defining metrical parameters for schemata: this would look at previous research and music analyses to find tendencies of schemata in certain metrical positions.

    • Thanks for the clarification. My sense is that the background literature that deals specifically with musical schemata might be a bit thin, so you might have to do some digging. Also, one potential challenge is to actually find enough examples to adapt for the experiment. You don’t have to actually implement the experiment as part of your term project, but if this is the direction you are going, I would like to see a well thought-out proposal with most of the experimental design worked out.

      You might consider choosing only a few schemata that seem most promising from the point of view of finding enough materials. You will also need to find a balance between controlled and ecological design.

  3. This is a really fascinating project, and I have to think about it more before making any serious comments. I was struck, however, by some of the comments made in the opening paragraph, and I think they warrant discussion.

    For one, it has been suggested by many theorists/musicologists (e.g., Rosen, Caplin, Landon) that the symmetrical nature of the classical style is a myth. On the contrary, many argue that it’s actually highly asymmetrical, especially in contrast to music of the “romantic” generation, in which binary phrase structure truly did take hold. Rosen suggests, for instance, that our skewed notion of what constitutes a classical style comes from the emphasis placed on Beethoven’s music by eighteenth-century theorists. I think he’s right. And even modern-day theorists are guilty of perpetuating this myth of asymmetry: I can see how anyone who has read Caplin’s Classical Form might easily assume that most classical themes come in neat eight-measure packages.

    In any case, the point here is that the misguided assumption of symmetry in this music undermines the question regarding its origin. In other words, it no longer makes sense to ask whether symmetry emerged in this style due to cognitive constraints, precisely because the music isn’t symmetrical.

    As for the temporal displacement of schemata, what do partimenti have to say about your question? You want to know whether or not temporal factors form an integral component of a given schemata. It’s a good question, but I’m not sure you need an experimental study to find your answer. Is it possible that the answer to your question lies in partimenti treatises themselves? How often, for example, does a partimenti treatise advise a pupil to begin, say, a prinner on a weak beat? I would guess that the answer is never. And so, this hypothetical construct was never built into the language with which composers communicated to their audience. I’m not sure I’m making myself 100% clear, but there’s a tautology here somewhere…I’m just not putting my finger on it at the moment, though I can definitely sense its presence.

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