Melodic expectation

In music cognition and musical analysis, the study of melodic expectation considers the engagement of the brain's predictive mechanisms in response to music.[1] For example, if the ascending musical partial octave "do-re-mi-fa-sol-la-ti-..." is heard, listeners familiar with Western music will have a strong expectation to hear or provide one more note, "do", to complete the octave.

Melodic expectation can be considered at the esthesic level,[2] in which case the focus lies on the listener and its response to music.[1] It can be considered at the neutral level,[2] in which case the focus switches to the actual musical content, such as the "printed notes themselves".[3] At the neutral level, the observer may consider logical implications projected onto future elements by past elements[4][5] or derive statistical observations from information theory.[6]

A multifaceted concept

The notion of melodic expectation has prompted the existence of a corpus of studies in which authors often choose to provide their own terminology in place of using the literature's.[5] This results in an important number of different terms that all point towards the phenomenon of musical expectation:[5][7]

Expectation can also be found mentioned in relation to concepts originating from the field of information theory such as entropy.[6][8][11][16][29][30][31][32] Hybridization of information theory and humanities results in the birth of yet other notions, particularly variations upon the notion of entropy modified for the need of description of musical content.[36]

Consideration of musical expectation can be sorted into four trends.[5]

Leonard Meyer

Leonard Meyer's Emotion and Meaning in Music[38] is the classic text in music expectation. Meyer's starting point is the belief that the experience of music (as a listener) is derived from one's emotions and feelings about the music, which themselves are a function of relationships within the music itself. Meyer writes that listeners bring with them a vast body of musical experiences that, as one listens to a piece, conditions one's response to that piece as it unfolds. Meyer argued that music's evocative power derives from its capacity to generate, suspend, prolongate, or violate these expectations.

Meyer models listener expectation in two levels. On a perceptual level, Meyer draws on Gestalt psychology to explain how listeners build mental representations of auditory phenomena. Above this raw perceptual level, Meyer argues that learning shapes (and re-shapes) one's expectations over time.

Generative Theory of Tonal Music (GTTM)

Implication-Realization model

Narmour's (1992) Implication-Realization (I-R) Model is a detailed formalization based on Meyer's work on expectation. A fundamental difference between Narmour's models and most theories of expectation lies in the author's conviction according to which a genuine theory should be formulated in falsifiable terms. According to Narmour, prior knowledge of musical expectation is based too heavily upon percepts, introspection and internalization, which bring insoluble epistemological problems.[3] The theory focuses on how implicative intervals set up expectations for certain realizations to follow. The I-R model includes two primary factors: proximity and direction.[3][4][24][25] Lerdahl extended the system by developing a tonal pitch space and adding a stability factor (based on Lerdahl's prior work) and a mobility factor.[39]

Bimbot and al.'s System & Contrast model

Mainly developed at IRISA since 2011 by Frédéric Bimbot and Emmanuel Deruty, the system & contrast or S&C model of implication[5][40][41][42][43] derives from the two fundamental hypotheses underlying the I-R model.[4] It is rooted in Narmour's conviction according to which any model of expectation should be expressed in logical, falsifiable terms.[3] It operates at the neutral level and differs from the I-R model in several regards:

Margulis's model of melodic expectation

Margulis's 2005 model[15] further extends the I-R model. First, Margulis added a melodic attraction factor, from some of Lerdahl's work. Second, while the I-R model relies on a single (local) interval to establish an implication (an expectation), Margulis attempts to model intervalic (local) expectation as well as more deeply schematic (global) expectation. For this, Margulis relies on Lerdahl's and Jackendoff's GTTM[34] to provide a time-span reduction. At each hierarchical level (a different time scale) in the reduction, Margulis applies her model. These separate levels of analysis are combined through averaging, with each level weighted according to values derived from the time-span reduction. Finally, Margulis's model is explicit and realizable, and yields quantitative output. The output - melodic expectation at each time instant - is a single function of time.

Margulis's model describes three distinct types of listener reactions, each derived from listener-experienced tension:


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