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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. -
Ideazione E Coordinamento Della Programmazione a Cura Di Massimo Di Pinto Con La Collaborazione Di Leonardo Gragnoli
Ideazione e coordinamento della programmazione a cura di Massimo Di Pinto con la collaborazione di Leonardo Gragnoli gli orari indicati possono variare nell'ambito di 4 minuti per eccesso o difetto Martedì 7 febbraio 2017 00:00 - 02:00 euroclassic notturno schubert, franz (1797-1828) sei danze tedesche (D 820) orchestraz di anton webern dall'orig. per pf. in la bem mag - in la bem mag - in la bem mag - in si bem mag - in si bem mag - in si bem mag. luxembourg philharmonic orch dir. justin brown (reg. lussemburgo, 20/12/1996) durata: 8.56 RSL radio televisione lussemburghese larsson, lars-erik (1908-1986) croquiser, sei schizzi per pf op. 38 capriccioso - grazioso - semplice - scherzando - espressivo - ritmico. marten landström, pf durata: 11.59 SR radio svedese bruch, max (1838-1920) kol nidrei, per vcl e orch op. 47 adam krzeszowiec, vcl; polish radio symphony orch dir. lukasz borowicz (reg. varsavia, 21/04/2013) durata: 12.26 PR radio polacca poulenc, francis (1899-1963) sept chansons per coro la blanche neige - à peine défigurée - par une nuit nouvelle - tous les droits - belle et ressemblante - marie - luire. jutland chamber choir dir. mogens dahl durata: 12.59 DR radiotelevisione di stato danese händel, georg friedrich (1685-1759) concerto in si bem mag per arpa e orch op. 4 n. 6 (HWV 294) andante, allegro - larghetto - allegro moderato. sofija ristic, arpa; slovenian radio television symphony orch dir. pavle despalj durata: 13.06 RTVS radiotelevisione slovena elgar, edward (1857-1934) sea pictures op. 37 sea slumber song - in haven - sabbath morning at sea - where corals lie - the swimmer. -
FRENCH SYMPHONIES from the Nineteenth Century to the Present
FRENCH SYMPHONIES From the Nineteenth Century To The Present A Discography Of CDs And LPs Prepared by Michael Herman NICOLAS BACRI (b. 1961) Born in Paris. He began piano lessons at the age of seven and continued with the study of harmony, counterpoint, analysis and composition as a teenager with Françoise Gangloff-Levéchin, Christian Manen and Louis Saguer. He then entered the Paris Conservatory where he studied with a number of composers including Claude Ballif, Marius Constant, Serge Nigg, and Michel Philippot. He attended the French Academy in Rome and after returning to Paris, he worked as head of chamber music for Radio France. He has since concentrated on composing. He has composed orchestral, chamber, instrumental, vocal and choral works. His unrecorded Symphonies are: Nos. 1, Op. 11 (1983-4), 2, Op. 22 (1986-8), 3, Op. 33 "Sinfonia da Requiem" (1988-94) and 5 , Op. 55 "Concerto for Orchestra" (1996-7).There is also a Sinfonietta for String Orchestra, Op. 72 (2001) and a Sinfonia Concertante for Orchestra, Op. 83a (1995-96/rév.2006) . Symphony No. 4, Op. 49 "Symphonie Classique - Sturm und Drang" (1995-6) Jean-Jacques Kantorow/Tapiola Sinfonietta ( + Flute Concerto, Concerto Amoroso, Concerto Nostalgico and Nocturne for Cello and Strings) BIS CD-1579 (2009) Symphony No. 6, Op. 60 (1998) Leonard Slatkin/Orchestre National de France ( + Henderson: Einstein's Violin, El Khoury: Les Fleuves Engloutis, Maskats: Tango, Plate: You Must Finish Your Journey Alone, and Theofanidis: Rainbow Body) GRAMOPHONE MASTE (2003) (issued by Gramophone Magazine) CLAUDE BALLIF (1924-2004) Born in Paris. His musical training began at the Bordeaux Conservatory but he went on to the Paris Conservatory where he was taught by Tony Aubin, Noël Gallon and Olivier Messiaen. -
Mozart's Die Zauberflöte: a Kingdom of Notes and Numbers
