Use of the Exclusion Relation to Profile Pitch-Class Sets

1983 ◽  
Vol 27 (2) ◽  
pp. 181 ◽  
Author(s):  
John Clough
Keyword(s):  
Pitch Class ◽  
Pitch Class Sets

The Interplay of Set Content and Temporal Context in a Functional Theory of Tonality Perception

1988 ◽  
Vol 5 (3) ◽  
pp. 219-249 ◽  
Author(s):  
Helen Brown
Keyword(s):  
Structural Characteristics ◽  
Perceptual Cues ◽  
Tonal Music ◽  
Critical Feature ◽  
Functional Interpretation ◽  
Pitch Class ◽  
Functional Relationships ◽  
Musical Excerpt ◽  
Musical Excerpts ◽  
Pitch Class Sets

The purpose of this study was to provide evidence for the perceptual component of an analysis of pitch relationships in tonal music that includes consideration of both formal analytic systems and musical listeners' responses to tonal relationships in musical contexts. It was hypothesized (1) that perception of tonal centers in music develops from listeners' interpretations of time-dependent contextual (functional) relationships among pitches, rather than primarily through knowledge of psychoacoustical or structural characteristics of the pitch content of sets or scales and (2) that critical perceptual cues to functional relationships among pitches are provided by the manner in which particular intervallic relationships are expressed in musical time. Excerpts of tonal music were chosen to represent familiar harmonic relationships across a spectrum of tonal ambiguity/specificity. The pitch-class sets derived from these excerpts were ordered: (1) to evoke the same tonic response as the corresponding musical excerpt, 2) to evoke another tonal center, and (3) to be tonally ambiguous. The effect of the intervallic contents of musical excerpts and strings of pitches in determining listeners' choices of tonic and the effect of contextual manipulations of tones in the strings in directing subjects' responses were measured and compared. Results showed that the musically trained listeners in the study were very sensitive to tonal implications of temporal orderings of pitches in determining tonal centers. Temporal manipulations of intervallic relationships in stimuli had significant effects on concurrences of tonic responses and on tonal clarity ratings reported by listeners. The interval rarest in the diatonic set, the tritone, was the interval most effective in guiding tonal choices. These data indicate that perception of tonality is too complex a phenomenon to be explained in the time-independent terms of psychoacoustics or pitch- class collections, that perceived tonal relationships are too flexible to be forced into static structural representations, and that a functional interpretation of rare intervals in optimal temporal orderings in musical contexts is a critical feature of tonal listening strategy.

Generic (Mod-7) Voice-Leading Spaces

2019 ◽  
Vol 63 (2) ◽  
pp. 167-207
Author(s):  
Leah Frederick
Keyword(s):  
Topological Space ◽  
Set Theory ◽  
Final Section ◽  
Voice Leading ◽  
Pitch Class ◽  
Mathematical Properties ◽  
Pitch Class Sets

This article constructs generic voice-leading spaces by combining geometric approaches to voice leading with diatonic set theory. Unlike the continuous mod-12 spaces developed by Callender, Quinn, and Tymoczko, these mod-7 spaces are fundamentally discrete. The mathematical properties of these spaces derive from the properties of diatonic pitch-class sets and generic pitch spaces developed by Clough and Hook. After presenting the construction of these voice-leading spaces and defining the OPTIC relations in mod-7 space, this article presents the mod-7 OPTIC-, OPTI-, OPT-, and OP-spaces of two- and three-note chords. The final section of the study shows that, although the discrete mod-7 versions of these lattices appear quite different from their continuous mod-12 counterparts, the topological space underlying each of these graphs depends solely on the number of notes in the chords and the particular OPTIC relations applied.

Packing my Library

2007 ◽  
Vol 1 (2) ◽  
pp. 295-300
Author(s):  
James Deaville
Keyword(s):  
Comparative Analysis ◽  
Computer Technology ◽  
Pitch Class ◽  
Pitch Class Sets ◽  
Critical Type

In reviewing and packing my musicological library in preparation for a move, I came across documentation for a variety of studies and projects from the late 1970s and early 1980s that were based upon an electronic future for musical scholarship. Twenty years ago, such pioneering musicologists as Ian Bent, Barry S. Brook, Jan LaRue, and William Malm were assembling large searchable databases of writings, music, and instruments, even as theorists like Mario Baroni, Allen Forte, and Arthur Wenk were exploring computer technology to analyze and devise “grammars” of melodic construction and to identify and compare pitch-class sets. In those pre-Oakland (barely pre-Contemplating Music) days of the American Musicological Society, the gathering of such sources was considered an honorable practice—indeed, we owe the eminently useful RILM to the perspicacious Brook. While these collections of data ostensibly were to enable comprehensiveness in study and serve the purposes of comparative analysis, they ultimately did not lead to interpretation, not at least of the critical type that Joseph Kerman and later Lawrence Kramer and Susan McClary were advocating.

Diatonic Connotations of Pitch-Class Sets

1997 ◽  
Vol 15 (1) ◽  
pp. 1-29 ◽  
Author(s):  
René Van Egmond ◽  
David Butler
Keyword(s):  
Set Theory ◽  
Theoretical Study ◽  
Class Relations ◽  
Tonal Music ◽  
Pitch Class ◽  
Tonal Pitch ◽  
Relationship Of ◽  
The Relationship ◽  
Pitch Class Sets

This is a music-theoretical study of the relationship of two-, three-, four-, five-, and six-member subsets of the major (pure minor), harmonic minor, and melodic (ascending) minor reference collections, using pitchclass set analytic techniques. These three collections will be referred to as the diatonic sets. Several new terms are introduced to facilitate the application of pitch-class set theory to descriptions of tonal pitch relations and to retain characteristic intervallic relationships in tonal music typically not found in discussions of atonal pitch-class relations. The description comprises three parts. First, pitch sets are converted to pitchclass sets. Second, the pitch- class sets are categorized by transpositional types. Third, the relations of these transpositional types are described in terms of their key center and modal references to the three diatonic sets. Further, it is suggested that the probability of a specific key interpretation by a listener may depend on the scale-degree functions of the tones.

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