Structural Segmentation of Toru Takemitsu’s Piece, Itinerant, by Advanced Level Music Graduate Students

This work attempts to study the way higher music graduate students segment a contemporary music work, Itinerant, and to understand the influence of musical feature on segmentation. It attempts to test the theory stating that saliences contribute to organising the music surface. The 42 students listened to the work several times and, in real time, they were requested to indicate the places on the score where they perceived structural boundaries. This work is characterised by its linearity, which could hinder identification of saliences and thereby, the establishment of structural boundaries. The participants show stability in the points of segmentation chosen. The results show significant coincidences among the participants in strategic places of the work, which leads us to conclude, in line with other researches, although in a work with different characteristics, that listeners can find a structural organisation in contemporary music that could allow them to understand it.The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by ''Secretaria de Estado del Gobierno de Espana'' under grant number I+D+I 2008-2011. EDU-2008-03401

Post-tonal analytical techniques: Stravinsky’s symphonies of wind instruments

The analysis of post-tonal music remains problematic. Analytical methodologies designed specifically for tonal or atonal music require substantial modification if they are to effectively analyse post-tonal works. Stravinsky's Symphonies of Wind Instruments is a fine model of post-tonal originality and is a difficult piece for analysis. Following a discussion of various analytical approaches, this paper presents a detailed analytical examination of Symphonies of Wind Instruments. The paper closes by developing conclusions and acknowledging the continuing advances of music analysis

Spatial and Psychoacoustic Factors in Atonal Prolongation

Lerdahl's atonal analysis takes the prolongation approach. He explains the method through examples in Weber and others

Towards a Hybrid Theoretical Model for Neoclassical Music: Schenkerian, Neo-Riemannian and Pitch-Class Set Theories

This thesis explores the necessity for theoretical hybridity as an analytical tool to overcome the challenges faced in works that embody both tonal and post-tonal elements. This hybridised model responds to the lack of a single theory that accounts for neoclassical harmonic practices: Schenkerian methods prove useful in drawing out different structural levels whilst Neo-Riemannian theory recognises non-traditional chordal relationships, and the application of set theory can fill the gaps where none of the aforementioned methods are applicable. Although some have responded to this problem by extending the individual methods’ application (e.g. Baker, 1990) or by simultaneously using more than one analytical approach (e.g. Cinnamon, 1993; Pople, 1989), none of these authors have fully integrated the methods into one unified approach. And despite the large body of research that has examined perceptions of tension in tonal (Lerdahl and Jackendoff, 1983) and atonal (Dibben 1999) harmonies, there is no work that explores the perception of post-tonal harmonies. The project begins with an appraisal of literature surrounding the conceptual issues around hybridity within music and various existing combined approaches to analyse music. This is then followed by the methodology – Voice-leading (VL) Reduction, Rhythmic Segmentation and Calculation, Beat-Class BC Set Theory, and an experimental enquiry into the measurement of post-tonal harmonic tension – exemplified through selected sections from a small number of studies: Mathis der Mahler by Paul Hindemith, “Tanec Loutek” (No. 5) from Puppets by Bohuslav Martinu, Passacaglia by Aaron Copland, Violin Concerto in D Minor by Ralph Vaughan Williams, Sonata No. 3 by George Enescu, Sonatine by Maurice Ravel, Piano Sonata No. 2 by Paul Hindemith, and Concerto for Piano and Wind Instruments by Igor Stravinsky. The application of the model is then carried out through two complete case studies: First Movement of Hindemith’s Second Piano Sonata, and the first movement of Stravinsky’s Concerto for Piano and Wind Instruments. My analyses first perform the three approaches separately, before synthesising the results. To determine which pitch collections will be examined, the music is segmented into its core beat classes. My voice-leading analysis overlays three systems (treble and bass voice-leading reductions, pitch collection), describing the transformation between pitch collections. Line graphs chart the voice-leading movement between pitch collections against the treble voice-leading reduction, capturing the correlation between the melodic and harmonic factors. The rhythmic-phrase analysis is then integrated into the diagrams as a set of tables detailing its different hierarchies. The results reveal the correlation between middleground layers and phrase design, and between rhythmic features and other musical parameters. In all, the detailed examination of different musical parameters reveals that this hybridised model enables a comprehensive structural narrative for each piece, filling in existing theories’ lacunae by revealing a more detailed explanation of the harmonic content, an enriched middleground chart, and its articulation in other musical parameters. This thus reveals the model’s potential to revolutionise analytical approaches to neoclassical compositions and to understand their compositional techniques. Current findings also indicate that these graphical representations account for all types of chords as pitch collections and illustrate the relationship between each vertical sonority; that the aggregated voice-leading movement (AVL) – the total amount of voice-leading movement – can better account for the identification of post-tonal closure, and the results from the empirical study suggest that external factors need to be accounted for along with the AVL in order to relate theoretical to perceived tension. This research will therefore not only contribute to post-tonal theory and analysis but also to music perception, to understand better how we conceive harmonic tension in music that embodies tonal and atonal elements

