DOCSLIB.ORG

1 a NEW MUSIC COMPOSITION TECHNIQUE USING NATURAL SCIENCE DATA D.M.A Document Presented in Partial Fulfillment of the Requiremen

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
1 a NEW MUSIC COMPOSITION TECHNIQUE USING NATURAL SCIENCE DATA D.M.A Document Presented in Partial Fulfillment of the Requiremen A NEW MUSIC COMPOSITION TECHNIQUE USING NATURAL SCIENCE DATA D.M.A Document Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Musical Arts in the Graduate School of The Ohio State University By Joungmin Lee, B.A., M.M. Graduate Program in Music The Ohio State University 2019 D.M.A. Document Committee Dr. Thomas Wells, Advisor Dr. Jan Radzynski Dr. Arved Ashby 1 Copyrighted by Joungmin Lee 2019 2 ABSTRACT The relationship of music and mathematics are well documented since the time of ancient Greece, and this relationship is evidenced in the mathematical or quasi- mathematical nature of compositional approaches by composers such as Xenakis, Schoenberg, Charles Dodge, and composers who employ computer-assisted-composition techniques in their work. This study is an attempt to create a composition with data collected over the course 32 years from melting glaciers in seven areas in Greenland, and at the same time produce a work that is expressive and expands my compositional palette. To begin with, numeric values from data were rounded to four-digits and converted into frequencies in Hz. Moreover, the other data are rounded to two-digit values that determine note durations. Using these transformations, a prototype composition was developed, with data from each of the seven Greenland-glacier areas used to compose individual instrument parts in a septet. The composition Contrast and Conflict is a pilot study based on 20 data sets. Serves as a practical example of the methods the author used to develop and transform data. One of the author’s significant findings is that data analysis, albeit sometimes painful and time-consuming, reduced his overall composing time. The variety and richness of data that exists from all academic areas and disciplines conceivably provide a rich reservoir of material from which to fashion compositions. As more composers ii explore this avenue of work, different methodologies will develop, and the value of works produced by this method will be evaluated. iii Dedicated to my wife, Hyejin iv ACKNOWLEDGMENTS I am heartily thankful to my advisor, Dr. Thomas Wells, who provided encouragement, guidance, and advice from beginning to end. Completing a DMA degree is a long journey, one which I would not have been able to achieve without his steadfast support and enthusiasm. I also would like to express my gratitude towards Dr. Jan Radzynski and Dr. Arved Ashby for their outstanding teaching and guidance. Furthermore I would like to express my gratitude to Dr. Seongsu Jeong who provided the scientific data for this study, and to my former mentors, Dr. David Gompper and Dr. Hyunsook Choi. I want to thank my wife Hyejin Hong and our family for their support and patience. Most of all I wish to give thanks to God for my musical gift, opportunities, blessings, and everything He has done for me. - Joungmin Lee v VITA April 18, 1975 ………………………………Born Kwangju, South Korea 2001…………………………….……………B.A. Church Music, Seoul Jangsin University, South Korea 2004……………………………….…………M.M. Computer Music, SangMyung University, South Korea 2010…………………………………….……M.M. Music Technology, New York University 2004……………………………………….…Lecturer of Computer Music/Recording, Changwon College, South Korea 2002-2005……………………………………Vice Director of Image Enterprise Inc. for Film, TV, Online Game, South Korea 2003-2005…………………………………....Lecturer of Composition/Computer Music Seoul Artist Music School Commercial Music Academy, South Korea 2010-2012……………………………………Lecturer of Composition/Computer Music Apple Bridge Academy. Annandale, VA 2011-2013……………………………………Director of Music, Annandale United Methodist Church, Annandale, VA vi 2013-2014……………………………………Director of Music, The Korean Choir of Greater Kansas City, KS 2016-Present…………………………………Director of Music, Bethel International United Methodist Church, Columbus, OH PUBLICATIONS 2016………………………………... CD by Editor Sconfinarte at XXI Century Archives, Milan string quartet ‘Vexatious’ 2016…………………………………CD by the 31st volume Series of the SCI CD for string quartet ‘Vexatious’ 2016…………………………………CD by ABLAZE Records on Electronic Masters Vol. 5 for 'Heterogeneous' 2016…………………………………CD by ABLAZE Records on Hong Kong New Music Ensemble Live from Prague Vol. 1 for string quartet ‘Vexatious’ 2018………………………………….CD by ABLAZE Records Electronic, Masters Series Vol. 7, ‘3 Sounds’ for fixed media 2019………………………………….Offered CD release by ABLAZE Records on Pierrot Ensemble Series Vol. 4 for 'Abandoned' vii FIELDS OF STUDY Major Field: Music Studies in Music Composition and Electroacoustic Dr. Thomas Wells Dr. Jan Radzynski Studies in Choral Conducting Dr. Robert J. Ward viii TABLE OF CONTENTS Abstract………………………………………………………………………….