The Implication-Realization Model (I-R)

Meyer’s book Explaining Music (1973, part 2) offered a theory of musical expectation based on identifying a small number of melodic archetypes. Framed largely within Gestalt laws (continuations, similarities, proximities, common fates, streaming, symmetries, etc.), this work spurred a new interest in expectation in both music theory and in cognitive psychology.

Narmour coined the term implication-realization model in the 1970s, and over the next few decades he refined and formalized Meyer’s theory so as to make portions of it empirically testable. Specifically he expanded the model to encompass two distinct sources of implication and realization, one from the bottom up (BU) and the other from the top down (TD).

Specifically, the implication-realization model (I-R) hypothesizes simultaneously generative systems. BU is hypothesized as perceptually mechanistic, automatic, and largely implicit, whereas TD is stylistically flexible, cognitively learned, and stylistically explicit. This makes possible interactions between two different types of implications. The former scales the parametric elements of style and thus defines function (closure vs. nonclosure).

The given parametric materials (intervals, chords, durational patterns, dynamics, tempos, etc.) of each parameter, whether continuous (discriminable) or incremental (proportional), are ranked and categorized according to each pattern’s degree of inherent implication or realization. In contrast, the latter tracks form (similarity vs. differentiation). The separation between the two precludes the analysis of implication from confounding the analysis of realization. In effect BU parametric scales are cognitive maps that guide TD composition, interpretive decision making, and listening comprehension.

Ranging from perception to emotion, expectation constitutes a central topic in psychology because humans are future-oriented animals. Consequently, the I-R model affords vast combinatorial possibilities (discrete and overlapping structures) sufficiently variable to account for many styles of music, countless expressive performances, and numerous experiences of emotions, affects, and moods. Moreover, the model allows for analytical application to all kinds of scaled phenomena (e.g., intonation in speech, colors sequences in painting, etc.).

The parametric approach invokes three structural constants: reversal (R), process (P), and return (aba). These three, voice by voice, are treated as isomorphic analogues. Given that any implication, whether BU or TD, can be completely realized, partially realized, partially denied, or completely denied, a finite number of structural derivations are detectable.

As stated elsewhere (Narmour, 2014), “the I-R model hypothesizes that post-sensory signals are encoded in a primary BU system, which extracts events according to separate parameters (pitch sets, contours, consonances and dissonances, timbres, durations, meters, etc.). Secondary BU processing then operates on these primitives according to Gestalt principles, creating coherent implications and realizations for higher-level syntactic analysis.

“From this parsing, primary TD processing subsequently identifies modes, scale-step functions, chord types, metric hierarchies and other such pre-primed information. The TD system likewise activates a secondary level that relies on mapping previously learned, hierarchically complex, time-ordered schematic expectations (voice leading, harmonic processes, tonal strategies, formal constancies, etc.). In short, the BU system is essentially a servo-mechanism that enables the TD system to access stylistic norms of implications and realizations, whether conditioned, habituated, or associated. Fed back to the BU system, TD levels of complexity channel our attention to implicative input that deviates from explicit mapping. When the auditory world is as we expect it, the BU system runs unconsciously in the background.

“Bi-focal operations such as this minimize implicative error. Feedforward causes the higher-level system to hunt continuously for conformance in order to invoke the most statistically relevant schemata, while feedback frees up lower-level systems to abstract novel or nuanced auditory information. Neither system overrides the other since novelty must always be learned, updated, and transformed into higher-level memory. Likewise, TD schemata must remain attuned to redundant input, which statistically codifies or rejuvenates old memory in order to anticipate complexities apt to recur in upcoming contexts. Significant mismatches between what was implied vis-à-vis what was realized produce felt arousal and tension (i.e., moods, affects, emotions).” [E, Narmour, “The Implication-Realization Model,” Music in the Social and Behavioral Sciences, ed. Bill Thompson. Thousand Oaks, CA: SAGE Reference, 2014.]

In sum, the IR-model claims that at a unified or a universal level, implications and realizations are based largely on either prospectively or retrospectively realized structures and returns. Together, P, R, and aba create parametrically isomorphic analogues. Their partial and complete realizations afford infinite combinatorial possibilities and innumerable potential for all manner of congruent (matched) and noncongruent (mismatched) moods, affects, and emotions.







Beethoven, Symphony no. 9, main theme, movement IV. P = ascending process; P = descending process; R = reversal up/down; R = reversal down/up; underline = structure begins or ends with pitch repetition; 0 = same intervals; ~ similar intervals; (os) = intraopus style refers to motivic repetition, which alters the sense from retrospection to prospection; A0 = model for the four-bar form; A1 = second four-bar form altered (m. 8 cadence).