Scriabin\u27s transpositional wills : a diachronic approach to Alexander Scriabin\u27s late piano miniatures (1910-1915)

Alexander Scriabin’s late music has long fascinated music theorists by its unprecedented exploration of harmony. Accordingly, many analysts have attempted to capture Scriabin’s self-professed theoretical system, in which he states, “there is not one note unaccounted for.” However, no theorist has currently developed a comprehensive system of analysis for this music. While scholars have succeeded in relating members of the same set class through maximally invariant transposition, there are persistent issues in relating members of different set classes. The variety of conflicting methods of analysis attempting to relate members of different set classes suggests the following conclusion: there is no purely music-analytical theory that can explain Scriabin’s post-tonal compositional language. However, new analytical approaches to Scriabin’s late music have been achieved by consulting his philosophical influences. The benefits of this diachronic approach to Scriabin’s late music are shown in the works of Richard Taruskin and Anna Gawboy, who analyze large passages of Scriabin’s music through maximally invariant transposition. This study extends this diachronic approach to develop a comprehensive system of analysis for relating different set classes in Scriabin’s late music. This study compares Scriabin’s most significant philosophical influences of Vladimir Solovyov, Arthur Schopenhauer, Friedrich Nietzsche, Vyacheslav Ivanov, and Helena Blavatsky to uncover his underlying principle of unifying desire. This desire to create unity is then related Scriabin’s use of maximally invariant transposition, suggesting that each collection has a will to create unity based on its maximally invariant transpositions. This theory of transpositional will is combined with Straus’s fuzzy transposition to create a comprehensive and hermeneutical system of analysis of Scriabin’s late music. My study finds the intervals of fuzzy transposition are related to the maximally invariant transpositions of the underlying collections, which represents their transpositional wills. Since different set classes can have different maximally invariant transpositions, the interval of transposition may exclusively satisfy the transposition will of one collection, while rejecting the transpositional will of the other collection. In turn, one can use this theory to completely analyze Scriabin’s late works through a series of unifying or competing transpositional wills, based on the similar and different maximally invariant transpositions of the collections in the pcset structure

The Computational Attitude in Music Theory

Music studies’s turn to computation during the twentieth century has engendered particular habits of thought about music, habits that remain in operation long after the music scholar has stepped away from the computer. The computational attitude is a way of thinking about music that is learned at the computer but can be applied away from it. It may be manifest in actual computer use, or in invocations of computationalism, a theory of mind whose influence on twentieth-century music theory is palpable. It may also be manifest in more informal discussions about music, which make liberal use of computational metaphors. In Chapter 1, I describe this attitude, the stakes for considering the computer as one of its instruments, and the kinds of historical sources and methodologies we might draw on to chart its ascendance. The remainder of this dissertation considers distinct and varied cases from the mid-twentieth century in which computers or computationalist musical ideas were used to pursue new musical objects, to quantify and classify musical scores as data, and to instantiate a generally music-structuralist mode of analysis. I present an account of the decades-long effort to prepare an exhaustive and accurate catalog of the all-interval twelve-tone series (Chapter 2). This problem was first posed in the 1920s but was not solved until 1959, when the composer Hanns Jelinek collaborated with the computer engineer Heinz Zemanek to jointly develop and run a computer program. Recognizing the transformation wrought on modern statistics and communications technology by information theory, I revisit Abraham Moles’s book Information Theory and Esthetic Perception (orig. 1958) and use its vocabulary to contextualize contemporary information-theoretic work on music that various evokes the computational mind by John. R. Pierce and Mary Shannon, Wilhelm Fucks, and Henry Quastler (Chapter 3). I conclude with a detailed look into a score-segmentation algorithm of the influential American music theorist Allen Forte (Chapter 4). Forte was a skilled programmer who spent several years at MIT in the 1960s, with cutting-edge computers and the company of first-rank figures in the nascent fields of computer science and artificial intelligence. Each one of the researchers whose work is treated in these case studies—at some stage in their relationship with music—adopted what I call the computational attitude to music, to varying degrees and for diverse ends. Of the many questions this dissertation seeks to answer: what was gained by adopting such an attitude? What was lost? Having understood these past explorations of the computational attitude to music, we are better suited ask of ourselves the same questions today