MOZART’S DIE ZAUBERFLÖTE: A KINGDOM OF NOTES AND NUMBERS by Daemon Garafallo A Thesis Submitted to the Faculty of The Dorothy F. Schmidt College of Arts and Letters In Partial Fulfillment of the Requirements for the Degree of Master of Arts Florida Atlantic University Boca Raton, FL May 2016 Copyright 2016 by Daemon Garafallo ii ACKNOWLEDGMENTS The author wishes to express his thanks to his committee members for their guidance, especially to his thesis advisor, Dr. Ken Keaton, for helping the author through a difficult time these past few years, and to Dr. Sandra McClain for going above and beyond in her dual role of committee member and academic advisor and for doing an excellent job at both. He also would like to acknowledge Dr. James Cunningham for his help and guidance throughout his degree. iv ABSTRACT Author: Daemon Garafallo Title: Mozart’s Die Zauberflöte: A Kingdom of Notes and Numbers Institution: Florida Atlantic University Thesis Advisor: Dr. Ken Keaton Degree: Master of Arts Year: 2016 Wolfgang Amadeus Mozart composed Die Zauberflöte in the last year of his life. It was intended in part to glorify Freemasonry as a new Emperor, more hostile to the Masons, took his office. After a brief survey of his life and works, this paper shows how Mozart used number symbolism in the opera, and will equip the reader with an understanding of this as practiced by the Freemasons. Further, it will show how Mozart associated the characters of the opera with specific musical tones. It will expose a deeper understanding of the question of meaning in word and text in his opera. -
Medieval Music in Practice Studies in Honor of RICHARD CROCKER Medieval Music in Practice Studies in Honor of Medieval Music in Practice Richard Crocker
CrockerCover_v16a_MISCCover2013 5/2/13 3:13 PM Page 1 MISC $60.00 8 8 Miscellanea Medieval Music in Practice Studies in Honor of RICHARD CROCKER RICHARD of Honor in Studies Practice in Music Medieval Studies in Honor of Medieval Music in Practice Richard Crocker Richard Crocker once wrote “we understand many things about the history of music—specifically its development—better from the earlier periods.” Since his first publications in 1958, Crocker pio neered a radically phenomenological and critical approach to the study of early music and musical style. Medieval Music in Practice: Studies in Honor Studies in Honor of of Richard Crocker brings together eleven essays that take up Crocker’s call to consider the conti nuity of medieval and later musical practices in Photo (c) Kathleen Karn Richard Crocker performance, composition, and pedagogy. Two in troductory essays open this collection. Judith Peraino surveys the disciplinary questions that RICHARD LINCOLN CROCKER was born Feb Edited by emerge in Crocker’s work: What constitutes a co ruary 17, 1927 in Roxbury Massachusetts, and Judith A. Peraino herent category of music? What are the “ruling attended Yale University, receiving a B.A. (1950) ideas” of musicology? Richard Taruskin pays trib and a Ph.D. (1957) with a dissertation on “The ute to Crocker’s remarkable prescience in the Repertoire of Proses at St Martial de Limoges 1960s of antiessentialist and antiuniversalist ar (Tenth and Eleventh Centuries),” directed by Leo guments that characterized “new musicology” in Schrade. Crocker taught at Yale from 1955 until the 1980s. 1963, and at the University of California, Berkeley, Nine further essays focus on repertories from from 1963 until his retirement in 1994. -
GOLDBERG VARIATIONS - English Suite No
