TONE TONALITY Faculty of Graduate Studies
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Baker Eastman School of Music [email protected] I
A Cyclic Approach to Harmony in Robert Glasper’s Music Society for Music Theory Columbus, OH November 7, 2019 Ben Baker Eastman School of Music [email protected] I. Introduction Robert Glasper hip-hop R&B jazz neo-soul gospel I. Introduction Robert Glasper Blue Note releases: Canvas (2005) piano trio In My Element (2007) piano trio + R.G. Experiment Double-Booked (2009) Black Radio (2012) R.G. Experiment Black Radio 2 (2013) piano trio Covered (2015) R.G. Experiment ArtScience (2016) I. Introduction Robert Glasper “…probably the most prominent jazz musician of his generation. He’s gotten there by playing within and without jazz, and pushing the music to reconsider its boundaries.” -Russonello (NYT, 2018) I. Introduction Glasper’s Harmonic Language diatonic collections clear tonal centers tertian harmonies root motion by: 3rd (ex. Imaj7 - vi7 - IVmaj7 - ii7) descending 5th (ii7 - V7 - Imaj7) two primary chord qualities: major 7th chords + upper extensions minor 7th chords I. Introduction “Rise and Shine” (Canvas, 2005) Fmaj9 Dbmaj9 Bbm9 Gm11 ™ ™ C œ œ œ bœ œ œ œ j œ œ &b œ J bœ œ œ ˙ ˙ œ Dmaj9 Gm11 D/F# Fmaj9 ™ ™ b œ œ œ j Œ & ˙ J œ œ œ œw ˙ œ œ Dbmaj9 C7 F Bbm11 Gm11 ™ ™ b œ œ œ œ œ œ œ b˙ œw w & bœ œ œ œ œ œ œ J œ 1. Gm11 Dm11 ™ j ™ &b w œ œ œ œw w w 2. Gbmaj9 C7alt F7sus4 ™ b˙ bwœ w ˙ &b ˙ œ œ œ œ œ œ &b∑ ∑ ∑ ∑ ∑ ∑ ∑ I. Introduction “Rise and Shine” (Canvas, 2005) Fmaj9 Dbmaj9 Bbm9 Gm11 ™ ™ C œ œ œ bœ œ œ œ j œ œ &b œ J bœ œ œ ˙ ˙ œ Dmaj9 Gm11 D/F# Fmaj9 ™ ™ b œ œ œ j Œ & ˙ J œ œ œ œw ˙ œ œ Dbmaj9 C7 F Bbm11 Gm11 ™ ™ b œ œ œ œ œ œ œ b˙ œw w & bœ œ œ œ œ œ œ J œ 1. -
A Heretic in the Schoenberg Circle: Roberto Gerhard's First Engagement with Twelve-Tone Procedures in Andantino
Twentieth-Century Music 16/3, 557–588 © Cambridge University Press 2019. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. doi: 10.1017/S1478572219000306 A Heretic in the Schoenberg Circle: Roberto Gerhard’s First Engagement with Twelve-Tone Procedures in Andantino DIEGO ALONSO TOMÁS Abstract Shortly before finishing his studies with Arnold Schoenberg, Roberto Gerhard composed Andantino,a short piece in which he used for the first time a compositional technique for the systematic circu- lation of all pitch classes in both the melodic and the harmonic dimensions of the music. He mod- elled this technique on the tri-tetrachordal procedure in Schoenberg’s Prelude from the Suite for Piano, Op. 25 but, unlike his teacher, Gerhard treated the tetrachords as internally unordered pitch-class collections. This decision was possibly encouraged by his exposure from the mid- 1920s onwards to Josef Matthias Hauer’s writings on ‘trope theory’. Although rarely discussed by scholars, Andantino occupies a special place in Gerhard’s creative output for being his first attempt at ‘twelve-tone composition’ and foreshadowing the permutation techniques that would become a distinctive feature of his later serial compositions. This article analyses Andantino within the context of the early history of twelve-tone music and theory. How well I do remember our Berlin days, what a couple we made, you and I; you (at that time) the anti-Schoenberguian [sic], or the very reluctant Schoenberguian, and I, the non-conformist, or the Schoenberguian malgré moi. -
The Social Economic and Environmental Impacts of Trade
Journal of Modern Education Review, ISSN 2155-7993, USA August 2020, Volume 10, No. 8, pp. 597–603 Doi: 10.15341/jmer(2155-7993)/08.10.2020/007 © Academic Star Publishing Company, 2020 http://www.academicstar.us Musical Vectors and Spaces Candace Carroll, J. X. Carteret (1. Department of Mathematics, Computer Science, and Engineering, Gordon State College, USA; 2. Department of Fine and Performing Arts, Gordon State College, USA) Abstract: A vector is a quantity which has both magnitude and direction. In music, since an interval has both magnitude and direction, an interval is a vector. In his seminal work Generalized Musical Intervals and Transformations, David Lewin depicts an interval i as an arrow or vector from a point s to a point t in musical space. Using Lewin’s text as a point of departure, this article discusses the notion of musical vectors in musical spaces. Key words: Pitch space, pitch class space, chord space, vector space, affine space 1. Introduction A vector is a quantity which has both magnitude and direction. In music, since an interval has both magnitude and direction, an interval is a vector. In his seminal work Generalized Musical Intervals and Transformations, David Lewin (2012) depicts an interval i as an arrow or vector from a point s to a point t in musical space (p. xxix). Using Lewin’s text as a point of departure, this article further discusses the notion of musical vectors in musical spaces. t i s Figure 1 David Lewin’s Depiction of an Interval i as a Vector Throughout the discussion, enharmonic equivalence will be assumed. -
