Implication-RealizationFrom Wikipedia, the free encyclopedia

The Implication-Realization (I-R) model of melodic expectation was developed by Eugene Narmour as analternative to Schenkerian analysis centered less on music analysis and more on cognitive aspects ofexpectation. The model is one of the most significant modern theories of melodic expectation, going intogreat detail about how certain melodic structures arouse particular expectations.

Contents1 History2 Theory

2.1 Basic Melodic Structures2.1.1 General Claims2.1.2 Syntactic Parametric Scale2.1.3 Top-Down and Bottom-Up Processing2.1.4 Five Principles

2.1.4.1 1. Registral direction2.1.4.2 2. Intervallic difference2.1.4.3 3. Registral return2.1.4.4 4. Proximity2.1.4.5 5. Closure

2.2 Melodic Complexity3 Criticism4 References

HistoryMeyer (1956) applied Gestalt psychology principles to musical expectation, resulting in his ideas aboutcompletion, closure, and his Law of Good Continuation. In 1977, Narmour's book laid out problems he hadwith Schenkerian analysis and sketched ideas for a new model of analysis based on musical expectation asinformed by the work of Meyer. Narmour mentioned a forthcoming book, The Melodic Structure of TonalMusic, but it did not appear. Much time passed without the alternative theory, but finally in 1989 Narmourpublished his I-R model, detailed in the 1990 and 1992 books.

As of 2007, Narmour is working on a new book, which will extend the I-R theory to the parameters ofharmony and rhythm and explore potential applications to the analysis of performance.

TheoryNarmour's I-R model was published in two separate books, dealing with "basic melodic structures" and"melodic complexity". Each book is quite complex; only a few key points are mentioned here. The MusicPerception review by Ian Cross and the article by Schellenberg provide introductions to the theory.

Basic Melodic StructuresGeneral Claims

The Analysis and Cognition of Basic Melodic Structures: The Implication-Realization Model begins withtwo general claims. The first is given by "two universal formal hypotheses" describing what listenersexpect. The process of melody perception is based on "the realization or denial" of these hypotheses (1990,3):

1. A + A A2. A + B C

Here, A, B, and C are melodic items of either form, interval patterns, or pitches. A + A A indicates thathearing two similar items yields an expectation of repetition of the item. A + B C, on the other hand,indicates that hearing two different items yields an expected change in the implied item.

The second claim is that the "forms" above function to provide either closure or nonclosure. Narmour goeson to describe the five melodic archetypes of his theory:

1. process [P] or iteration (duplication) [D] (A + A without closure)2. reversal [R] (A + B with closure)3. registral return [aba] (exact or nearly exact return to same pitch)4. dyad (two implicative items, as in 1 and 2, without a realization)5. monad (one element which does not yield an implication)

Central to the discussion is the notion of registral direction (direction of motion) and size of intervalsbetween pairs of pitches. [P] (process) refers to motion in the same registral direction combined withsimilar intervallic motion (two small intervals or two large intervals). [D] refers to identical intervallicmotion with lateral registral direction. [R] refers to changing intervallic motion (large to smaller) withdifferent registral directions.

P, D, and R only account for cases where registral direction and intervalic motion are working in unison tosatisfy the implications. When one of these two factors is denied, there are more possibilities, the fivearchetypal derivatives:

1. intervallic process [IP]: small interval to similar small interval, different registral directions2. registral process [VP]: small to large interval, same registral direction3. intervallic reversal [IR]: large interval to small interval, same registral direction4. registral reversal [VR]: large interval to larger interval, different registral direction5. intervallic duplication [ID]: small interval to identical small interval, different registral directions

Each of these 8 fundamental symbols can refer to a "prospective or retrospective dimension". The symbolsare enclosed in parentheses like so: (VR) to indicate a "retrospective realization". Narmour (1990, 6)considers these symbols to be representative of cognitive structures: "As symbological tokens, all sixteenprospective and retrospective letters purport to represent the listener's encoding of many of the basicstructures of melody."

From these foundations, the theory gets more detailed, and problems of style, pitch, harmony, rhythm, etc.are all discussed.

Syntactic Parametric Scale

Top-Down and Bottom-Up Processing

Five Principles

Schellenberg's work has involved testing and simplifying specific implementations of the I-R model. His1997 article gives an overview of the I-R theory that describes it in terms of five governing principles:

1. Registral direction2. Intervallic difference3. Registral return4. Proximity5. Closure

1. Registral direction

Small intervals imply continuation of pitch directionLarge intervals imply a change of direction

2. Intervallic difference

Small intervals imply similar-sized realized intervalsWhen the registral direction changes, a "small" realized interval is defined as the originalinterval size +/- 2 semitonesIn the absence of direction change, a "small" interval is the original interval +/- 3 semitones

Large implicative intervals imply smaller realized intervals

3. Registral return

This is the melodic archetype aba or aba\' where the second tone of a realized interval is very similar tothe original pitch (within 2 semitones). This archetype describes symmetric or near-symmetric patternssuch as C-G-C#. Patterns are less archetypical as they deviate more from this symmetry.

4. Proximity

Small realized intervals are more implied than large intervals. Also, implications are stronger forsmaller-sized intervals.

5. Closure

Closure describes how listeners segment melodies based on pitch direction and interval size. Closure occursin two cases:

Melody changes direction. That is, implicative and realized intervals are in different directions.A larger implicative interval is followed by a smaller realized interval.

Melodic Complexity...

CriticismReferences

Cross, I. (1995) "Review of The analysis and cognition of melodic complexity: the implication-

realization model, by E. Narmour, Univ. of Chicago Press, Chicago, 1992." Music Perception 12(4),486-509.

Meyer, L. B. (1956). Emotion and Meaning in Music. Chicago: University of Chicago Press. ISBN 0-226-52139-7.

Meyer, L. B. (1973) Explaining Music: Essays and explorations. Chicago: University of ChicagoPress. ISBN 0-226-52142-7.

Narmour, E. (1977) Beyond Schenkerism: The Need for Alternatives in Music Analysis. Chicago:University of Chicago Press. ISBN 0-226-56847-4.

Narmour, E. (1989) "The 'Genetic code' of melody: Cognitive structures generated by theimplication-realization model. In Music and the cognitive sciences, ed. Stephen McAdams and IrneDelige. London: Harwood Academic.

Narmour, E. (1990) The Analysis and Cognition of Basic Melodic Structures: The Implication-Realization Model. Chicago: University of Chicago Press. ISBN 0-226-56845-8.

Narmour, E. (1992) The Analysis and Cognition of Melodic Complexity: The Implication-RealizationModel. Chicago: University of Chicago Press. ISBN 0-226-56842-3.

Schellenberg, E. (1997). "Simplifying the Implication-Realization Model of Musical Expectancy."Music Perception 14(3), 295-318.

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