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MTO 0.7: Alphonce, Dissonance and Schumann's Reckless Counterpoint
Volume 0, Number 7, March 1994 Copyright © 1994 Society for Music Theory Bo H. Alphonce KEYWORDS: Schumann, piano music, counterpoint, dissonance, rhythmic shift ABSTRACT: Work in progress about linearity in early romantic music. The essay discusses non-traditional dissonance treatment in some contrapuntal passages from Schumann’s Kreisleriana, opus 16, and his Grande Sonate F minor, opus 14, in particular some that involve a wedge-shaped linear motion or a rhythmic shift of one line relative to the harmonic progression. [1] The present paper is the first result of a planned project on linearity and other features of person- and period-style in early romantic music.(1) It is limited to Schumann's piano music from the eighteen-thirties and refers to score excerpts drawn exclusively from opus 14 and 16, the Grande Sonate in F minor and the Kreisleriana—the Finale of the former and the first two pieces of the latter. It deals with dissonance in foreground terms only and without reference to expressive connotations. Also, Eusebius, Florestan, E.T.A. Hoffmann, and Herr Kapellmeister Kreisler are kept gently off stage. [2] Schumann favours friction dissonances, especially the minor ninth and the major seventh, and he likes them raw: with little preparation and scant resolution. The sforzato clash of C and D in measures 131 and 261 of the Finale of the G minor Sonata, opus 22, offers a brilliant example, a peculiarly compressed dominant arrival just before the return of the main theme in G minor. The minor ninth often occurs exposed at the beginning of a phrase as in the second piece of the Davidsbuendler, opus 6: the opening chord is a V with an appoggiatura 6; as 6 goes to 5, the minor ninth enters together with the fundamental in, respectively, high and low peak registers. -
Andrián Pertout
Andrián Pertout Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition Volume 1 Submitted in partial fulfilment of the requirements of the degree of Doctor of Philosophy Produced on acid-free paper Faculty of Music The University of Melbourne March, 2007 Abstract Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition encompasses the work undertaken by Lou Harrison (widely regarded as one of America’s most influential and original composers) with regards to just intonation, and tuning and scale systems from around the globe – also taking into account the influential work of Alain Daniélou (Introduction to the Study of Musical Scales), Harry Partch (Genesis of a Music), and Ben Johnston (Scalar Order as a Compositional Resource). The essence of the project being to reveal the compositional applications of a selection of Persian, Indonesian, and Japanese musical scales utilized in three very distinct systems: theory versus performance practice and the ‘Scale of Fifths’, or cyclic division of the octave; the equally-tempered division of the octave; and the ‘Scale of Proportions’, or harmonic division of the octave championed by Harrison, among others – outlining their theoretical and aesthetic rationale, as well as their historical foundations. The project begins with the creation of three new microtonal works tailored to address some of the compositional issues of each system, and ending with an articulated exposition; obtained via the investigation of written sources, disclosure -
Generalized Interval System and Its Applications
Generalized Interval System and Its Applications Minseon Song May 17, 2014 Abstract Transformational theory is a modern branch of music theory developed by David Lewin. This theory focuses on the transformation of musical objects rather than the objects them- selves to find meaningful patterns in both tonal and atonal music. A generalized interval system is an integral part of transformational theory. It takes the concept of an interval, most commonly used with pitches, and through the application of group theory, generalizes beyond pitches. In this paper we examine generalized interval systems, beginning with the definition, then exploring the ways they can be transformed, and finally explaining com- monly used musical transformation techniques with ideas from group theory. We then apply the the tools given to both tonal and atonal music. A basic understanding of group theory and post tonal music theory will be useful in fully understanding this paper. Contents 1 Introduction 2 2 A Crash Course in Music Theory 2 3 Introduction to the Generalized Interval System 8 4 Transforming GISs 11 5 Developmental Techniques in GIS 13 5.1 Transpositions . 