BHP 901 - BACH: GOLDBERG VARIATIONS - English Suite No. 5 in e - Millicent Silver, Harpsichord _____________________________________________________________________________________________________________________ This disc, the first in our Heritage Performances Series, celebrates the career and the artistry of Millicent Silver, who for some forty years was well-known as a regular performer in London and on BBC Radio both as soloist and as harpsichordist with the London Harpsichord Ensemble which she founded with her husband John Francis. Though she made very few recordings, we are delighted to preserve this recording of the Goldberg Variations for its musical integrity, its warmth, and particularly the use of tonal dynamics (adding or subtracting of 4’ and 16’ stops to the basic 8’) which enhances the dramatic architecture. Millicent Irene Silver was born in South London on 17 November 1905. Her father, Alfred Silver, had been a boy chorister at St. George’s Chapel, Windsor where his singing attracted the attention of Queen Victoria, who had him give special performances for her. He earned his living playing the violin and oboe. His wife Amelia was an accomplished and busy piano teacher. Millicent was the second of their four children, and her musical talent became evident in time-honoured fashion when she was discovered at the age of three picking out on the family’s piano the tunes she had heard her elder brother practising. Eventually Millicent Silver won a scholarship to the Royal College of Music in London where, as was more common in those days, she studied equally both piano and violin. She was awarded the Chappell Silver Medal for piano playing and, in 1928, the College’s Tagore Gold Medal for the best student of her year. -
Kammerakademie Potsdam Trevor Pinnock Emmanuel Pahud
Kammerakademie Potsdam Orquestra de Câmara de Potsdam Trevor Pinnock regência Emmanuel Pahud flauta O MINISTÉRIO DA CULTURA, O GOVERNO DO ESTADO DE SÃO PAULO, A SECRETARIA DA CULTURA E A CULTURA ARTÍSTICA APRESENTAM MOMENTO MUSICAL Momento Musical do Le Concert de la Loge (foto Heloisa Bortz) Você conhece o Momento Musical? Sempre às 20h, antes de cada concerto da Temporada Cultura Artística, o jornalista e crítico musical Irineu Franco Perpetuo comenta de forma descontraída sobre os compositores, as obras e os intérpretes que se apresentam naquela noite. Participe deste encontro! realização MINISTÉRIO DA CULTURA Anúncio Momento Musical FINAL.indd 1 19/05/17 10:16 O Ministério da Cultura, o Governo do Estado de São Paulo, a Secretária da Cultura e a Cultura Artística apresentam Kammerakademie Potsdam Orquestra de Câmara de Potsdam Trevor Pinnock regência Emmanuel Pahud flauta PATROCÍNIO REALIZAÇÃO Gioconda Bordon 3 Programa 4 Notas sobre o programa 6 Mônica Lucas Biografias 13 SOCIEDADE DE CULTURA ARTÍSTICA DIRETORIA PRESIDENTE Antonio Hermann D. Menezes de Azevedo VICE-PRESIDENTE Gioconda Bordon DIRETORES Carlos Mendes Pinheiro Júnior, Fernando Lohmann, Gioconda Bordon, Ricardo Becker, Rodolfo Villela Marino SUPERINTENDENTE Frederico Lohmann CONSELHO DE ADMINISTRAÇÃO PRESIDENTE Fernando Carramaschi VICE-PRESIDENTE Roberto Crissiuma Mesquita CONSELHEIROS Antonio Hermann D. Menezes de Azevedo, Carlos José Rauscher, Francisco Mesquita Neto, Gérard Loeb, Henri Philippe Reichstul, Henrique Meirelles, Jayme Sverner, Marcelo Kayath, Milú Villela, -
The Aquitanian Sacred Repertoire in Its Cultural Context
THE AQUITANIAN SACRED REPERTOIRE IN ITS CULTURAL CONTEXT: AN EXAMINATION OF PETRI CLA VIGER! KARl, IN HOC ANNI CIRCULO, AND CANTUMIRO SUMMA LAUDE by ANDREA ROSE RECEK A THESIS Presented to the School ofMusic and Dance and the Graduate School ofthe University of Oregon in partial fulfillment ofthe requirements for the degree of Master of Arts September 2008 11 "The Aquitanian Sacred Repertoire in Its Cultural Context: An Examination ofPetri clavigeri kari, In hoc anni circulo, and Cantu miro summa laude," a thesis prepared by Andrea Rose Recek in partial fulfillment ofthe requirements for the Master ofArts degree in the School ofMusic and Dance. This thesis has been approved and accepted by: Dr. Lori Kruckenberg, Chair ofth xamining