………...ii Dedication…………………………………………………………………………….…..iv Acknowledgements………………………………………………………………….…….v Vita………………………………………………………………………………….…….vi Publications………………………………………………………………………….…...vii Fields of Study………………………………………………………………….….…... viii Table of Contents………………………………………………………………………....ix List of Tables…………………………………………………………….……………...xiv List of Figures…………………………………………………………………………...xvi List of Picture…………………………………………………………………………..xvii List of Scores..………..………………………………………………………………..xviii Chapter 1. Introduction……………………………………………………………………1 Chapter 2. Music and Mathematics: Their Relatedness…………………………………...3 Part 1. Introduction…………………………………….………………………......……3 Part 2. Philosophy in Music History…………………….…...………………………….3 1. Ancient Greece and the Idea of Music…………………………………….….........4 2. Medieval Philosophy………….…………………………………...…………...…..4 ix 3. Premodern Music Philosophy………………………...……………...…………….5 3.1 Renaissance………………………………………...……………...…………...5 3.2 The 17th and 18th Centuries……………………………....……………….…..5 3.3 The 19th Century……………………………………….……….……………...6 3.4 Modern Music Philosophy……………………………….……….….……..…..7 Part 3. Overview other Works Related to Mathematics & Music………….….….….…8 1. Schillinger System of Musical Composition………………….……….……………8 1.1 Joseph Schillinger………………………………………………………………8 1.2 Joseph Schillinger and Scientific Principles……………………………………8 1.3 Inference………………………………………………………………………..9 2. Set Theory and Probability in Iannis Xenakis’s Herma…………………………..11 2.1 Iannis Xenakis………………………………………………………………...11 2.2 Herma…………………………………………………...…………………….12 Chapter 3. The Strengths and Weaknesses of the Use Scientific Data As a Compositional Resource……………..…..……………………………………………………………….14 Part 1. Strengths………………………………………………..……...………………14 1. Productivity………………………………………………………...……………..14 2. Cross-Genre Collaboration………………………………………...….…………..15 3. Composition with Software………………………….…...…………...…………..15 Part 2. Weaknesses……………………………………….………………...………….15 Chapter 4. Discussion of Electroacoustic & Acoustic Works by using Natural Science Data ……………………………………………………………………………………………16 x Part 1. Discussion, ‘Threatened By’, an Electroacoustic Work…………...……..….…16 1. Introduction…………………………………………………………...…………..16 2. Purpose…………….…………………………………………...…………………17 3. Discussion the Data in Graphics…….………………………...………………….17 3.1 The Velocity Data………………………...……………………...……..……..17 3.2 Discussion the Process of Music Composition………….…….………………19 3.3 Discussion about Composition Styles for Music inspired by Science Data ………………………………………………….…………………......………………….21 3.4 Discussion of Sine Waves……………………………………………………..21 4. Video……………………………….………...…………...………………………22 5. Discussion of Audience Reactions and Responses at the AGU Meeting………….23 6. Result………………………………………………...……………………....……24 Part 2. Analyses, “Contrast & Conflict”, a New Acoustic Work………….…….…….24 1. Introduction……………………………………………………………...….…….24 2. Purpose……………..…………………………………......………………………25 3. Method………..………………………………………………...……………...…26 3.1 Overview - Data Analysis………….………………………………………….26 3.2 Data for Helheim Area………………….……………………………………..26 3.3 Humboldt Area…………………………………….…………………....…….31 3.4 Jakobshavn Area………………………………….……………...……………37 3.5 Kangerdlugssuaq Area……………………………...…….…………………..40 3.6 Kongoscar Area………………………………….……….……………...……43 xi 3.7 Petermann Area………………………………….…………………...……….47 3.8 Upernavik Area………………………………….……………………...…….51 4. Discussion………………..…………………..……………………………...……54 4.1 Enharmonicity and the Autonomy of the Octave……….……………………..54 4.2 Atonal (in C)……………….……………………………………...…………..54 4.3 The Length of Notes……….…………………………………………...……..55 Chapter 5. Composition, Contrast & Conflict, a New Acoustic Work……………………56 1. Autonomy of the Octave…….…………………………………………………….56 2. Repetitive High-Pitch Sound……………..………….………………...………….57 3. Enharmonicity as Cure for Monotony……………..………………………………57 4. Use of Complex Rhythms………………..…………………………..…………...57 5. Performance Levels…………..……………………………………...……………57 6. Shortening Composition Time……………..………………………..……………58 7. Liquidity of Data Analysis………………..……………………………...………..58 8. Philosophy…………………..