14 5.2 Interval Preserving Functions . 16 5.3 Inversion Functions . 18 5.4 Interval Reversing Functions . 23 6 Rhythmic GIS 24 7 Application of GIS 28 7.1 Analysis of Atonal Music . 28 7.1.1 Luigi Dallapiccola: Quaderno Musicale di Annalibera, No. 3 . 29 7.1.2 Karlheinz Stockhausen: Kreuzspiel, Part 1 . 34 7.2 Analysis of Tonal Music: Der Spiegel Duet . 38 8 Conclusion 41 A Just Intonation 44 1 1 Introduction David Lewin(1933 - 2003) is an American music theorist. -
8.1.4 Intervals in the Equal Temperament The
8.1 Tonal systems 8-13 8.1.4 Intervals in the equal temperament The interval (inter vallum = space in between) is the distance of two notes; expressed numerically by the relation (ratio) of the frequencies of the corresponding tones. The names of the intervals are derived from the place numbers within the scale – for the C-major-scale, this implies: C = prime, D = second, E = third, F = fourth, G = fifth, A = sixth, B = seventh, C' = octave. Between the 3rd and 4th notes, and between the 7th and 8th notes, we find a half- step, all other notes are a whole-step apart each. In the equal-temperament tuning, a whole- step consists of two equal-size half-step (HS). All intervals can be represented by multiples of a HS: Distance between notes (intervals) in the diatonic scale, represented by half-steps: C-C = 0, C-D = 2, C-E = 4, C-F = 5, C-G = 7, C-A = 9, C-B = 11, C-C' = 12. Intervals are not just definable as HS-multiples in their relation to the root note C of the C- scale, but also between all notes: e.g. D-E = 2 HS, G-H = 4 HS, F-A = 4 HS. By the subdivision of the whole-step into two half-steps, new notes are obtained; they are designated by the chromatic sign relative to their neighbors: C# = C-augmented-by-one-HS, and (in the equal-temperament tuning) identical to the Db = D-diminished-by-one-HS. Corresponding: D# = Eb, F# = Gb, G# = Ab, A# = Bb. -
Hexatonic Cycles
CHAPTER Two H e x a t o n i c C y c l e s Chapter 1 proposed that triads could be related by voice leading, independently of roots, diatonic collections, and other central premises of classical theory. Th is chapter pursues that proposal, considering two triads to be closely related if they share two common tones and their remaining tones are separated by semitone. Motion between them thus involves a single unit of work. Positioning each triad beside its closest relations produces a preliminary map of the triadic universe. Th e map serves some analytical purposes, which are explored in this chapter. Because it is not fully connected, it will be supplemented with other relations developed in chapters 4 and 5. Th e simplicity of the model is a pedagogical advantage, as it presents a circum- scribed environment in which to develop some central concepts, terms, and modes of representation that are used throughout the book. Th e model highlights the central role of what is traditionally called the chromatic major-third relation, although that relation is theorized here without reference to harmonic roots. It draws attention to the contrary-motion property that is inherent in and exclusive to triadic pairs in that relation. Th at property, I argue, underlies the association of chromatic major-third relations with supernatural phenomena and altered states of consciousness in the early nineteenth century. Finally, the model is suffi cient to provide preliminary support for the central theoretical claim of this study: that the capacity for minimal voice leading between chords of a single type is a special property of consonant triads, resulting from their status as minimal perturbations of perfectly even augmented triads. -
Information to Users
INFORMATION TO USERS This manuscript has been reproduced from the microfihn 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 of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely afreet 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. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI University Microfilms International A Bell & Howell Information Company 3 0 0 North Z eeb Road. Ann Arbor. Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9401386 Enharmonicism in theory and practice in 18 th-century music Telesco, Paula Jean, Ph.D. The Ohio State University, 1993 Copyright ©1993 by Telesco, Paula Jean. -
