DOCSLIB.ORG

Harmonic Visualizations of Tonal Music

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Harmonic Visualizations of Tonal Music Harmonic Visualizations of Tonal Music Craig Stuart Sapp Center for Computer Assisted Research in the Humanities Center for Computer Research in Music and Acoustics Stanford University email: [email protected] Abstract KS algorithm analyses BWV notated key prelude fugue Multi-timescale visualization techniques for displaying the 846 1. C major C major C major output from key-finding algorithms are presented in this pa- 847 2. C minor C minor C minor ] ] per. The horizontal axis of the key graphs represents time in 848 3. C] major C major G major ] ] the score, while the vertical axis represents the duration of 849 4. C] minor C minor C minor an analysis window used to select music for the key-finding 850 5. D major D major D major algorithm. Each analysis window result is shaded according 851 6. D minor D minor D minor [ [ to the output key’s tonic pitch. The resulting diagrams can be 852 7. E[ major E major E major ] [ ] used to compare differences between key-finding algorithms 853 8. E[/D min. E minor D minor at different time scales and to view the harmonic structure 854 9. E major E major E major and relationships between key regions in a musical composi- 855 10. E minor E minor E minor tion. 856 11. F major D minor Fmajor 857 12. F minor F minor F minor 1 Motivation Table 1: KS algorithm results when applied to entire WTC book 1 compositions compared to actual tonic keys of the A tonal composition is usually described as being in a par- music. Identification errors are underlined. ticular key, such as Brahms’ Symphony No. 4 in E minor, or Beethoven’s Piano Sonata in F minor, Op. 57; however, rarely does a piece of music maintain a single key center through- gorithm based on probe-tone ratings generated from experi- out its entirety. The key of a piece typically starts and ends mental results (Krumhansl 1990). The KS algorithm is im- the piece, but other key centers are used somewhere in the plemented in the key program contained in the Humdrum middle of a piece to give form to the music. A simple stereo- Toolkit for musical analysis (Huron). Applying the KS algo- typical tonal piece might start in the tonic key, modulate to rithm to an entire piece, table 1 lists the analyzed keys for the dominant, and then return to the tonic key by the end of the first half of the first book of J.S. Bach’s Well-Tempered the piece. Clavier using the key program. The Well-Tempered Clavier Currently available key-finding algorithms are not very is an excellent source of test material for testing key-finding sensitive to identifying modulations, and if given a selection algorithms, because each set of prelude and fugue in the col- of music which contains several modulations, the algorithms lection are in a different key, starting in C major and then pro- can only identify what the most likely key is for the entire gressing chromatically through all 24 major and minor keys. selection. If there are two key areas in a selection of mu- Table 1 points out two common errors generated by key- sic, then the algorithm hopefully assigns the stronger key the finding algorithms in general. The first error is in fugue no. 3 best score while the other key area hopefully is assigned the where the KS algorithm identifies the dominant rather than second best score. A key identification error may occur if the correct tonic key of C] major. The second error occurs an entire piece of music is presented to a key-finding algo- in the eleventh prelude where the relative minor is identified rithm, since the secondary key areas may overpower the start- rather than the key of F major. ing/ending key or bias the primary key towards a closely re- These two errors are primarily due to more than one key- lated key, such as the dominant or relative minor key areas. area being present in the analyzed music, causing slight off- One of the best algorithms for determining the key in a sets in the tonic key weightings such that a closely related key region of music is the Krumhansl-Schmuckler key-finding al- becomes more likely for the algorithm than the actual key. A fifth-relation error can occur if the secondary key areas are 2 Diagram Types predominantly all above or below the tonic key in the circle of fifths. The second error is a modality error. The correct 2.1 Key-To-Color Mappings key signature was identified, but the distribution of notes in the music was such that the tonic was incorrectly identified. To display data from key-finding algorithms in a compact Of course, the key identification errors in the two com- visual manner, each key is mapped to a different color. The positions from the Well-Tempered Clavier could be fixed by principle key-to-color mapping being used is shown in ta- only applying the algorithm to the first and last parts of the ble 2. The colors of the rainbow are mapped onto the circle music, since these sections are more likely to contain the tonic of fifths collapsed to the seven diatonic pitches. For example, key. However, side-stepping the issue in this manner creates the key C is assigned the color green. Ascending the circle other problems: (1) How much of the beginning and ending of fifths yields G (blue), D (indigo blue), A(purple), E (red). of the piece should be examined? and (2) What if the compo- Going the opposite direction in the circle of fifths takes you sition starts in one key and ends in another? The true problem