…………………………………………………….58 Chapter 6. Conclusions…………………………………………………………………...61 Bibliography…………………………………………………………………………….. 63 xii LIST OF TABLES Table 1. Base frequency and the frequency variation used for each glacier………..……19 Table 2. a: Value before round-off; b: value after post-decimal point round-off for the Helheim area……………….…………...…………………………………………..……27 Table 3. Frequencies of equal temperament……….……………………………….……27 Table 4. Frequency-to-musical note conversion for the Helheim area…………………..28 Table 5. Length of notes for the Helheim area………………………………..…………30 Table 6. Result of the pitch and length for the Helheim area…………..……..…………..31 Table 7. a: Value before round-off; b: value after post-decimal point round-off for the Humboldt
Load more

Recommended publications
  • Computer-Assisted Composition a Short Historical Review
    MUMT 303 New Media Production II Charalampos Saitis Winter 2010 Computer-Assisted Composition A short historical review Computer-assisted composition is considered amongst the major musical developments that characterized the twentieth century. The quest for ‘new music’ started with Erik Satie and the early electronic instruments (Telharmonium, Theremin), explored the use of electricity, moved into the magnetic tape recording (Stockhausen, Varese, Cage), and soon arrived to the computer era. Computers, science, and technology promised new perspectives into sound, music, and composition. In this context computer-assisted composition soon became a creative challenge – if not necessity. After all, composers were the first artists to make substantive use of computers. The first traces of computer-assisted composition are found in the Bells Labs, in the U.S.A, at the late 50s. It was Max Matthews, an engineer there, who saw the possibilities of computer music while experimenting on digital transmission of telephone calls. In 1957, the first ever computer programme to create sounds was built. It was named Music I. Of course, this first attempt had many problems, e.g. it was monophonic and had no attack or decay. Max Matthews went on improving the programme, introducing a series of programmes named Music II, Music III, and so on until Music V. The idea of unit generators that could be put together to from bigger blocks was introduced in Music III. Meanwhile, Lejaren Hiller was creating the first ever computer-composed musical work: The Illiac Suit for String Quartet. This marked also a first attempt towards algorithmic composition. A binary code was processed in the Illiac Computer at the University of Illinois, producing the very first computer algorithmic composition.
    [Show full text]
  • Chuck: a Strongly Timed Computer Music Language
    Ge Wang,∗ Perry R. Cook,† ChucK: A Strongly Timed and Spencer Salazar∗ ∗Center for Computer Research in Music Computer Music Language and Acoustics (CCRMA) Stanford University 660 Lomita Drive, Stanford, California 94306, USA {ge, spencer}@ccrma.stanford.edu †Department of Computer Science Princeton University 35 Olden Street, Princeton, New Jersey 08540, USA [email protected] Abstract: ChucK is a programming language designed for computer music. It aims to be expressive and straightforward to read and write with respect to time and concurrency, and to provide a platform for precise audio synthesis and analysis and for rapid experimentation in computer music. In particular, ChucK defines the notion of a strongly timed audio programming language, comprising a versatile time-based programming model that allows programmers to flexibly and precisely control the flow of time in code and use the keyword now as a time-aware control construct, and gives programmers the ability to use the timing mechanism to realize sample-accurate concurrent programming. Several case studies are presented that illustrate the workings, properties, and personality of the language. We also discuss applications of ChucK in laptop orchestras, computer music pedagogy, and mobile music instruments. Properties and affordances of the language and its future directions are outlined. What Is ChucK? form the notion of a strongly timed computer music programming language. ChucK (Wang 2008) is a computer music program- ming language. First released in 2003, it is designed to support a wide array of real-time and interactive Two Observations about Audio Programming tasks such as sound synthesis, physical modeling, gesture mapping, algorithmic composition, sonifi- Time is intimately connected with sound and is cation, audio analysis, and live performance.