Perception of structure in auditory patterns

The present research utilised five tasks to investigate non-musicians' perception of phrase, rhythm, pitch and beat structure in unaccompanied Gaelic melodies and musical sequences. Perception of phrase structure was examined using: i) a segmentation task in which listeners segmented Gaelic melodies into a series of meaningful units and ii) a novel click localisation task whereby listeners indicated where they perceived a superimposed click in the melody had occurred. Listeners consistently segmented the melodies into units of 2.4 - 5.4 seconds. Clicks which were positioned before and after perceived boundaries (identified by segmentation) were perceptually migrated towards the boundary. These results suggest that listeners perceptually differentiate between phrasal groups in melodies (See Sloboda & Gregory, 1980; Stoffer, 1985, for similar results with musicians). Short term memory for rhythmic structure was examined using rhythm recall of computer generated sequences and Gaelic melodies. Computer generated rhythms with small tonal pitch intervals (1 - 4 semitones) were easier to recall than large atonal intervals (predominantly greater than 4 semitones). Recall of Gaelic melodies, containing repetitive rhythmic units, was better than recall of computer sequences. Pitch reversal of Gaelic melodies did not effect recall. Beat-tapping with three Gaelic melodies revealed that the majority of listeners established the underlying beat 1.5 - 3 seconds (5 - 6 notes) after the start of the melodies. Perception of meaning and content in two note melodic intervals and three Gaelic melodies was examined using an adjective pair two-alternative forced choice task. Responses to musical intervals showed evidence of perceptual similarity based mainly on interval size. Perceived information content in the melodies increased significantly by the fourth note. The results suggest that the amounts of Gaelic melody which are: i) required to establish an underlying beat, ii) remembered after one hearing, and iii) perceptually grouped into a meaningful unit, include the unit of melody which is necessary to establish a basic meaning

A Theory of Music Analysis: On Segmentation and Associative Organization by Dora A. Hanninen (review)