Committee Committee in Charge: Dr. Lori Kruckenberg, Chair Dr. Marc Vanscheeuwijck Dr. Marian Smith Accepted by: Dean ofthe Graduate School 111 © 2008 Andrea Rose Recek IV An Abstract ofthe Thesis of Andrea Rose Recek for the degree of Master ofArts in the School ofMusic and Dance to be taken September 2008 Title: THE AQUITANIAN SACRED REPERTOIRE IN ITS CULTURAL CONTEXT: AN EXAMINATION OF PETRI CLA VIGER! KARl, INHOC ANNI CIRCULO, AND CANTU MIRa SUMMA LAUDE Approved: ~~ _ Lori Kruckenberg Medieval Aquitaine was a vibrant region in terms of its politics, religion, and culture, and these interrelated aspects oflife created a fertile environment for musical production. A rich manuscript tradition has facilitated numerous studies ofAquitanian sacred music, but to date most previous research has focused on one particular facet of the repertoire, often in isolation from its cultural context. This study seeks to view Aquitanian musical culture through several intersecting sacred and secular concerns and to relate the various musical traditions to the region's broader societal forces. -
Trevor Pinnock Journey
TREVOR PINNOCK JOURNEY Two Hundred Years of Harpsichord Music TREVOR PINNOCK JOURNEY Two Hundred Years of Harpsichord Music ANTONIO DE CABEZÓN (c.1510–1566) GIROLAMO FRESCOBALdi (1583–1643) 1. Diferencias sobre 15. Toccata nona ................................ 4:32 ‘El canto del caballero’ .................. 3:10 16. Balletto primo e secondo .............. 5:39 from Toccate d’intavolatura di cimbalo et WILLIAM BYRD (c.1540–1623) organo,1637 2. The Carman’s Whistle .................. 3:58 GEORGE FRIDERIC HAndel (1685–1759) THOMAS TaLLIS (c.1505–1585) 17. Chaconne in G major, HWV 435 ... 6:36 3. O ye tender babes ........................ 2:37 DOMENICO SCARLAtti (1685–1757) JOHN Bull (1562/3–1628) Three Sonatas in D major, K. 490–92 4. The King’s Hunt ............................ 3:25 18. Sonata, K. 490: Cantabile ............ 5:02 JAN PIETERSZOON SWEELINCK 19. Sonata, K. 491: Allegro ................ 4:57 (1562–1621) 20. Sonata, K. 492: Presto ................. 4:17 5. Variations on ‘Mein junges Leben hat ein End’, SwWV 324 .............. 6:10 Total Running Time: 68 minutes JOHANN SEBASTIAN BACh (1685–1750) French Suite No. 6 in E major, BWV 817 6. Prélude ......................................... 1:31 7. Allemande .................................... 3:28 8. Courante ...................................... 1:47 9. Sarabande ................................... 3:22 10. Gavotte ........................................ 1:07 11. Polonaise ...................................... 1:20 12. Bourrée ........................................ 1:41 13. -
The First Mirror Inside the Contrapunctus 6 of the Art of Fugue by Johann Sebastian Bach (BWV 1080, 6) 1
The First Mirror inside the Contrapunctus 6 of the Art of Fugue by Johann Sebastian Bach (BWV 1080, 6) 1 Konstantinos G. Alevizos Abstract Johann Sebastian Bach had already elaborated the tool of double inversion, inside the Contrapunctus “in stylo francese” of the Art of Fugue. However, the counterpoint tool of double inversion is typical for the two later pairs of fugues BWV 1080, 12-13 a, b. After an examination of the global asset of the Contrapunctus 6, a particular attention is shown to the technique of inversion (mirror) in relation to fugues 12 and 13. Consequently a brief, but methodical, analysis succeeds to demonstrate the existence of totally symmetrical thematic phases inside Contrapunctus 6. The existence of double inversion inside an earlier Contrapunctus can indicate the level of premeditated elaboration in the whole work. Additionally, it could also suppose a parallel or contiguous time of the compositional process among the BWV 1080, 6, 12 and 13, which could re-impose a new examination of the correct