Individual Project Proposal – Scale Categorization, Mental Schemata Creation, and Musical Form

In 1987, Nicholas Cook studied the limits of large-scale tonal perception. He tested effects of tonal closure (or non-closure) on aesthetic response and found no correlation for time spans longer than 1 minute. Thus, he concluded that while large-scale tonal form was defined as a theoretical and even compositional concept, it served no real effect on perception of music (Cook 1987, p. 203). Thus, Cook argues, theories of tonal form are better suited for understanding the practice of composition but not of listening and affect.

A large quantity of research and modeling been accomplished on musical boundary perception of shorter time-scale musical objects (melodies, motives, etc.). This research is based on defining similarity and difference, derived from basic underlying Gestalt principles that are imperative for musical organization, perception, and structural analysis (Deliège 2001, pp. 235-236). Boundary formation arising from similarity and difference functions as categorization, which in turn, is a mental process that is “essential in the study of the formation of a mental schema while listening to a musical work.” (Deliège 2001, p. 236).

As Robert Gjerdingen explains, mental schemata are stereotypes developed to organize knowledge, prototypes created from “generalized abstractions.” (Gjerdingen 2007, p. 10). He has identified schemata, or general musical patterns, in galant music that he argues “lead to a greater awareness of subtle differences in galant music…the music may seem to develop more meaning.” In a sense, Gjerdingen is arguing that, by acquainting ourselves with musical schemata, we can gain better understanding or meaning in music, contrasting with Nicholas Cook’s prior argument. While Gjerdingen’s schematas are specifically musical patterns arising from treble and bass partimenti, he argues they can be any exemplar from a basic instrumental timbre to a “symphony.” One could extrapolate this to mean any mental construct, including large-scale musical forms such as a period, a sentence, or even larger such as a sonata or rondo form.

The question then arises: what happens when musical schemata are extrapolated to a larger temporal realm? Do mental processes of categorization still apply in processing musical form beyond simple conceptualization or theoretical analysis? The answer, I presume would be a resounding yes based on schema formation in other psychological realms (see Piaget’s theory of intelligence and other social work, for example). In either case, the proposal herein relies on an investigation of the existing literature: how categorization functions in larger-temporal spans of music, how schemata are formed in these cases, and how schematic forms aid in perception of musical structures. A further point is raised regarding memory and how mental schematas aid in memory processing of musical structures (did Cook’s experiment fail based on lack of mental schematas for tonal forms?).

SOME ANNOTATIONS (All of these found on JSTOR)

Clarke, Eric F. & Carol Krumhansl (1990). Perceiving Musical Time.” Music Perception 7(3), 213-251.

ABSTRACT: Three experiments are described that investigate listeners’ perceptions of the segmentation of a piece of atonal piano music, the location of seg-ments extracted from the piece, and the duration and structural qualities of each segment. The experiments showed that listeners segmented the music in broad agreement with the grouping principles proposed by Lerdahl and Jackendoff (1983) and perceived the location of randomly presented segments of the music in a strongly veridical manner. Listeners’ location judgments did, however, show systematic departures from veridicality, segments towards the beginning and end of the piece appearing to be located closer to the center of the piece than was actually the case. Judgments of the duration of extracted segments also were strongly veridical and were unaffected by concurrent ratings of structural properties of the segments. In order to assess possible effects of the unfamiliar musical style, the same three experiments were carried out on a piece of tonal piano music of comparable length, yielding essentially identical results. It is argued that the pattern of departures from veridicality in the location judgments for both pieces may indicate systematic changes in attention in the course of listening to the music, linked to large-scale properties of musical structure that are found in music from a variety of styles and periods. The independence of the segmental duration judgments from structural properties of the music may be a consequence of the performance skills of the musically trained listeners used in this study (a sense of absolute tempo is one of the abilities that a performer must acquire) and/ or the particular methods used in the experiments.

This article gives a succinct, even if outdated, review of prevalent literature for my topic, mainly regarding segmentation principles stemming from Gestalt principles (a la Lerdahl/Jackendoff), memory for different musical time spans and relations, and time perception models. The experiments test multiple temporal issues on excerpts drawn from Stockhausen’s Klavierstück IX and Mozart’s K. 475. In the segmentation task participants were asked to segment the piece as they seemed fit: for both pieces, boundaries were found to be similar by a majority of participants. A location task in which participants were to indicate the original location of isolated excerpts throughout the piece found that median values corresponded with the actual locations of the pieces and subjects tended to displace the segments toward the middle of the pieces. The third experiment was geared toward seeing if structural properties affected perceived duration of isolated excerpts; they were quite accurate in perception and no musical features seemed to have an effect.
Cook, Nicholas (1987). “The Perception of Large-Scale Tonal Closure.” Music Perception 5(2), 197-205.


Music of the tonal period generally begins and ends in the same key, although passing through other keys in the course of a movement. Theorists of music generally ascribe great significance to such large-scale tonal closure. In order to test the effect of such closure upon aesthetic response, listeners were required to evaluate a number of compositions in two versions, one of which was in each case tonally closed while the other was not. The results indicate that the direct influence of tonal closure on listeners’ responses is relatively weak and is restricted to fairly short time spans – much shorter than the duration of most tonal compositions. Although large-scale tonal structure may not in itself be perceptible, it plays an important role as a means of compositional organization, and it is argued that the theory of tonal music is more usefully regarded as a means of understanding such organization than as a means of making empirically verifiable predictions regarding the effects of music upon listeners.

