Melodic expectation

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. • Anticipation • Deduction • Implication / realization • Implication (independent from realization) • Musical force(s) • Resolution • Tension / release, tension / relaxation as a group boundary, Consideration of musical expectation can be sorted into four trends. • A second trend may concern the more recent publications that include a step-by-step music analysis process at the neutral level, such as the generative theory of tonal music == Leonard Meyer ==

Leonard Meyer's Emotion and Meaning in Music 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 ==

== 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. 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. == 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 derives from the two fundamental hypotheses underlying the I-R model. It is rooted in Narmour's conviction according to which any model of expectation should be expressed in logical, falsifiable terms. It operates at the neutral level and differs from the I-R model in several regards: • while Narmour's two fundamental hypotheses address the relations between three elements, as well as to popular music forms; the S&C model includes relations on two potentially independent dimensions; • the S&C model may encompass all aspects of the musical language, not only the melodic structure. == Margulis's model of melodic expectation ==

Margulis's 2005 model 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 Generative Theory of Tonal Music 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: • Surprise-Tension: inversely proportional to degree of expectancy; results in intensity or dynamism. • Denial-Tension: proportional to the discrepancy between the expectancy of the most expected event and the expectancy of the actually perceived event; results in desire, drive, will. • Expectancy-Tension: proportional to the degree of expectancy of the most expected event (in other words, if the listener had no idea what to expect next, the expectancy-tension would be low); results in strain or yearning. == Farbood's model of musical tension ==

== Huron's theory of general expectation ==