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Symmetry in Music As a Stylistic Index for the Transition from the Middle Ages to the Renaissance, Arthur L

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Symmetry in Music As a Stylistic Index for the Transition from the Middle Ages to the Renaissance, Arthur L Symmetry: The Quarterly of the International Society for the Interdisciplinary Study of Symmetry (ISIS-Symmetry) Volume 9, Numbers 1 - 2, 1999 INTERNATIONAL SOCIETY FOR THE INTERDISCIPLINARY STUDY OF SYMMETRY (ISIS-SYMMETRY) President Members of the Board D~nes Nagy, Institute of Applied Physics, Liz Ashburn, School of Art, College of Fine Arts, University of Tsukuba, Tsukuba 305, Japan; The University of New South Wales, P.O.B. 259, [email protected] ac jp Paddington, NSW 2021, Australia, e [email protected] au Chatrman of the Advisory Board Arthur L. Loeb, Carpenter Center for the Vxsual Siglind Bruhn, Department of Musicology and Arts, Harvard University, Cambridge, MA 02138, Institute for the Humamties, University of U.S.A, alloeb @ fas harvard edu M~chigan, 1105 Spring St, Ann Arbor, M148103, U.S A.; [email protected] Honorary Presidents Ted Goranson, Sirius Beta Inc., 1976 Munden Konstantin V. Frolov, Institute of Mechanical Point, Virginia Beach, VA 23457-1227, U.S.A., Engineering, Russian Academy of Sciences, Malyl tedg@sirius-beta com Hanton’evskix per. 4, 101830 Moscow, Russia and Laurence I. Gould, Physics Department, Dana Yuval Ne’eman, M. and R. Saclder Institute of Hall 230, University of Hartford, 200 Bloomfield Advanced Studies, Tel-Aviv Umvers~ty, Ramat- Avenue, West Hartford, CT 06117, U.S.A ; Aviv, Tel-Aviv, 69978, Israel; lgould@mail hartford.edu MatddaE@tauex tau.ac.il, and Center for particle Physics, University of Texas, Austin, TX 78712, Claudio Guerri, Facultad de Arquitectura, Disefio U S.A. y Urbanlsmo, Universidad de Buenos Aires, Olleros 2532 2~A - (1426) Buenos Aires, Honorary Members Argentina; claudioguerri@amet com.ar Johann Jakob Burckhardt (Zurich, Switzerland) Harold S. M. Coxeter (Toronto, Canada) Slavik Vo Jablan, Mathematical Institute, Knez Istv~in Hargittai (Budapest, Hungary; Mihailova, 35, pp. 367, 11001 Belgrade, hargittm @tki aak.bme.hu) Yugoslavia; jablans@mJ sanu.ac.yu Kodi Husimi (Tokyo, Japan) Vladimir A. Koptsik (Moscow, Russia; Sergei Petoukhov, Institute of Mechanical kopts~k @polly phys.msu.su) Engineering, Russian Academy of Sciences, Malyi Dan Shechtman (Haifa, Israel; Hadton’evskii per. 4, 101830 Moscow, Russia; mtrdan@techunix technion ac d) petoukhov @hotmail.com Passed away Honorary Members Janusz Rebielak, Department of Arclutecture, Cyril Smith (U,S.A.) Faculty of Bmldxng Structures, Technical llarion I. Shafranovsldi (Russia) University of Wroctaw, ul. B. Prusa 53/55, PL 50- Victor A. Frank-Kamenetsky (Russxa) 317 Wroctaw, Poland; Eugene P. Wigner (U.S.A.) j anusz@ novell.arch.pwr.wroc.pl Heinrich Heesch (Germany) lnformatton Network Advisor Secretary General Mihfily Szoboszlai, Department of Architectural Gyiirgy Darvas, Symmetrion, and Institute for Representation, Faculty of Architecture, Technical Research Orgamsation of the Hungarian Academy University of Budapest,, 3 Miiegyetem rkp, of Sciences, 18 Nfidor St, P.O.Box 994, Budapest, Budapest, H-I 111 Hungary; H- 1245 Hungary, darvasg @helka.i~f.hu szoboszlm @ arch bme hu See th~ Advisory Board inside back cover Symmetry: Founding editors: G. Darvas and D. Nagy The Quarterly of the International Society for the Interdisciplinary Study of Symmetry (ISIS-Symmetry) Temporarily edited by the curatory of the International Symmetry Foundation Published by the International Symmetry Foundation Volume 10, Numbers1 - 2, 1-208, 1999 SPECIAL ISSUE: CHAPTERS FROM THE HISTORY OF SYMMETRY Edited by Gy~rgy Darvas CONTENTS EDITORIAL 3 ¯ Introduction, Gy6rgy Darvas 5 SYMMETRY." ART AND SCIENCE ,~ ¯ The concept of symmetry in early Renaissance art theory. Leon Battista Alberti, De pictura, Gdbor Hajn6czi ~" 7 ¯ Mean, proportion and symmetry in Greek and Renaissance art, Clara Silvia Roero 17 ¯ Symmetry in music as a stylistic index for the transition from the Middle Ages to the Renaissance, Arthur L. Loeb 49 ¯ The concept of the mass form within the context of visual art and architecture of the Italian Renaissance, Irina Guletsky 69 ¯ Symmetry in music: A historical perspective, Dalia Cohen and Judith Cohen 89 SYMMETRY: SCIENCE AND ART ¯ The emergence of symmetry concepts by the way of the study of crystals (1600-1900), Louis Bonpunt 127 ¯ Symmetry as the leitmotif at the fundamental level in the twentieth century physics, Yuval Ne’eman .. 