through the rainbow colors in the opposite direction: F (yel- [ to solve is how to identify correctly regions of stable key cen- low), B[ (orange), E (red). ters and regions of modulation in a piece of music. diatonic diatonic If a more detailed view of a pieces’s key structure is de- pitch class color pitch class color G sired beyond the “key” of the piece, then a moment-by-moment E red blue D view of the key centers in the piece will give a much more de- B orange indigo A tailed description of the piece. Krumhansl proposes applying F yellow violet a sliding analysis window to the notes in a piece to generate C green localized key measurements. This gives a good overview of the key relationships in the music, but results can be sensitive root (R, G, B) root (R, G, B) to the analysis window size. A problem with this sliding win- [ C[ ( 36, 255, 0) G ( 54, 200, 218) dow technique is that the global importance of a local key is C ( 0, 255, 0) G ( 63, 191, 255) not apparent in the local context. A music theorists would as- ] C] ( 9, 246, 36) G ( 63, 177, 255) sign a sequence of key centers to a piece of music using both [ D[ ( 63, 109, 255) A (118, 41, 255) the global and local characteristics of the music. If a region D ( 63, 95, 255) A (127, 31, 255) is difficult to assign a key label, then music outside the local ] D] ( 73, 86, 255) A (145, 27, 219) region will be considered. It is very difficult to have a com- [ E [ (237, 4, 36) B (255, 109, 0) puter generate a reasonably accurate sequence of musically E (255, 0, 0) B (255, 127, 0) relevant key centers. ] E ] (255, 18, 0) B (255, 145, 0) Key visualization techniques described in the following ] F[ (255, 237, 0) F (218, 255, 0) section avoid the problem of choosing a fixed analysis win- F (255, 255, 0) dow duration by instead using all possible analysis window Table 2: Sample RGB color mappings for key tonics. durations. The interpretation of the local key problem is par- tially solved with these display methods because the height to which a key region survives in a diagram demonstrates the This color mapping is designed to be intuitively easy to relative strength of that key region. Strong modulations are navigate, since closely related keys map into closely related represented by large vertical structures, while tonicizations colors. The only drawback of this mapping is that there are are represented by smaller vertical structures. only 7 colors while there are 12 (or more) pitch classes— It is also possible to view the behavior between various notice that E and E[ have the same red color. Since enhar- key-finding algorithms at different analysis window sizes and monic keys are located far apart in key space, this mapping to see how they interact around regions of modulation. Key- is unambiguous for most tonal music and should only cause algorithms can then be compared using the diagram methods confusion in rare cases. A monochromatic color mapping has below to see how the different algorithms handle the same been used in this paper for printing in black-and-white, but music at various time scales. Numerous computational algo- it is possible to view example figures from this paper on the rithms for identifying keys using computers have been pro- World Wide Web (Sapp). posed since the 1960’s. See recent work and surveys on key- Of course, the choice of a color mapping from key to color finding algorithms by Temperley (1997), Chew (2000) and is arbitrary, and different color mappings may be suitable for Shmulevich and Yli-Harja (2000).
Load more

Recommended publications
  • Schenkerian Analysis in the Modern Context of the Musical Analysis
    Mathematics and Computers in Biology, Business and Acoustics THE SCHENKERIAN ANALYSIS IN THE MODERN CONTEXT OF THE MUSICAL ANALYSIS ANCA PREDA, PETRUTA-MARIA COROIU Faculty of Music Transilvania University of Brasov 9 Eroilor Blvd ROMANIA [email protected], [email protected] Abstract: - Music analysis represents the most useful way of exploration and innovation of musical interpretations. Performers who use music analysis efficiently will find it a valuable method for finding the kind of musical richness they desire in their interpretations. The use of Schenkerian analysis in performance offers a rational basis and an unique way of interpreting music in performance. Key-Words: - Schenkerian analysis, structural hearing, prolongation, progression,modernity. 1 Introduction Even in a simple piece of piano music, the ear Musical analysis is a musicological approach in hears a vast number of notes, many of them played order to determine the structural components of a simultaneously. The situation is similar to that found musical text, the technical development of the in language. Although music is quite different to discourse, the morphological descriptions and the spoken language, most listeners will still group the understanding of the meaning of the work. Analysis different sounds they hear into motifs, phrases and has complete autonomy in the context of the even longer sections. musicological disciplines as the music philosophy, Schenker was not afraid to criticize what he saw the musical aesthetics, the compositional technique, as a general lack of theoretical and practical the music history and the musical criticism. understanding amongst musicians. As a dedicated performer, composer, teacher and editor of music himself, he believed that the professional practice of 2 Problem Formulation all these activities suffered from serious misunderstandings of how tonal music works.