    [Show full text]
  • An Exploration of the Relationship Between Mathematics and Music
    An Exploration of the Relationship between Mathematics and Music Shah, Saloni 2010 MIMS EPrint: 2010.103 Manchester Institute for Mathematical Sciences School of Mathematics The University of Manchester Reports available from: http://eprints.maths.manchester.ac.uk/ And by contacting: The MIMS Secretary School of Mathematics The University of Manchester Manchester, M13 9PL, UK ISSN 1749-9097 An Exploration of ! Relation"ip Between Ma#ematics and Music MATH30000, 3rd Year Project Saloni Shah, ID 7177223 University of Manchester May 2010 Project Supervisor: Professor Roger Plymen ! 1 TABLE OF CONTENTS Preface! 3 1.0 Music and Mathematics: An Introduction to their Relationship! 6 2.0 Historical Connections Between Mathematics and Music! 9 2.1 Music Theorists and Mathematicians: Are they one in the same?! 9 2.2 Why are mathematicians so fascinated by music theory?! 15 3.0 The Mathematics of Music! 19 3.1 Pythagoras and the Theory of Music Intervals! 19 3.2 The Move Away From Pythagorean Scales! 29 3.3 Rameau Adds to the Discovery of Pythagoras! 32 3.4 Music and Fibonacci! 36 3.5 Circle of Fifths! 42 4.0 Messiaen: The Mathematics of his Musical Language! 45 4.1 Modes of Limited Transposition! 51 4.2 Non-retrogradable Rhythms! 58 5.0 Religious Symbolism and Mathematics in Music! 64 5.1 Numbers are God"s Tools! 65 5.2 Religious Symbolism and Numbers in Bach"s Music! 67 5.3 Messiaen"s Use of Mathematical Ideas to Convey Religious Ones! 73 6.0 Musical Mathematics: The Artistic Aspect of Mathematics! 76 6.1 Mathematics as Art! 78 6.2 Mathematical Periods! 81 6.3 Mathematics Periods vs.
    [Show full text]
  • Chunking: a New Approach to Algorithmic Composition of Rhythm and Metre for Csound
    Chunking: A new Approach to Algorithmic Composition of Rhythm and Metre for Csound Georg Boenn University of Lethbridge, Faculty of Fine Arts, Music Department [email protected] Abstract. A new concept for generating non-isochronous musical me- tres is introduced, which produces complete rhythmic sequences on the basis of integer partitions and combinatorics. It was realized as a command- line tool called chunking, written in C++ and published under the GPL licence. Chunking 1 produces scores for Csound2 and standard notation output using Lilypond3. A new shorthand notation for rhythm is pre- sented as intermediate data that can be sent to different backends. The algorithm uses a musical hierarchy of sentences, phrases, patterns and rhythmic chunks. The design of the algorithms was influenced by recent studies in music phenomenology, and makes references to psychology and cognition as well. Keywords: Rhythm, NI-Metre, Musical Sentence, Algorithmic Compo- sition, Symmetry, Csound Score Generators. 1 Introduction There are a large number of powerful tools that enable algorithmic composition with Csound: CsoundAC [8], blue[11], or Common Music[9], for example. For a good overview about the subject, the reader is also referred to the book by Nierhaus[7]. This paper focuses on a specific algorithm written in C++ to produce musical sentences and to generate input files for Csound and lilypond. Non-isochronous metres (NI metres) are metres that have different beat lengths, which alternate in very specific patterns. They have been analyzed by London[5] who defines them with a series of well-formedness rules. With the software presented in this paper (from now on called chunking) it is possible to generate NI metres.