Schoenberg's Chordal Experimentalism Revealed Through
Music Theory Spectrum Advance Access published September 18, 2015 Schoenberg’s Chordal Experimentalism Revealed through Representational Hierarchy Association (RHA), Contour Motives, and Binary State Switching This article considers the chronological flow of Schoenberg’s chordal atonal music, using melodic contour and other contextual features to prioritize some chordal events over others. These non- consecutive chords are tracked and compared for their coloristic contrasts, producing an unfolding akin to Klangfarbenmelodie, but paced more like a narrative trajectory in a drama. The dramatic pacing enhances discernment of nuance among atonal dissonant chords, thereby emancipating them from subordinate obscurity to vivid distinctness. Thus Schoenberg’s music is strategically configured to differentiate its own pitch material. This approach is theorized in terms of represen- Downloaded from tational hierarchy association (RHA) among chords, and demonstrated in analyses of Op. 11, No. 2, Op. 21, No. 4, and Op. 19, No. 3. In support, the analyses consider: (1) the combinatorics of voicing as effecting contrasts of timbre; (2) an application of Lewin’s Binary State Generalized Interval System (GIS) to melodic contour and motivic transformation based on binary-state switch- ing; (3) Klumpenhouwer Networks to model chord-to-chord connections hierarchically; and (4) the role of pitch-class set genera (families of chords) in projecting a palindromic arch form. http://mts.oxfordjournals.org/ Keywords: dualism, chords, Schoenberg, segmentation, -
The Conclusion of Lulu, Act II
Octatonic Formations, Motivic Correspondences, and Symbolism in Alwa’s Hymne: The Conclusion of Lulu, Act II Master’s Thesis Presented to The Faculty of the Graduate School of Arts and Sciences Brandeis University Department of Musicology Allan Keiler, Advisor In Partial Fulfillment of the Requirements for Master’s of Fine Arts Degree by Alexander G. Lane May 2010 ABSTRACT Octatonic Formations, Motivic Correspondences, and Symbolism in Alwa’s Hymne: The Conclusion of Lulu, Act II A thesis presented to the Department of Musicology Graduate School of Arts and Sciences Brandeis University Waltham, Massachusetts By Alexander G. Lane In this study of the final number from Act II of Alban Berg’s Lulu, I examine Alwa’s Hymne from three different perspectives. First, I analyze the Hymne as if it were a free-standing composition. In this portion of the paper, I enumerate the tone-rows and motives out of which the Hymne is constructed and I discuss how these basic materials are related to each other. I place special emphasis on the multiple roles which the octatonic collection plays in this number: it functions as a subset of twelve-note formations, as a superset encompassing shorter motives, and as an agent of harmonic and melodic coherence in those sections of the Hymne that are not governed by twelve-tone sets. In this part of the paper, I also discuss the ways in which the text and the music of the Hymne may help to clarify the nature of Alwa’s relationship with Lulu. In the second section of this study, I examine the Hymne’s relation to other parts of the Lulu. -
Miriam Gideon's Cantata, the Habitable Earth
Louisiana State University LSU Digital Commons LSU Major Papers Graduate School 2003 Miriam Gideon's cantata, The aH bitable Earth: a conductor's analysis Stella Panayotova Bonilla Louisiana State University and Agricultural and Mechanical College, [email protected] Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_majorpapers Part of the Music Commons Recommended Citation Bonilla, Stella Panayotova, "Miriam Gideon's cantata, The aH bitable Earth: a conductor's analysis" (2003). LSU Major Papers. 20. https://digitalcommons.lsu.edu/gradschool_majorpapers/20 This Major Paper 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 Major Papers by an authorized graduate school editor of LSU Digital Commons. For more information, please contact [email protected]. MIRIAM GIDEON’S CANTATA, THE HABITABLE EARTH: A CONDUCTOR’S ANALYSIS A Monograph Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Musical Arts in The School of Music by Stella Panayotova Bonilla B.M., State Academy of Music, Sofia, Bulgaria, 1991 M.M., Louisiana State University, 1994 August 2003 ©Copyright 2003 Stella Panayotova Bonilla All rights reserved ii DEDICATION To you mom, and to the memory of my beloved father. iii ACKNOWLEDGMENTS Thanks to Dr. Kenneth Fulton for his guidance through the years, his faith in me and his invaluable help in accomplishing this project. Thanks to Dr. Robert Peck for his inspirational insight. Thanks to Dr. Cornelia Yarbrough and Dr. -