    [Show full text]
  • Point Counter Point"
    University of Montana ScholarWorks at University of Montana Graduate Student Theses, Dissertations, & Professional Papers Graduate School 1940 Aldous Huxley's use of music in "Point Counter Point" Bennett Brudevold The University of Montana Follow this and additional works at: https://scholarworks.umt.edu/etd Let us know how access to this document benefits ou.y Recommended Citation Brudevold, Bennett, "Aldous Huxley's use of music in "Point Counter Point"" (1940). Graduate Student Theses, Dissertations, & Professional Papers. 1499. https://scholarworks.umt.edu/etd/1499 This Thesis is brought to you for free and open access by the Graduate School at ScholarWorks at University of Montana. It has been accepted for inclusion in Graduate Student Theses, Dissertations, & Professional Papers by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact [email protected]. A1D005 HUXLEY'S USE OF MUSIC IB F o m r c o i m m by Bennett BruAevold Presented in P&rtlel Fulfillment of the Requirement for the Degree of Master of Arte State University of Montana 1940 Approveds û&^'rman of Ëxaminl]^^ ttee W- Sfiairraan’ of Graduate Ccmmlttee UMI Number; EP35823 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation RMishing UMI EP35823 Published by ProQuest LLC (2012). Copyright in the Dissertation held by the Author.
    [Show full text]
  • Harmonic, Melodic, and Functional Automatic Analysis
    HARMONIC, MELODIC, AND FUNCTIONAL AUTOMATIC ANALYSIS Placido´ R. Illescas, David Rizo, Jose´ M. Inesta˜ Dept. Lenguajes y Sistemas Informaticos´ Universidad de Alicante, E-03071 Alicante, Spain [email protected] fdrizo,[email protected] ABSTRACT Besides the interpretation, there are many applications of this automatic analysis to diverse areas of music: edu- This work is an effort towards the development of a cation, score reduction, pitch spelling, harmonic compar- system for the automation of traditional harmonic analy- ison of works [10], etc. sis of polyphonic scores in symbolic format. A number of stages have been designed in this procedure: melodic The automatic tonal analysis has been tackled under analysis of harmonic and non-harmonic tones, vertical har- different approaches and objectives. Some works use gram- monic analysis, tonality, and tonal functions. All these in- mars to solve the problem [3, 14], or an expert system [6]. formations are represented as a weighted directed acyclic There are probabilistic models like that in [11] and others graph. The best possible analysis is the path that maxi- based on preference rules or scoring techniques [9, 13]. mizes the sum of weights in the graph, obtained through The work in [4] tries to solve the problem using neural a dynamic programming algorithm. The feasibility of the networks. Maybe the best effort so far, from our point proposed approach has been tested on six J. S. Bach’s har- of view is that of Taube [12], who solves the problem by monized chorales. means of model matching. A more comprehensive review of these works can be found in [1].