    [Show full text]
  • This Electronic Thesis Or Dissertation Has Been Downloaded from Explore Bristol Research
    This electronic thesis or dissertation has been downloaded from Explore Bristol Research, http://research-information.bristol.ac.uk Author: Vagopoulou, Evaggelia Title: Cultural tradition and contemporary thought in Iannis Xenakis's vocal works General rights Access to the thesis is subject to the Creative Commons Attribution - NonCommercial-No Derivatives 4.0 International Public License. A copy of this may be found at https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode This license sets out your rights and the restrictions that apply to your access to the thesis so it is important you read this before proceeding. Take down policy Some pages of this thesis may have been removed for copyright restrictions prior to having it been deposited in Explore Bristol Research. However, if you have discovered material within the thesis that you consider to be unlawful e.g. breaches of copyright (either yours or that of a third party) or any other law, including but not limited to those relating to patent, trademark, confidentiality, data protection, obscenity, defamation, libel, then please contact [email protected] and include the following information in your message: •Your contact details •Bibliographic details for the item, including a URL •An outline nature of the complaint Your claim will be investigated and, where appropriate, the item in question will be removed from public view as soon as possible. Cultural Tradition and Contemporary Thought in lannis Xenakis's Vocal Works Volume I: Thesis Text Evaggelia Vagopoulou A dissertation submitted to the University of Bristol in accordancewith the degree requirements of the of Doctor of Philosophy in the Faculty of Arts, Music Department.
    [Show full text]
  • Contributors to This Issue
    Contributors to this Issue Stuart I. Feldman received an A.B. from Princeton in Astrophysi- cal Sciences in 1968 and a Ph.D. from MIT in Applied Mathemat- ics in 1973. He was a member of technical staf from 1973-1983 in the Computing Science Research center at Bell Laboratories. He has been at Bellcore in Morristown, New Jersey since 1984; he is now division manager of Computer Systems Research. He is Vice Chair of ACM SIGPLAN and a member of the Technical Policy Board of the Numerical Algorithms Group. Feldman is best known for having written several important UNIX utilities, includ- ing the MAKE program for maintaining computer programs and the first portable Fortran 77 compiler (F77). His main technical interests are programming languages and compilers, software confrguration management, software development environments, and program debugging. He has worked in many computing areas, including aþbraic manipulation (the portable Altran sys- tem), operating systems (the venerable Multics system), and sili- con compilation. W. Morven Gentleman is a Principal Research Oftcer in the Com- puting Technology Section of the National Research Council of Canada, the main research laboratory of the Canadian govern- ment. He has a B.Sc. (Hon. Mathematical Physics) from McGill University (1963) and a Ph.D. (Mathematics) from princeton University (1966). His experience includes 15 years in the Com- puter Science Department at the University of Waterloo, ûve years at Bell Laboratories, and time at the National Physical Laboratories in England. His interests include software engi- neering, embedded systems, computer architecture, numerical analysis, and symbolic algebraic computation. He has had a long term involvement with program portability, going back to the Altran symbolic algebra system, the Bell Laboratories Library One, and earlier.
    [Show full text]
  • Exploring Xenakis Performance, Practice, Philosophy
    Exploring Xenakis Performance, Practice, Philosophy Edited by Alfia Nakipbekova University of Leeds, UK Series in Music Copyright © 2019 Vernon Press, an imprint of Vernon Art and Science Inc, on behalf of the author. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Vernon Art and Science Inc. www.vernonpress.com In the Americas: In the rest of the world: Vernon Press Vernon Press 1000 N West Street, C/Sancti Espiritu 17, Suite 1200, Wilmington, Malaga, 29006 Delaware 19801 Spain United States Series in Music Library of Congress Control Number: 2019931087 ISBN: 978-1-62273-323-1 Cover design by Vernon Press. Cover image: Photo of Iannis Xenakis courtesy of Mâkhi Xenakis. Product and company names mentioned in this work are the trademarks of their respective owners. While every care has been taken in preparing this work, neither the authors nor Vernon Art and Science Inc. may be held responsible for any loss or damage caused or alleged to be caused directly or indirectly by the information contained in it. Every effort has been made to trace all copyright holders, but if any have been inadvertently overlooked the publisher will be pleased to include any necessary credits in any subsequent reprint or edition. Table of contents Introduction v Alfia Nakipbekova Part I - Xenakis and the avant-garde 1 Chapter 1 ‘Xenakis, not Gounod’: Xenakis, the avant garde, and May ’68 3 Alannah Marie Halay and Michael D.