In lieu of an abstract, here is a brief excerpt of the content: Comprising research spanning over a decade, A Theory of Music Analysis constitutes a comprehensive account and a culmination of Dora A. Hanninen’s work to date. To the extent that no theory of music is independent of analysis, this work is indispensable as a theory of analysis. The main (philosophical) concern of the book is how to create a precise analytical language, one that can secure a credible interpretation; intertwined with this is a (practical) concern with how to employ this language in a way that reflects the individual analyst’s flair. Analytical applications are not set against theory as singular instances of ready-made methods; on the contrary, by negating the usual rhetoric of theory and analysis, Hanninen sets out to provide a kind of metatheory, independent of the particular existing music-theoretic tools that it aims to encompass. This level of interaction between Hanninen’s overarching metatheory (or simply “theory”) and particular, or what she calls orienting theories is, I think, most intriguing and—although at times not easy to ascertain—promising. From the outset, the author wishes to safeguard the “interpretive autonomy and imagination of the individual analysts” who use the theory (p. 4). In this spirit, the book addresses music theorists, analysts, and musicologists. It is ideal for a postgraduate and academic readership and it could serve as a main reference item in analysis courses. Analysis scholars will appreciate its focus on segmentation. From atonal-theoretic to semiotic methods, segmentation relies on interpretation of the music score. Hanninen endeavors to formalize segmentation protocols by constructing three basic types of criteria; although she provides comprehensive lists for the three types, these lists are left open-ended. The book encompasses a wide range of Western music traditions from the baroque onward. This feature is one among its several qualities of methodological flexibility, afforded precisely by the relation between metatheory and orienting theory. From Bach to Brahms and from Varèse to Babbitt, the first half of the book abounds in examples and indicative applications of analytical tools and concepts. The second half comprises a set of six detailed analyses of mostly piano-based music, two European (Beethoven and Debussy), and four American (Nancarrow, Riley, Feldman, and Morris). Analytically, the book employs, and thus presupposes, a firm knowledge of common-practice tonality, serial systems, atonal theory, and Schenkerian analysis. These four approaches suffice to cover the repertoire with which Hanninen engages. Having said that, the flexibility just mentioned should provide enough space for one to apply new orienting theories to analysis (e.g., the often-idiosyncratic approaches by Iannis Xenakis, who is mentioned briefly). Orientations and criteria for segmentation form the theory’s conceptual part, while associative sets and organization lie on the objective end, segments being the interface. The schematic of the theory is a synoptic representation of these five levels, which interact within three domains: sonic (psychoacoustic), contextual (associative), structural (theoretical). Thus, orientations refer respectively to disjunction, association, theory; and criteria can be sonic, contextual, structural, or linked as structural–sonic, structural–contextual. Any analyst of the post-tonal repertoire will appreciate the difficulties around segmentation strategies. Allen Forte’s distinction between primary and composite segments, or the practice of imbrication, can be useful, but his reference to contextual criteria for segmentation was left un-systematized. In practice, this was counter-balanced by a refining of the segmentation process according to both those contextual criteria and set relations (The Structure of Atonal Music [New Haven, CT: Yale University Press, 1973], 91). Such practices point to a conundrum of theory and analysis: to what extent should we allow (the orienting) theory to affect our interpretation? Such problematics are usually confronted in analysis classes, where students are required to provide a convincing (as opposed to convenient) segmentation. The three types of criteria that Hanninen’s theory provides refer to disjunction (bottom-up feature extraction; sonic), association (by some kind of repetition; contextual), and specific orienting theory (compositional/analytical strategies; structural). The interaction between these three provides a sufficiently rigorous (albeit at times demanding) framework for segmentation. Following this rigorously allows one to mitigate the tension between theory and “the music.

Towards a general computational theory of musical structure

The General Computational Theory of Musical Structure (GCTMS) is a theory that may be employed to obtain a structural description (or set of descriptions) of a musical surface. This theory is based on general cognitive and logical principles, is independent of any specific musical style or idiom, and can be applied to any musical surface. The musical work is presented to GCTMS as a sequence of discrete symbolically represented events (e.g. notes) without higher-level structural elements (e.g. articulation marks, timesignature etc.)- although such information may be used to guide the analytic process. The aim of the application of the theory is to reach a structural description of the musical work that may be considered as 'plausible' or 'permissible' by a human music analyst. As styledependent knowledge is not embodied in the general theory, highly sophisticated analyses (similar to those an expert analyst may provide) are not expected. The theory gives, however, higher rating to descriptions that may be considered more reasonable or acceptable by human analysts and lower to descriptions that are less plausible

Musical Expertise and Statistical Learning of Musical and Linguistic Structures

Adults and infants can use the statistical properties of syllable sequences to extract words from continuous speech. Here we present a review of a series of electrophysiological studies investigating (1) Speech segmentation resulting from exposure to spoken and sung sequences (2) The extraction of linguistic versus musical information from a sung sequence (3) Differences between musicians and non-musicians in both linguistic and musical dimensions. The results show that segmentation is better after exposure to sung compared to spoken material and moreover, that linguistic structure is better learned than the musical structure when using sung material. In addition, musical expertise facilitates the learning of both linguistic and musical structures. Finally, an electrophysiological approach, which directly measures brain activity, appears to be more sensitive than a behavioral one