    [Show full text]
  • Birdsong in the Music of Olivier Messiaen a Thesis Submitted To
    P Birdsongin the Music of Olivier Messiaen A thesissubmitted to MiddlesexUniversity in partial fulfilment of the requirementsfor the degreeof Doctor of Philosophy David Kraft School of Art, Design and Performing Arts Nfiddlesex University December2000 Abstract 7be intentionof this investigationis to formulatea chronologicalsurvey of Messiaen'streatment of birdsong,taking into accountthe speciesinvolved and the composer'sevolving methods of motivic manipulation,instrumentation, incorporation of intrinsic characteristicsand structure.The approachtaken in this studyis to surveyselected works in turn, developingappropriate tabular formswith regardto Messiaen'suse of 'style oiseau',identified bird vocalisationsand eventhe frequentappearances of musicthat includesfamiliar characteristicsof bird style, althoughnot so labelledin the score.Due to the repetitivenature of so manymotivic fragmentsin birdsong,it has becomenecessary to developnew terminology and incorporatederivations from other research findings.7be 'motivic classification'tables, for instance,present the essentialmotivic featuresin somevery complexbirdsong. The studybegins by establishingthe importanceof the uniquemusical procedures developed by Messiaen:these involve, for example,questions of form, melodyand rhythm.7he problemof is 'authenticity' - that is, the degreeof accuracywith which Messiaenchooses to treat birdsong- then examined.A chronologicalsurvey of Messiaen'suse of birdsongin selectedmajor works follows, demonstratingan evolutionfrom the ge-eralterm 'oiseau' to the preciseattribution
    [Show full text]
  • Figured Bass and Tonality Recognition
    Figured Bass and Tonality Recognition Jerome Barthélemy Alain Bonardi Ircam Ircam 1 Place Igor Stravinsky 1 Place Igor Stravinsky 75004 Paris France 75004 Paris France 33 01 44 78 48 43 33 01 44 78 48 43 [email protected] [email protected] ABSTRACT The aim of the figured bass was, in principle, oriented towards interpretation. Rameau turned it into a genuine theory of tonality In the course of the WedelMusic project [15], we are currently with the introduction of the fundamental concept of root. Successive refinements of the theory have been introduced in the implementing retrieval engines based on musical content th automatically extracted from a musical score. By musical content, 18 , 19th (e.g., by Reicha and Fetis) and 20th (e.g., Schoenberg we mean not only main melodic motives, but also harmony, or [10, 11]) centuries. For a general history of the theory of tonality. harmony, one can refer to Ian Bent [1] or Jacques Chailley [2] In this paper, we first review previous research in the domain of harmonic analysis of tonal music. Several processes can be build on the top of a harmonic reduction We then present a method for automated harmonic analysis of a • detection of tonality, music score based on the extraction of a figured bass. The figured • recognition of cadence, bass is determined by means of a template-matching algorithm, where templates for chords can be entirely and easily redefined by • detection of similar structures the end-user. We also address the problem of tonality recognition Following a brief review of systems addressing the problem of with a simple algorithm based on the figured bass.
    [Show full text]
  • A General Theory of Comparative Music Analysis
    A General Theory of Comparative Music Analysis by Richard R. Randall Submitted in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy Supervised by Professor Robert D. Morris Department of Music Theory Eastman School of Music University of Rochester Rochester, New York 2006 Curriculum Vitæ Richard Randall was born in Washington, DC, in 1969. He received his un- dergraduate musical training at the New England Conservatory in Boston, MA. He was awarded a Bachelor of Music in Theoretical Studies with a Distinction in Performance in 1995 and, in 1997, received a Master of Arts degree in music theory from Queens College of the City University of New York. Mr. Randall studied classical guitar with Robert Paul Sullivan, jazz guitar with Frank Rumoro, Walter Johns, and Rick Whitehead, and solfege and conducting with F. John Adams. In 1997, Mr. Randall entered the Ph.D. program in music theory at the University of Rochester’s Eastman School of Music. His research at the Eastman School was advised by Robert Morris. He received teaching assistantships and graduate scholarships in 1998, 1999, 2000. He was adjunct instructor in music at Northeastern Illi- nois University from 2002 to 2003. Additionally, Mr. Randall taught music theory and guitar at the Old Town School of Folk Music in Chicago as a private guitar instructor from 2001 to 2003. In 2003, Mr. Randall was ap- pointed Visiting Assistant Professor of Music in the Department of Music and Dance at the University of Massachusetts, Amherst. i Acknowledgments TBA ii Abstract This dissertation establishes a kind of comparative music analysis such that what we understand as musical features in a particular case are dependent on the music analytic systems that provide the framework by which we can contemplate (and communicate our thoughts about) music.