    [Show full text]
  • Iannis Xenakis, Roberta Brown, John Rahn Source: Perspectives of New Music, Vol
    Xenakis on Xenakis Author(s): Iannis Xenakis, Roberta Brown, John Rahn Source: Perspectives of New Music, Vol. 25, No. 1/2, 25th Anniversary Issue (Winter - Summer, 1987), pp. 16-63 Published by: Perspectives of New Music Stable URL: http://www.jstor.org/stable/833091 Accessed: 29/04/2009 05:06 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=pnm. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit organization founded in 1995 to build trusted digital archives for scholarship. We work with the scholarly community to preserve their work and the materials they rely upon, and to build a common research platform that promotes the discovery and use of these resources. For more information about JSTOR, please contact [email protected]. Perspectives of New Music is collaborating with JSTOR to digitize, preserve and extend access to Perspectives of New Music. http://www.jstor.org XENAKIS ON XENAKIS 47W/ IANNIS XENAKIS INTRODUCTION ITSTBECAUSE he wasborn in Greece?That he wentthrough the doorsof the Poly- technicUniversity before those of the Conservatory?That he thoughtas an architect beforehe heardas a musician?Iannis Xenakis occupies an extraodinaryplace in the musicof our time.
    [Show full text]
  • C:\Users\Hhowe\Dropbox\Courses
    Iannis Xenakis (1922-2001): Catalogue of Musical Compositions (from www.iannis-xenakis.org) Seven untitled pieces, Menuet, Air populaire, Allegro molto, Mélodie, Andante : 1949-50; piano, unpublished. Six Chansons : 1951; piano; 8’. Dhipli Zyia :1952; duo (vln, vlc); 5’30. Zyia :1952; 2 versions: a) soprano, men’s chorus (minimum 10) and duo (fl, pno); b) soprano, fl, pno; 10’. Trois poèmes : 1952; narrator and pno; unpublished. La colombe de la paix : 1953; alto and 4-voice mixed chorus; unpublished. Anastenaria. Procession aux eaux claires : 1953; mixed chorus (30), men chorus (15) and orchestra (62); 11’. Anastenaria. Le Sacrifice :1953; orchestra (51); 6’. Stamatis Katotakis, chanson de table : 1953; voice and 3-voice men chorus; unpublished. Metastasis : 1953-4; orchestra (60); 7’ Pithoprakta :1955-6; string orchestra (46), 2 trb and perc; 10’ Achorripsis :1956-7; orchestra (21); 7’ Diamorphoses :1957-8; electroacoustic tape. 7’. Concret PH :1958; electroacoustic tape; 2’45". Analogiques A & B :1958-9; string ensemble (9) and electroacoustic tape; 7’30". Syrmos :1959; string ensemble (18 or 36); 14". Duel :1959; 2 orchestras (56 total) and 2 conductors; variable duration (circa 10’). Orient-Occident :1960; electroacoustic tape; 12’. Herma : 1961; for solo piano; 10’ ST/48,1-240162 :1956-62); orchestra (48); 11’ ST/10, 1-080262 : 1956-62; ensemble (10); 12’ ST/4, 1-080262 : 1956-62; string quartet; 11’ Morsima - Amorsima (ST/4, 2-030762) :1956-62); quartet (pno, vln, vlc, db); 11’ Atrées (ST/10, 3-060962) : 1956-62; ensemble (11); 15’. Stratégie : 1962; 2 orchestras (82 total) and 2 conductors; variable duration (10 to 30’) Polla ta dhina :1962; children's chorus (20) and orchestra (48); 6’ Bohor :1962; electroacoustic tape; 21’30".
