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Closure
Closure refers to a state of being closed, as well as a tendency to perceive objects and events as closed. The term may be applied at multiple levels of abstraction to a range of static and dynamic media, and the experience of closure depends on perceptual and psychological processes that are not fully understood. Gestalt psychologists considered closure one of several interrelated psychological tendencies or laws that describe the perception of form, along with others such as similarity, proximity, and good continuation.
For static images, a state of closure can be illustrated by a shape such as a circle that has a continuous, unbroken boundary that encloses space within that shape (see Figure 1, left panel), whereas perceptual closure is a psychological tendency to perceive closure in spite of incomplete sensory information (see Figure 1, right panel). At a higher level of abstraction, images such as paintings and sculptures are said to exhibit closure when they are experienced as integrated, complete, and stable. Experiences of closure are not fully determined by stimulus attributes, indicating the existence of processes that function to generate idealized representations of form from limited information. More generally, perceptual mechanisms underlying closure may form part of a suite of mechanisms that assist in auditory and visual scene analysis and that operate under nonoptimal conditions when perceptual information is incomplete or ambiguous. Evidence that people “fill in the gaps” when observing an incomplete visual object supports the view that experiences of closure partially reflect perceptual processes.
Figure 1A circle (left panel) exemplifies a state of closure. The circle is also perceived when sensory information is incomplete (right panel), illustrating perceptual closure.

For dynamic media such as a story, film, dance, or a piece of music, closure describes the experience of a temporary or permanent end point, with the degree of closure varying along a continuum from strong to weak. Strong experiences of closure are associated with conclusiveness, stability, and finality, and little or no expectation for continuation of the ongoing material. Conversely, an expectation for continuation implies an absence of closure and is associated with psychological tension and instability. Closure and expectation are opposite ends of a continuum of experience.
For music, as in other temporal arts, closure both emerges from and gives rise to temporal grouping (see Figure 2). The capacity to detect points of closure is a prerequisite for some of the most meaningful perceptual units in music, such as motifs, themes, phrases, melodies, and movements. Quite often, small groups of events (such as motifs or themes) are nested within larger groups such as phrases, which are nested within sections, movements, and whole pieces. That is, closure is at the heart of musical grouping structure and may be hierarchically organized.
Figure 2Illustration of points of closure in a well-known melody

Expectation and Grouping
Closure is thus intimately tied to two related constructs in music: expectation and grouping. The implication-realization (I-R) model of melodic structure, proposed by Eugene Narmour in 1990, draws on these two constructs. In this model, any melody can be analyzed as an assemblage of more elementary melodic patterns. All melodic groups, by definition, are separated by points of closure. Conversely, events that do not occur at points of closure are said to be implicative (they generate expectations for continuations, which may be fulfilled or denied). According to the I-R model, six musical conditions determine the degree of closure that delineates a melodic group: (1) stopping, (2) metric emphasis, (3) consonance resolving dissonance, (4) durational cumulation (short to long note), (5) intervallic motion from large to small, and (6) a change in registral direction. Depending on these conditions, the strength of melodic closure can be assessed. Weak closure is called articulation, moderate levels of closure are called formation, and strong levels of closure are called transformation.
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