143 ¯ Symmetry as key-notion in the interre.lationship between science and constructivist art, Fr~ Ilgen 163 ¯ Geometries in the East and the West in the 19th century, Hiroshi Okumura 189 BOOK REVIEW 199 ¯ Cover image: Geometric computer graphics art by Sdndor Kabai 201 SYMMETRY: CULTURE AND SCIENCE is published and edited by the International Symmetry Foundation. Its Editorial Board coincides with the Board and Advisory Board of the International Society for the Interdisciplinary Study of Symmetry (ISIS- Symmetry). The views expressed are those of individual authors, and not necessarily shared by the Society or the editors. Curatory of the International Symmetry Foundation: Szaniszl6 B6rczi (head), J~inos F. Btihm, GySrgy Darvas, S~indor Kabai Any correspondence should be addressed to the International Symmetry Foundation c/o Symmetrion P.O. Box 994, Budapest, H-1245 Hungary Phone: 36-1-331-8326 Fax: 36-1-331-3161 E-mail: [email protected], [email protected], [email protected], Assistant Editor: Csaba Mezei Subscription: Annual membership fee of the Society: Benefactors, US$780.00; Ordinary Members, US$78.00 (includes the subscription to the journal), Student Members, US$63.00 (includes the subscription to the journal); Institutional Members, please contact the Secretary General. Annual subscription rate for non-members: US$100.00. Make checks payable to ISIS-Symmetry and mail to G. Darvas, Secretary General, or transfer to the following account number: ISIS-Symmetry, International Symmetry Foundation, 10300002-50400004-21004015, Hungarian Foreign Trade Bank, Budapest, Szt. Istv~in t~r 11, H-1821 Hungary; Swift MKKB HU HB. Checks and transfers in Euro (90.00 for Ordinary Members) are also accepted. © International Symmetry Foundation. No part of this publication may be reproduced without written permission from the publisher. ISSN 0865-4824 Cover layout: G0nter Schmitz; Images on the front and back covers: Rhombtc trtacontahedron and rhombic hexacontahedron combinattons by Sfindor Kabai Ambigram on the back cover: Douglas R. Hofstadter 25437 Akaprint Kft. F. v.. Freier Lhszl6 Symmetry: Culture and Sctence VoL 10, Nos. 1-2, 3, 1999 EDITORIAL This issue publishes a few of the papers presented in the Special Session History of Symmetry in the Sciences, Technology, and the Arts at the XXth International Congress of History of Science, held in Liege, Belgium, 22nd July 1997. The session was organised by the editor of this issue. He elaborated the concept, the structure of the session, to which he selected and invited individually the lecturers. This issue publishes nine of the papers presented at the session. This booklet picks out a few chapters from the history of symmetry, according to the concept described by the issue editor in the Introduction on the next pages. Let us express our hope that further chapters will follow in later issues. Just one year passed since the curatory of the Foundation took over the editorship of the journal. We edited two and a half volumes during these 12 months. We hope to continue the work at a similar pace to regain your faith. February, 2002 Symmetry: Culture and Sctence Vol 10, Nos 1-2, 5-6, 1999 INTRODUCTION History of Symmetry in the Sciences and the Arts Chapters from the history of symmetry Traditional approach in history of science focuses either to a discipline in a period, or to the works of a certain person. We followed a different path. We aimed at the role of a phenomenon, the evolution of a concept and its applications in different disciplines both in the arts and the sciences. This concept and phenomenon was symmetry. The historical role of symmetry can be investigated in two dimensions. One can investigate it in different historical periods, starting with the Ancient times, through the Middle ages, the Renaissance, the Baroque, and the Romantics, up to the Modern age (temporal axis). The different disciplines form an other dimension of the investigation. One can study the role of symmetry in Physics, Chemistry, Biology, Technology, and other sciences, as well as in Literature, Linguistics, Philosophy, and other humanities, and also in Fine arts, Design, Music, Dance, etc., (disciplinary axis). Any of the two dimensions can demonstrate only a narrow slice of the subject. The concept of symmetry and its applications within a given discipline changed during the centuries. On the other side, the appearance of symmetry in a discipline in different periods has never been intact from influences of the usage of the term and applications in other disciplines. Moreover, the essence of symmetry can be understood only in its interdisciplinary character. This interdisciplinary character means, that our interest is concentrated on how this phenomenon could mediate methods and ideas among the arts and the sciences, among disciplines, among cultures. Therefore, the authors of this collection were asked by the editor to place the subject of their papers along the diagonal between the two axes. The sequence of the papers in this issue follows more or less this line. 6 [NTR OD UCTION The first papers start from the Renaissance. G. Hajn6czi investigated how the ancient notion of symmetry took its roots in the Renaissance of the European culture, and appeared in the modern languages. S. Roero compared the treatment of the phenomenon in the Greek and in the Renaissance science and art. A. Loeb studied the same questions through the development of the composition of music, while L Guletsky compared the role of symmetry in Renaissance architecture, music and also in visual art. D. Cohen and J. Cohen dealt with the role of symmetry in music in later periods. L. Bonpunt investigated how symmetry became the subject of the exact sciences on the example of the development of crystallography.
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