Musical Elements in the Discrete-Time Representation of Sound
0 Musical elements in the discrete-time representation of sound RENATO FABBRI, University of Sao˜ Paulo VILSON VIEIRA DA SILVA JUNIOR, Cod.ai ANTONIOˆ CARLOS SILVANO PESSOTTI, Universidade Metodista de Piracicaba DEBORA´ CRISTINA CORREA,ˆ University of Western Australia OSVALDO N. OLIVEIRA JR., University of Sao˜ Paulo e representation of basic elements of music in terms of discrete audio signals is oen used in soware for musical creation and design. Nevertheless, there is no unied approach that relates these elements to the discrete samples of digitized sound. In this article, each musical element is related by equations and algorithms to the discrete-time samples of sounds, and each of these relations are implemented in scripts within a soware toolbox, referred to as MASS (Music and Audio in Sample Sequences). e fundamental element, the musical note with duration, volume, pitch and timbre, is related quantitatively to characteristics of the digital signal. Internal variations of a note, such as tremolos, vibratos and spectral uctuations, are also considered, which enables the synthesis of notes inspired by real instruments and new sonorities. With this representation of notes, resources are provided for the generation of higher scale musical structures, such as rhythmic meter, pitch intervals and cycles. is framework enables precise and trustful scientic experiments, data sonication and is useful for education and art. e ecacy of MASS is conrmed by the synthesis of small musical pieces using basic notes, elaborated notes and notes in music, which reects the organization of the toolbox and thus of this article. It is possible to synthesize whole albums through collage of the scripts and seings specied by the user. -
The Augmented Sixth Chord
CHAPTER24 The Augmented Sixth Chord Characteristics, Derivation, and Behavior The two excerpts in Example 24.1 are from different style periods, yet they share several features. In terms of form and harmony, both divide into two subphrases and close with strong half cadences. Further, the pre-dominant harmony in both examples is the same: an altered iv6 chord. Indeed, we hear not a Phrygian cadence (iv6-V), but rather some chromatic version, where the diatonic major sixth above the bass is raised a half step to create the strongly directed interval of the augmented sixth (+6). The new half-step ascent (#4-5) mirrors the bass's half-step descent (6-5). We refer to such chromatic pre-dominants as augmented sixth chords because of the characteristic interval between the bass 6 and the upper-voice #4. Listen to both excerpts in Example 24.1, noting the striking sound of the augmented sixth chords. EXAMPLE 24.1 A. Schubert, WaltzinG minor, Die letzte Walzer, op. 127, no. 12, D. 146 472 CHAPTER 24 THE AUGMENTED SIXTH CHORD 473 B. Handel, "Since by Man Came Death," Messiah, HWV 56 Example 24.2 demonstrates the derivation of the augmented sixth chord from the Phrygian cadence. Example 24.2A represents a traditional Phrygian half cadence. In Example 24.2B, the chromatic F# fills the space between F and G, and the passing motion creates an interval of an augmented sixth. Finally, Example 24.2C shows the augmented sixth chord as a harmonic entity, with no consonant preparation. EXAMPLE 24.2 Phrygian Cadence Generates the Augmented Sixth Chord Given that the augmented sixth chord also occurs in major, one might ask if it is an example of an applied chord or a mixture chord? To answer this question, consider the diatonic progression in Example 24.3A. -
Encyclopedia of the History of Arabic Science. Volume 2, Mathematics
Encyclopedia of the History of Arabic Science Encyclopedia of the History of Arabic Science Volume 2 Edited by ROSHDI RASHED in collaboration with RÉGIS MORELON LONDON AND NEW YORK First published in 1996 by Routledge 11 New Fetter Lane, London EC4P 4EE 29 West 35th Street, New York, NY 10001 This edition published in the Taylor & Francis e-Library, 2009. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk. Structure and editorial matter © 1996 Routledge The chapters © 1996 Routledge All rights reserved. No part of this book may be reprinted or reproduced or utilized in any form or by any electronic, mechanical or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. Library of Congress Cataloguing-in-Publication Data A catalogue record for this book is available on request. ISBN 0-203-40360-6 Master e-book ISBN ISBN 0-203-71184-X (Adobe ebook Reader Format) ISBN 0-415-12411-5 (Print Edition) 3 volume set ISBN 0-415-02063-8 Contents VOLUME 1 Contents v Preface ix 1 General survey of Arabic astronomy Régis Morelon 1 2 Eastern Arabic astronomy between the eighth and the eleventh centuries 20 Régis Morelon 3 Arabic planetary theories after the eleventh century AD 58 George Saliba 4 Astronomy and -
