The Micro- and Macrostructural Design of Improvised Music

1987 ◽  
Vol 5 (2) ◽  
pp. 133-172 ◽  
Author(s):  
Jeff Pressing
Keyword(s):  
Music Theory ◽  
Time Scale ◽  
Distribution Patterns ◽  
Traditional Music ◽  
Pitch Class ◽  
Microstructural Parameters ◽  
Performance Effects ◽  
Improvised Music ◽  
Automatic Transcription ◽  
Pitch Class Sets

Two short pieces of freely improvised music by the same performer were recorded in microstructural detail by the use of a specially constructed automatic transcription apparatus. The apparatus consists of a modified DX7 synthesizer and 2650 microprocessor which interfaces with other computers for data processing. The resultant music is transcribed into a modified form of traditional notation and subjected to both micro- and macrostructural analysis. Microanalysis includes the areas of timing (interonset and duration distributions, displacement, chordal spreads, etc.), dynamics ( key velocity, quantization, chordal patterns, etc.), and legatoness (relative, absolute, pedaling). Macroanalysis uses the full panoply of devices from traditional music theory (tonal procedures, rhythmic and motivic design, pitch class sets, etc.). Correlations between microstructural parameters, and with macrostructure, were found to be highly significant in Improvisation A, which had a supplied external pulse, but largely absent in Improvisation B, which had no such pulse. Where pulse was present, rhythmic design was found to be based largely on pulse subdivision and shifting. Some performance effects (e.g., chordal spreads) operated over a time scale of 10 msec or less. Others (e.g., synchronization to an external pulse) showed less resolution. Differences in the distribution patterns of interonset times, durations, and legatoness suggest three independent underlying temporal mechanisms that may sometimes link together in coordination with macrostructure. Quantization ("categorical production") of some variables (interonset times, key velocities) was clearly established. The results were also interpreted in relation to an earlier model of improvisation (Pressing, 1987).

scholarly journals Why Are There Twenty-Nine Tetrachords? A Tutorial on Combinatorics and Enumeration in Music Theory

2007 ◽  
Vol 13 (4) ◽  
Author(s):  
Julian Hook
Keyword(s):  
Eighteenth Century ◽  
Music Theory ◽  
Equivalence Classes ◽  
Equivalence Relations ◽  
Pitch Class ◽  
Musical Structures ◽  
Pitch Class Sets ◽  
Combinatorial Methods ◽  
Pólya’S Enumeration Theorem

Many techniques in combinatorial mathematics have applications in music theory. Standard formulas for permutations and combinations may be used to enumerate melodies, rhythms, rows, pitch-class sets, and other familiar musical entities subject to various constraints on their structure. Some music scholars in the eighteenth century advocated elementary combinatorial methods, including dice games, as aids in composition. Problems involving the enumeration of set classes, row classes, and other types of equivalence classes are more difficult and require advanced techniques for their solution, notably Pólya’s Enumeration Theorem. Such techniques are applicable in a wide variety of situations, enabling the enumeration of diverse musical structures in scales of various cardinalities and under various definitions of equivalence relations.

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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