    [Show full text]
  • The Euclidean Algorithm Generates Traditional Musical Rhythms
    The Euclidean Algorithm Generates Traditional Musical Rhythms Godfried Toussaint∗ School of Computer Science, McGill University Montreal,´ Quebec,´ Canada [email protected] Abstract The Euclidean algorithm (which comes down to us from Euclid’s Elements) computes the greatest com- mon divisor of two given integers. It is shown here that the structure of the Euclidean algorithm may be used to generate, very efficiently, a large family of rhythms used as timelines (ostinatos), in sub-Saharan African music in particular, and world music in general. These rhythms, here dubbed Euclidean rhythms, have the property that their onset patterns are distributed as evenly as possible. Euclidean rhythms also find application in nuclear physics accelerators and in computer science, and are closely related to several families of words and sequences of interest in the study of the combinatorics of words, such as Euclidean strings, to which the Euclidean rhythms are compared. 1. Introduction What do African rhythms, spallation neutron source (SNS) accelerators in nuclear physics, string theory (stringology) in computer science, and an ancient algorithm described by Euclid have in common? The short answer is: patterns distributed as evenly as possible. For the long answer please read on. Mathematics and music have been intimately intertwined since the days of Pythagoras. However, most of this interaction has been in the domain of pitch and scales. For some historical snapshots of this interaction the reader is referred to H. S. M. Coxeter’s delightful account [9]. Rhythm, on the other hand has been his- torically mostly ignored. Here we make some mathematical connections between musical rhythm and other areas of knowledge such as nuclear physics and computer science, as well as the work of another famous ancient Greek mathematician, Euclid of Alexandria.
    [Show full text]
  • Cellular Automata in Xenakis' Music. Theory and Practice
    CELLULAR AUTOMATA IN XENAKIS’ MUSIC. THEORY AND PRACTICE Makis Solomos Université Montpellier 3, Institut Universitaire de France [email protected] In Makis Solomos, Anastasia Georgaki, Giorgos Zervos (eds.), Definitive Proceedings of the International Symposium Iannis Xenakis (Athens, May 2005). Paper first published in A. Georgaki, M. Solomos (eds.), International Symposium Iannis Xenakis. Conference Proceedings, Athens, May 2005, p. 120-138. This paper was selected for the Definitive Proceedings by the scientific committee of the symposium: Anne-Sylvie Barthel-Calvet (France), Agostino Di Scipio (Italy), Anastasia Georgaki (Greece), Benoît Gibson (Portugal), James Harley (Canada), Peter Hoffmann (Germany), Mihu Iliescu (France), Sharon Kanach (France), Makis Solomos (France), Ronald Squibbs (USA), Georgos Zervos (Greece) This paper is dedicated to Agostino Di Scipio, Peter Hoffmann and Horacio Vaggione. The English version, edited here, has not been revised. ABSTRACT Cellular automata are developed since some decades, belonging to the field of abstract automata. In the beginning of the 1980s, they were popularized in relationship with the study of dynamic systems and chaos theories. They were also applied for modelling the evolution of natural systems (for instance biological ones), especially in relationship with the idea of auto-organization. From the end of the 1980s since nowadays, several composers begin to use cellular automata. Xenakis must have been one of the first (or the first), as he used them, probably for the first time, in Horos (1986), so as to produce harmonic progressions and new timbre combinations. His use of cellular automata seems to be limited. This paper has three aims: 1. To try to understand the reasons why Xenakis used cellular automata.
    [Show full text]
  • The Distance Geometry of Music
    The Distance Geometry of Music Erik D. Demaine∗ Francisco Gomez-Martin† Henk Meijer‡ David Rappaport§ Perouz Taslakian¶ Godfried T. Toussaint§k Terry Winograd∗∗ David R. Wood†† Abstract We demonstrate relationships between the classical Euclidean algorithm and many other fields of study, particularly in the context of music and distance geometry. Specifically, we show how the structure of the Euclidean algorithm defines a family of rhythms that encompass over forty timelines (ostinatos) from traditional world music. We prove that these Euclidean rhythms have the mathematical property that their onset patterns are distributed as evenly as possible: they maximize the sum of the Euclidean distances between all pairs of onsets, viewing onsets as points on a circle. Indeed, Euclidean rhythms are the unique rhythms that maximize this notion of evenness. We also show that essentially all Euclidean rhythms are deep: each distinct distance between onsets occurs with a unique multiplicity, and these multiplicities form an interval 1, 2, . , k − 1. Finally, we characterize all deep rhythms, showing that they form a subclass of generated rhythms, which in turn proves a useful property called shelling. All of our results for musical rhythms apply equally well to musical scales. In addition, many of the problems we explore are interesting in their own right as distance geometry problems on the circle; some of the same problems were explored by Erd˝osin the plane. ∗Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology,
    [Show full text]