An Analytic Method for Atonal Music that Combines Straus's Pattern Completion and Associational Models with Selection Criteria Based on Cognitive Considerations
Keywords: prolongational model, associational model, haupttontechnik, pattern-completion, prerequisite conditions, salient conditions
Abstract: In the early 1980s, Joseph Straus proposed the concept of pattern completion, which touched upon an interdisciplinary linkage between cognitive psychology and musical analysis. Straus later presented the associational model, in which tones interspersed in a large-scale tonal space could be interrelated through specific pitch-class sets and thereby established theoretical justifications for what he proposed in his earlier articles. However, the premises of these concepts raise some issues that still await further logical and theoretical explanation, most importantly the establishment of selection and segmentation criteria.
In this respect, I critically examine Straus's concepts and briefly survey analytic methods for twentieth-century music. Finally, I suggest my own analytic model, which synthesizes Straus's pattern completion and associational models with my prerequisite conditions (modified from Lerdahl's salient conditions), which considers the listener's cognition in the establishment of selection criteria.
As a test of my thesis, I apply this analytic method to two atonal works by Isang Yun, Glissees (1970) for solo cello and Gasa (1963) for violin and piano. This analytic tool may prove useful in illuminating structural secrets latent in other post-tonal music.
Keywords: 20th-century Music, Einojuhani Rautavaara, symmetry, visual composition, piano music
Abstract: 20th-century Finnish composer Einojuhani Rautavaara's propensity for symmetry played an integral role in his compositional evolution. Inherent in 12-to-the-octave composition, pitch symmetry has been exploited by many twentieth-century composers. One type of visual symmetry—bilateral keyboard symmetry—influences Rautavaara's compositions in both piano and non-piano settings. Bilateral keyboard symmetry organizes the piano keys into a symmetrical plane creating axes at pitch-classes 2 and 8. Every note consequently has a complement in mirrored respect to the axes (i.e., 7 complements 9 and 1 complements 3) which can then be used to generate harmonies and melodies. These harmonies and melodies coincide with tonal and aesthetic choices in the music of Rautavaara yielding triadic relationships such as D-major complementing G-minor. This non-transposing type of symmetry is not based upon auditory organization of pitches, but rather of visual organization of piano keys and is used accordingly with mirrored physiological motions of the hands at the piano. Non-symmetrical structures exhibit bilateral reflective motion of the hands as well. Specific operations acting upon the symmetry are recurrent throughout Rautavaara's music. Some of these operations include immediate realization (simultaneous complements), deferred realization (complements played separately from one another), interval expansion and contraction, and implied symmetry. This system can also be found in many non-piano pieces such as Ballad for Harp and Strings and Sonata for Solo Cello no. 1, which feature sections resembling bilateral keyboard symmetry. Using a novel system of analytic notation, bilateral keyboard symmetry can be examined on local and global levels. Rautavaara's use of the symmetrical plane of the piano as a compositional tool suggests a visual and spatial component to musical creation.
Keywords: behavior, function, harmonic analysis, kinship, notation, province, quality, roman numerals, Gregory Proctor, Jean-Philippe Rameau, Hugo Riemann
Abstract: Although the impact and pervasiveness of function in tonal theory today is undeniable, a single, unambiguous definition of the term has yet to be agreed upon. This is because function comprises at least four distinct aspects, which, when all called by the same name (function), create ambiguity, confusion and contradiction. In a response to David Kopp's challenge to "more clearly articulate and differentiate the myriad concepts which function has come to represent," a solution to this problem of ambiguity is proposed: the elimination of the term function. In place of function, four new terms—kinship, quality, province and behavior—are invoked, each uniquely corresponding to one of the four aspects of function identified in the article. The meanings of these new terms are elucidated by such harmonic topics as secondary dominants and six-four paradigms. An analytic notation is developed for behavior, in particular, which is used in conjunction with two standard types of harmonic analysis to form a three-fold system of analysis that yields a broader range of explanations for harmony characteristics.
Keywords: appoggiatura, embellishing tone, melodic embellishment, non-chord tone, non-harmonic tone, ornamentation, rhythmic embellishment, tone of figuration, Clendinning and Marvin, Kostka and Payne, Laitz, Piston, Ottman
Abstract: The labels used by textbook authors to describe non-harmonic tones, ornamentations, tone of figurations, etc. elevate a local description of a specific feature—rhythm, melody or harmony—to the status of a global descriptor in the same way that each blind man in the parable describes the whole elephant with an observation made upon a single body part. The labels non-chord tone and non-harmonic tone imply that elephants are harmonic events. Labels such as melodic embellishment or tone of figuration emphasize the melodic characteristics of elephants. The more obscure rhythmic embellishment elevates the rhythmic characteristics of an elephant. While these labels may function on a local level, their use as global labels for the totality of elephant behavior disregards two out of the following three musical frames: melody, harmony and rhythm. In this article I advance a methodology adapted from the approach to non-harmonic tones in Ottman's Elementary Harmony, in which elephants are discussed through a three-part framework of melody, harmony and rhythm.