Exploration of an Adaptable Just Intonation System Jeff Snyder
Exploration of an Adaptable Just Intonation System Jeff Snyder Submitted in partial fulfillment of the requirements of the degree of Doctor of Musical Arts in the Graduate School of Arts and Sciences Columbia University 2010 ABSTRACT Exploration of an Adaptable Just Intonation System Jeff Snyder In this paper, I describe my recent work, which is primarily focused around a dynamic tuning system, and the construction of new electro-acoustic instruments using this system. I provide an overview of my aesthetic and theoretical influences, in order to give some idea of the path that led me to my current project. I then explain the tuning system itself, which is a type of dynamically tuned just intonation, realized through electronics. The third section of this paper gives details on the design and construction of the instruments I have invented for my own compositional purposes. The final section of this paper gives an analysis of the first large-scale piece to be written for my instruments using my tuning system, Concerning the Nature of Things. Exploration of an Adaptable Just Intonation System Jeff Snyder I. Why Adaptable Just Intonation on Invented Instruments? 1.1 - Influences 1.1.1 - Inspiration from Medieval and Renaissance music 1.1.2 - Inspiration from Harry Partch 1.1.3 - Inspiration from American country music 1.2 - Tuning systems 1.2.1 - Why just? 1.2.1.1 – Non-prescriptive pitch systems 1.2.1.2 – Just pitch systems 1.2.1.3 – Tempered pitch systems 1.2.1.4 – Rationale for choice of Just tunings 1.2.1.4.1 – Consideration of non-prescriptive -
Shadings in the Chromatic Field: Intonations After Morton Feldman
Shadings in the Chromatic Field: Intonations after Morton Feldman Marc Sabat ... this could be an element of the aural plane, where I'm trying to balance, a kind of coexistence between the chromatic field and those notes selected from the chromatic field that are not in the chromatic series.1 Harmony, or how pitched sounds combine, implies microtonality, enharmonic variations of tuning. Historically, these came to be reflected in written music by having various ways of spelling pitches. A harmonic series over E leads to the notes B and G#, forming a just major triad. Writing Ab instead of G# implies a different structure, but in what way? How may such differences of notation be realized as differences of sound? The notion of enharmonic "equivalence," which smooths away such shadings, belongs to a 20th century atonal model: twelve-tone equal temperament. This system rasters the frequency glissando by constructing equal steps in the irrational proportion of vibration 1:12√2. Twelve successive steps divide an octave, at which interval the "pitch- classes" repeat their names. Their vertical combinations have been exhaustively demonstrated, most notably in Tom Johnson's Chord Catalogue. However, the actual sounding of pitches, tempered or not, always reveals a microtonally articulated sound continuum. Hearing out the complex tonal relations within it suggests a new exploration of harmony: composing intonations in writing, playing and hearing music. Morton Feldman recognized that this opening for composition is fundamentally a question of rethinking the notational image. In works composed for the most part between 1977 and 1985, inspired by his collaboration with violinist Paul Zukofsky, Feldman chose to distinguish between enharmonically spelled pitches. -
Information to Users
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 of 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. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road. Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9401223 Harmonic tonality in the theories of Jerome-Joseph Momigny Caldwell, Glenn Gerald, Ph.D. The Ohio State University, 1993 UMI 300 N.