    [Show full text]
  • Analysis, Performance, and Images of Musical Sound: Surfaces, Cyclical Relationships, and the Musical Work
    Analysis, Performance, and Images of Musical Sound: Surfaces, Cyclical Relationships, and the Musical Work John Latartara and Michael Gardiner Introduction It is not a question of junking these concepts, nor do we have the means to do so. Doubtless it is more necessary, from within semiology, to transform concepts, to displace them, to turn them against their presuppositions, to reinscribe them in other chains, and little by little to modify the terrain of our work and thereby produce new configurations. (Derrida 1981:24) Following Derrida, in this paper we hope to reinscribe the familiar musi­ cological concepts of analysis and performance, drawing them into new relationships, in order to turn them against their presuppositions and produce new configurations. Through an exploration of analysis, perfor­ mance, and images of musical sound, these new configurations highlight surface details and offer an alternative approach to previous analysis and performance paradigms, leading to a reformulation of the concept of the musical "work." The relationship between analysis and performance has posed challeng­ ing questions for musicologists, theorists, and performers, generating some of the most thought-provoking discussions in the literature. The endeavors of analysis and performance are closely related, yet historically they have em­ ployed different methods and participated in different traditions. Nicholas Cook writes, "I would like to counterpose not so much the analyst and the performer but rather the 'writing' and the 'performing' musician, or, more precisely, music as writing and music as performance" (1999:250). For the most part, analysts write about notated music, whereas performers play or sing music. While not inherently negative, these differences of activity have contributed to the chasm that often exists between music analysis and performance.
    [Show full text]
  • MTO 3.2: Latham, Review of Haimo
    Volume 3, Number 2, March 1997 Copyright © 1997 Society for Music Theory Edward D. Latham KEYWORDS: Haimo, Schoenberg, Forte, atonality, intentionality, set theory ABSTRACT: Ethan Haimo’s article, “Atonality, Analysis and the Intentional Fallacy,” provokes thought on three issues: 1) the issue of conscious vs. unconscious intentions; 2) the issue of documentary evidence and its uncritical acceptance; and 3) the evolution of pitch-class set theory in the last twenty-five years. The present author addresses these three issues and challenges Haimo’s conclusion that analyses that do not take intentions into account effectively replace the composer with the theorist as an authority figure. [1] Ethan Haimo’s recent article, “Atonality, Analysis, and the Intentional Fallacy,” is both interesting and provocative.(1) If read from a certain point of view, it would seem that Haimo is interested in resurrecting Nattiez’s tripartition (poietic/neutral /esthesic) and paradigmatic method of analysis, discussing as he does the notions of “coherence based on repetition,” “the score itself,” and “two types of statements about music,” involving composition (poietics) and perception (esthesics). But such is not the case, and the tripartition will have to wait for another time. What Haimo is interested in, however, is the issue of intentionality and its putative role in musical analysis, and Nattiez’s name will therefore resurface in this review in connection with this most thorny, but potentially revelatory of music-analytical topics. [2] Haimo divides his article into four sections, which might be labeled “Schoenberg and Intentionality,” “Intentionality Revisited,” “Forte and Intentionality,” and “Schoenberg and Developing Variation.” In his first section, he presents the case against Schoenberg’s intentional use of pitch-class sets (as they are conceived of in Allen Forte’s system) in his atonal compositions.
    [Show full text]
  • An Approach to the Musical Analysis of Wind Band Literature Based on Analytical Modes Used by Wind Band Specialists and Music Theorists
    Louisiana State University LSU Digital Commons LSU Historical Dissertations and Theses Graduate School 1995 An Approach to the Musical Analysis of Wind Band Literature Based on Analytical Modes Used by Wind Band Specialists and Music Theorists. Jerome Raymond Markoch Jr Louisiana State University and Agricultural & Mechanical College Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_disstheses Recommended Citation Markoch, Jerome Raymond Jr, "An Approach to the Musical Analysis of Wind Band Literature Based on Analytical Modes Used by Wind Band Specialists and Music Theorists." (1995). LSU Historical Dissertations and Theses. 6030. https://digitalcommons.lsu.edu/gradschool_disstheses/6030 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Historical Dissertations and Theses by an authorized administrator of LSU Digital Commons. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality o f the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion.