The Computational Attitude in Music Theory
The Computational Attitude in Music Theory Eamonn Bell Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2019 © 2019 Eamonn Bell All rights reserved ABSTRACT The Computational Attitude in Music Theory Eamonn Bell 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. -
The Strategic Half-Diminished Seventh Chord and the Emblematic Tristan Chord: a Survey from Beethoven to Berg
International Journal ofMusicology 4 . 1995 139 Mark DeVoto (Medford, Massachusetts) The Strategic Half-diminished Seventh Chord and The Emblematic Tristan Chord: A Survey from Beethoven to Berg Zusammenfassung: Der strategische halbverminderte Septakkord und der em blematische Tristan-Akkord von Beethoven bis Berg im Oberblick. Der halb verminderte Septakkord tauchte im 19. Jahrhundert als bedeutende eigen standige Hannonie und als Angelpunkt bei der chromatischen Modulation auf, bekam aber eine besondere symbolische Bedeutung durch seine Verwendung als Motiv in Wagners Tristan und Isolde. Seit der Premiere der Oper im Jahre 1865 lafit sich fast 100 Jahre lang die besondere Entfaltung des sogenannten Tristan-Akkords in dramatischen Werken veifolgen, die ihn als Emblem fUr Liebe und Tod verwenden. In Alban Bergs Lyrischer Suite und Lulu erreicht der Tristan-Akkord vielleicht seine hOchste emblematische Ausdruckskraft nach Wagner. If Wagner's Tristan und Isolde in general, and its Prelude in particular, have stood for more than a century as the defining work that liberated tonal chro maticism from its diatonic foundations of the century before it, then there is a particular focus within the entire chromatic conception that is so well known that it even has a name: the Tristan chord. This is the chord that occurs on the downbeat of the second measure of the opera. Considered enharmonically, tills chord is of course a familiar structure, described in many textbooks as a half diminished seventh chord. It is so called because it can be partitioned into a diminished triad and a minor triad; our example shows it in comparison with a minor seventh chord and an ordinary diminished seventh chord. -
Interval Cycles and the Emergence of Major-Minor Tonality
Empirical Musicology Review Vol. 5, No. 3, 2010 Modes on the Move: Interval Cycles and the Emergence of Major-Minor Tonality MATTHEW WOOLHOUSE Centre for Music and Science, Faculty of Music, University of Cambridge, United Kingdom ABSTRACT: The issue of the emergence of major-minor tonality is addressed by recourse to a novel pitch grouping process, referred to as interval cycle proximity (ICP). An interval cycle is the minimum number of (additive) iterations of an interval that are required for octave-related pitches to be re-stated, a property conjectured to be responsible for tonal attraction. It is hypothesised that the actuation of ICP in cognition, possibly in the latter part of the sixteenth century, led to a hierarchy of tonal attraction which favoured certain pitches over others, ostensibly the tonics of the modern major and minor system. An ICP model is described that calculates the level of tonal attraction between adjacent musical elements. The predictions of the model are shown to be consistent with music-theoretic accounts of common practice period tonality, including Piston’s Table of Usual Root Progressions. The development of tonality is illustrated with the historical quotations of commentators from the sixteenth to the eighteenth centuries, and can be characterised as follows. At the beginning of the seventeenth century multiple ‘finals’ were possible, each associated with a different interval configuration (mode). By the end of the seventeenth century, however, only two interval configurations were in regular use: those pertaining to the modern major- minor key system. The implications of this development are discussed with respect interval cycles and their hypothesised effect within music. -
2005: Boston/Cambridge