As described, Cook asked subjects to rate 7 real compositions (real music with transposed segments to create tonally closed or open sections) on an affective scales (pleasure, expressiveness, coherence, completion). He found no relations between the scales and the tonally closed vs. open versions (except for two, the shortest of all the pieces). He concludes that for musical time-spans longer than 1 minute, tonal form has no bearing on musical aesthetic or perception and that tonal forms are merely theoretical constructs to understand compositional process and concept.

Deliege, Irene (2001). “Similarity Perception – Categorization – Cue Abstraction.” Music Perception 18(3), 233-243.

Deliège’s article is an introduction to a special issue of Music Perception on similarity perception, categorization, and cue abstraction. It describes her and other work on categorization (based on the Gestalt principles of similarity and difference) and the musical listening process. Musical perception is drawn as a system of cues (points of reference for comparison) which are abstracted into levels/groups through categorization and schemata.

Rehashing some questions – Individual Project

BIG OVERARCHING QUESTION: What is musical form and how do we cognize it?

Smaller questions:
*What are the temporal parameters that influence perception of musical form? How do they influence structure?
*Are temporal parameters stronger or weaker than melodic/timbral/etc. parameters? Are they separate from the other parameters?
*NARROWER: How does musical temporality (rhythm/meter/etc.) affect categorization/similarity perception of musical structures? 


Clarke, Eric F. & Carol Krumhansl (1990). Perceiving Musical Time.” Music Perception 7(3), 213-251.

Cook, Nicholas. “The Perception of Large-Scale Tonal Closure.” Music Perception 5(2), 197-205.

Deliege, Irene. “Similarity Perception – Categorization – Cue Abstraction.” Music Perception 18(3), 233-243.

Reybrouck, Mark (2004). “Music Cognition, Semiotics and the Experience of Time: Ontosemantical and Epistemological Claims.” Journal of New Music Research 33(4), 411-428.

Tillmann, Barbara & Emmanuel Bigand (2004). “The Relative Importance of Local and Global Structures in Music Perception.” The Journal of Aesthetics and Art Criticism 62(2), 211-222.


Metric vs. Figural Hearing

Hi guys,

For next week, please read the Bamberger 1994 and the abstracts for Handel 1998 and Smith et al. 1994. Focus on the Bamberger’s opening areas (before the dialogue), and think about the implications of the results from the other experimental work.

Some questions to ask while you’re reading:

1) Reflect on what we think of when we speak of musical “knowledge”? Are there different types of musical knowledge? Is individual perspective important in “knowing” music? If so, how can we quantify musical knowledge, or should we even try?

2) On page 134, Bamberger states: “…it is because sound/time phenomena do not come already structured, but rather hold the potential for being structured that different hearings are possible.” What do you think about this statement? Does this imply the necessity for a human agent for something to be musical? Can non-musical sounds be structured? If music is based on inferred structures, can we ever arrive at objective knowledge about music (think about Bamberger’s later comments on metrical structure as objective and figural structure as subjective)? What are other implications for music-theoretic work that are brought about by this statement?

3) Further, Bamberger quotes Rosenfield: “We perceive the world without labels, and we can label it only when we have decided how its features should be organized.” While taking issue with what Rosenfield means by “decided”, Bamberger still requires some aspect of knowing for organization. Reflect on your thoughts about knowledge and questions about implicit versus explicit knowledge: Can we structure something, especially musical temporality, without knowing it? How do we come to know something (can we learn through passive exposure)? What would the “features” when referring to temporal parameters? Think about our past discussions on enculturation and training, and also embodied knowledge for music.

**Please bring up any other points, of course. I myself have only done a cursory reading up to now and will delve deeper this weekend! Just wanted to get something up in case people started working on this early…**

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).

Iannis Xenakis – Concret PH

There are multiple layers in this piece: an underlying background that pervades (which I have personally identified as a crackling-fire type of sound), and then foreground groups of sounds (which vary in timbre from ceramic, glassy, to coin-like). The interplay between these two layers are the most interesting. (After reading the program notes, all the sounds stem from burning charcoal – but differences and identification of different timbres, I find, allow for a better musical experience through narrative).

The background may appear as random durations of sound, which I perceive as a static, yet highly rhythmic, space. There are accents (caused by differences in amplitude and timbre) that are aperiodic, yet not entirely unexpected, perhaps predictable within the context of the space? Sound layers (the foreground) are juxtaposed, creating groups of sounds that are faded across auditory space (left to right on my stereo hearing) – an active layer of development. These interact with the background layer to create polyrhythms and alignments. There is, in my hearing, no underlying metrical feel, but there is an non-isochronous pulse that pervades from the background structure.

Like with other types of music concrete, I often ask myself if I consider these sounds as musical. It, of course, depends on my frame of mind and the context. If I were hearing a fire crackling at home, I may not think of it as musical. But contextually, listening to this for identification of rhythmic structures over iTunes, I hear musical structures. In either case, both instances are comprised of temporal spans, consisting of groups of sounds. So the question raised here is what exactly is the difference between musical and non-musical rhythm? This piece also constitutes a great example for raising questions about the differences between meter and rhythm (does anybody hear a tactus or underlying pulse? I can’t…).