    [Show full text]
  • Some Major Theoretical Problems Concerning the Concept of Hierarchy in the Analysis of Tonal Music Eugene Narmour University of Pennsylvania, [email protected]
    University of Pennsylvania ScholarlyCommons Departmental Papers (Music) Department of Music 1983 Some Major Theoretical Problems Concerning the Concept of Hierarchy in the Analysis of Tonal Music Eugene Narmour University of Pennsylvania, [email protected] Follow this and additional works at: http://repository.upenn.edu/music_papers Part of the Musicology Commons, and the Music Theory Commons Recommended Citation Narmour, E. (1983). Some Major Theoretical Problems Concerning the Concept of Hierarchy in the Analysis of Tonal Music. Music Perception: An Interdisciplinary Journal, 1 (2), 129-199. http://dx.doi.org/10.2307/40285255 This paper is posted at ScholarlyCommons. http://repository.upenn.edu/music_papers/6 For more information, please contact [email protected]. Some Major Theoretical Problems Concerning the Concept of Hierarchy in the Analysis of Tonal Music Abstract Level-analysis in the field of music theory today is rarely hierarchical, at least in the strict sense of the term. Most current musical theories view levels systemically. One problem with this approach is that it usually does not distinguish compositional structures from perceptual structures. Another is its failure to recognize that in an artifactual phenomenon the inherence of idiostructures is as crucial to the identity of an artwork as the inherence of style structures. But can the singularity of an idiostructure be captured in the generality of an analytical symbol? In music analysis, it would seem possible provided closure and nonclosure are admitted as simultaneous properties potentially present at all hierarchical levels. One complication of this assumption, however, is that both network and tree relationships result. Another is that such relationships span in both "horizontal" (temporal) and "vertical" (structural) directions.
    [Show full text]
  • Adorno and Musical Analysis Author(S): Andrew Edgar Source: the Journal of Aesthetics and Art Criticism , Autumn, 1999, Vol
    Adorno and Musical Analysis Author(s): Andrew Edgar Source: The Journal of Aesthetics and Art Criticism , Autumn, 1999, Vol. 57, No. 4 (Autumn, 1999), pp. 439-449 Published by: Wiley on behalf of The American Society for Aesthetics Stable URL: http://www.jstor.com/stable/432150 REFERENCES Linked references are available on JSTOR for this article: http://www.jstor.com/stable/432150?seq=1&cid=pdf- reference#references_tab_contents You may need to log in to JSTOR to access the linked references. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at https://about.jstor.org/terms Wiley and The American Society for Aesthetics are collaborating with JSTOR to digitize, preserve and extend access to The Journal of Aesthetics and Art Criticism This content downloaded from 68.4.47.192 on Fri, 08 Jan 2021 02:16:54 UTC All use subject to https://about.jstor.org/terms ANDREW EDGAR Adorno and Musical Analysis Nicholas Cook has defined musical analysis as dently of the act of analysis. The achievement of "the practical process of examining pieces of this goal is prevented only by the lack of refine- music in order to discover, or decide, how they ment in analytic techniques. work."' Analytical methods "ask whether it is The purpose of this essay is to outline a re- possible to chop up a piece of music into a series sponse to these issues, in part through reference of more-or-less independent sections.
    [Show full text]
  • Derivative Analysis and Serial Music: the Theme of Schoenberg's
    ALMADA, Carlos de Lemos. (2016) Derivative Analysis and Serial Music: the Theme of Schoenberg’s Orchestral Variations Op.31. Per Musi. Ed. by Fausto Borém, Eduardo Rosse and Débora Borburema. Belo Horizonte: UFMG, n.33, p.1‐24. DOI: 10.1590/permusi20163301 SCIENTIFIC ARTICLE Derivative Analysis and Serial Music: the Theme of Schoenberg’s Orchestral Variations Op.31 Análise derivativa e a música serial: O tema das Variações para Orquestra op.31 de Schoenberg Carlos de Lemos Almada Universidade Federal do Rio de Janeiro, Rio de Janeiro, Rio de Janeiro, Brasil. [email protected] Abstract: The main objective of this paper is to investigate the derivative relations between the constituent elements of the theme of Arnold Schoenberg’s Orchestral Variations Op.31 and its source of basic material or Grundgestalt, a theoretical principle elaborated by the composer. After a bibliographical revision concerned with the origins and motivations for the formulation of the concept, the paper discusses the problematic issue of the presence of thematic development in Schoenberg’s serial music, taking as reference analyzes by some authors (RUFER, 1954; BOSS, 1992; HAIMO, 1997; TARUSKIN, 2010). It is also proposed that the Grundgestalt of a twelve‐ tone piece can be manifested according to two levels, abstract and concrete, which adjusts to the analytical methodology adopted in this study, described in a specific section of the paper. The results obtained reveal an extraordinarily organic and economic thematic construction. Keywords : derivative analysis; Grundgestalt; developing variation in serial music; Arnold Schoenberg’s serial music. Resumo: Este artigo tem como objetivo principal investigar as relações de derivação entre os elementos componentes do tema das Variações para Orquestra op.31 de Arnold Schoenberg) e sua fonte de material básico, ou Grundgestalt, conceito teórico elaborado pelo próprio compositor.
    [Show full text]