PROGRAM and ABSTRACTS OF PAPERS READ at the Twenty–Eighth Annual Meeting of the SOCIETY FOR MUSIC THEORY 10–13 November 2005 Hyatt Regency Cambridge Boston/Cambridge, Massachusetts 2 SMT 2005 Annual Meeting Edited by Taylor A. Greer Chair, 2005 SMT Program Committee Local Arrangements Committee David Kopp, Deborah Stein, Co-Chairs Program Committee Taylor A. Greer, Chair, Dora A. Hanninen, Daphne Leong, Joel Lester (ex officio), Henry Martin, Shaugn O’Donnell, Deborah Stein Executive Board Joel Lester, President William Caplin, President-Elect Harald Krebs, Vice President Nancy Rogers, Secretary Claire Boge, Treasurer Kofi Agawu Lynne Rogers Warren Darcy Judy Lochhead Frank Samarotto Janna Saslaw Executive Director Victoria L. Long 3 Contents Program…………………………………………………………........ 5 Abstracts………………………………………………………….…... 16 Thursday afternoon, 10 November Combining Musical Systems……………………………………. 17 New Modes, New Measures…………………………………....... 19 Compositional Process and Analysis……………………………. 21 Pedagogy………………………………………………………… 22 Introspective/ Prospective Analysis……………………………... 23 Thursday evening Negotiating Career and Family………………………………….. 24 Poster Session…………………………………………………… 26 Friday morning, 11 November Traveling Through Space ……………………………………….. 28 Schenker: Interruption, Form, and Allusion…………………… 31 Sharakans, Epithets, and Sufis…………………………………... 33 Friday afternoon Jazz: Chord-Scale Theory and Improvisation…………………… 35 American Composers Since 1945……………………………….. 37 Tonal Reconstructions ………………………………………….. 40 Exploring Voice Leading.……………………………………….. -
Set Theory: a Gentle Introduction Dr
Mu2108 Set Theory: A Gentle Introduction Dr. Clark Ross Consider (and play) the opening to Schoenberg’s Three Piano Pieces, Op. 11, no. 1 (1909): If we wish to understand how it is organized, we could begin by looking at the melody, which seems to naturally break into two three-note cells: , and . We can see right away that the two cells are similar in contour, but not identical; the first descends m3rd - m2nd, but the second descends M3rd - m2nd. We can use the same method to compare the chords that accompany the melody. They too are similar (both span a M7th in the L. H.), but not exactly the same (the “alto” (lower voice in the R. H.) only moves up a diminished 3rd (=M2nd enh.) from B to Db, while the L. H. moves up a M3rd). Let’s use a different method of analysis to examine the same excerpt, called SET THEORY. WHAT? • SET THEORY is a method of musical analysis in which PITCH CLASSES are represented by numbers, and any grouping of these pitch classes is called a SET. • A PITCH CLASS (pc) is the class (or set) of pitches with the same letter (or solfège) name that are octave duplications of one another. “Middle C” is a pitch, but “C” is a pitch class that includes middle C, and all other octave duplications of C. WHY? Atonal music is often organized in pitch groups that form cells (both horizontal and vertical), many of which relate to one another. Set Theory provides a shorthand method to label these cells, just like Roman numerals and inversion figures do (i.e., ii 6 ) in tonal music. -
Evan Jones (Ed.), Intimate Voices: the Twentieth-Century String Quartet
Evan Jones (ed.), Intimate Voices: the Twentieth-Century String Quartet EVAN JONES (ED.), INTIMATE VOICES: THE TWENTIETH-CENTURY STRING QUARTET (Rochester: University of Rochester Press, 2009). Volume I: Debussy to Villa-Lobos, ISBN 978-1-58046-229-7; Volume 2: Shostakovich to the Avant-Garde, ISBN 978-1-58046-322-5; 295+338pp, £70 (hardback). Towards the end of the nineteenth century one might have been forgiven for thinking that the era of the string quartet was coming to an end. While Wagner cast his spell over European music, this erudite conversation between four equal players seemed to belong to the past. As we move into the twentieth century, the writing of musical history latches easily onto works such as Schoenberg’s Pierrot Lunaire, Stravinsky’s Symphonies of Wind Instruments and Boulez’s Le marteau sans maître as examples of new and developing engagements with instrumental sonority; but the old medium of the string quartet writes its own parallel history, as the chronologically arranged essays in these volumes demonstrate. Perhaps in another way, the persistence of the string quartet is not so surprising. For European or North American composers schooled in the Western European traditions, this is the ultimate genre for exploring purely musi- cal relationships. Many avant-garde composers have written string quartets and it ‘is ironic that it falls to the only medium held over from the past, the string quartet, to provide a means of comparing, contrasting, and evaluating the music, technique, and aesthetics of this generation’ (ii, 131). The string quartet is a medium for serious com- positional statements.