order of the Contrapuncti. Keywords: analysis; Johann Sebastian Bach; fugue; inversion; mirror. Résumé Cet article veut démontrer que Jean-Sébastien Bach avait déjà élaboré l’outil d’inversion complète (miroir) à l’intérieur du Contrapunctus in stylo francese de L’art de la fugue (BWV 1080, 6). L’outil de contrepoint de l’inversion complète est typique pour les deux paires ultérieures de fugues BWV 1080, 12-13 a, b. L’existence de l’inversion complète à l’intérieur d’un Contrapunctus antérieur (en relation avec les deux paires postérieurs) peut indiquer le niveau de préméditation dans l’élaboration du matériau de l’intégralité du recueil, en particulier dans la mesure où la notion de progression de complexité technique est concernée. -
MTO 3.4: Meeus, Music Theory and Analysis in France and Belgium
Volume 3, Number 4, July 1997 Copyright © 1997 Society for Music Theory Nicolas Meeus KEYWORDS: theory, analysis, France, Belgium, Europe, conservatory, university, Schenker ABSTRACT: The organizers of the forthcoming Fourth European Congress for Music Analysis decided to devote one of its sessions to European traditions and usages concerning theory and analysis. Some of my ideas on this topic are developed, with special reference to societies for analysis, journals, music education, and the reception of Schenker in France. 1. Introduction 2. European Societies and the European Congresses for Music Analysis 3. Journals 4. Music Education 5. The Reception of Schenker 6. Semiology 7. Conclusion 1. Introduction [1.1] Theory and analysis have known a fast development in Continental Europe during the last twenty years. Yet, for many reasons, the situation here remains quite different from what it is in English speaking countries. After the Third European Congress for Music Analysis in Montpellier in 1995, Jonathan Cross commented on this situation in the Bulletin of the SMA (the British Society for Music Analysis) for May 1995. His comments led the organizers of the forthcoming Fourth European Congress (see below) to devote one of its sessions to discussing European traditions and usages. The present note stems from my own reflection in this context—and I claim sole responsibility for what follows. I will begin with considerations of the recent history of analysis and musicology, before turning to more fundamental matters. [1.2] The recent development of analytical studies in Continental Europe owes much to the personality of Celestin Deliege, who founded the class of analysis in the Royal Conservatoire in Liege (Belgium). -
The First Mirror Inside the Contrapunctus 6 of the Art of Fugue by Johann Sebastian Bach (BWV 1080, 6) Konstantinos Alevizos
The First Mirror inside the Contrapunctus 6 of the Art of Fugue by Johann Sebastian Bach (BWV 1080, 6) Konstantinos Alevizos To cite this version: Konstantinos Alevizos. The First Mirror inside the Contrapunctus 6 of the Art of Fugue by Johann Sebastian Bach (BWV 1080, 6). Revue musicale OICRM, Observatoire interdisciplinaire de création et de recherche en musique, 2020. hal-03161655v1 HAL Id: hal-03161655 https://hal.archives-ouvertes.fr/hal-03161655v1 Submitted on 7 Mar 2021 (v1), last revised 17 Mar 2021 (v2) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The First Mirror inside the Contrapunctus 6 of the Art of Fugue by Johann Sebastian Bach (BWV 1080, 6) 1 Konstantinos G. Alevizos Abstract Johann Sebastian Bach had already elaborated the tool of double inversion, inside the Contrapunctus “in stylo francese” of the Art of Fugue. However, the counterpoint tool of double inversion is typical for the two later pairs of fugues BWV 1080, 12-13 a, b. After an examination of the global asset of the Contrapunctus 6, a particular attention is shown to the technique of inversion (mirror) in relation to fugues 12 and 13.