DOCSLIB.ORG

Proquest Dissertations

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Proquest Dissertations 00 UNIVERSITÉ D'OTTAWA ~ ÉCOLE DES GRADUÉS L'EPISTOLA DE ARMONICA INSTITVTIONE DE REGINON DE PRUM TEXTE ETABLI, TRADUIT ET COMMENTE par Yvon Chartier Thèse présentée à la Faculté des Arts de l'Université d'Ottawa en vue de l'obtention de la maîtrise es arts en langue et littérature latines. 1/ V 1 ^ * »// ^ , ,ij ç ^ Vf Ottawa, Canada \ J V 1965 Sy \/\ JJ UNIVERSITY OF OTTAWA" - lSHBOLtt>F CRADUATE STUDIES UMI Number EC56055 INFORMATION TO USERS The quahty of this reproduction is dépendent upon the quahty of the copy submitted Broken or indistinct pnnt, colored or poor quahty illustrations and photographs, pnnt bleed-through, substandard margins, and improper alignment can adversely affect reproduction In the unhkely event that the author did not send a complète manuscnpt and there are missing pages, thèse will be noted AIso, if unauthorized copyright matenal had to be removed, a note will indicate the deletion UMI UMI Microform EC56055 Copyright 2011 by ProQuest LLC Ail nghts reserved This microform édition is protected against unauthorized copying underTitle 17, United States Code ProQuest LLC 789 East Eisenhower Parkway PO Box 1346 AnnArbor, Ml 48106-1346 UNIVERSITÉ D'OTTAWA ~ ÉCOLE DES GRADUÉS RECONNAISSANCE Cette thèse a été préparée sous la direction du R. P. Etienne Gareau, o.m.i., docteur de l'Université de Paris, auquel l'auteur tient à marquer ici sa reconnaissance pour ses conseils judicieux et sa généreuse assistance. Nous tenons à manifester une gratitude particulière à l'endroit du Service de prêts entre bibliothèques de l'Université d'Ottawa, sans la collaboration duquel le pré­ sent travail eût été impossible. UNIVERSITY OF OTTAWA - SCHOOL OF GRADUATE STUDIES UNIVERSITÉ D'OTTAWA - ÉCOLE DES GRADUÉS CURRICVLVM STVDIORVM Yvon Chartier est né à Thetford-Mines, Province de Québec, Canada, le 10 août 1942. Il a étudié au Petit Sémi­ naire de Rimouski de 1954 à 1961, puis à la Faculté des Arts de l'Université d'Ottawa où il a obtenu son baccalauréat es arts avec spécialisation en français-latin en mai 1964. UNIVERSITY OF OTTAWA - SCHOOL OF GRADUATE STUDIES UNIVERSITÉ D'OTTAWA - ÉCOLE DES GRADUÉS TABLE DES MATIERES Pages I.- AVANT-PROPOS 1 II.- INTRODUCTION 6 1. Vie et oeuvres de Réginon 6 2. L'Epistola 17 îo Le Tonarius 17 2° Composition et sources 21 3. Histoire du texte 29 4. La tradition manuscrite 33 5. Principes de l'établissement du texte 55 6. Principes de la traduction 57 7. Plan du Commentaire 59 8. Conspectvs Siglorvm 59 III.- TEXTE 61 IV.- TRADUCTION 93 V.- COMMENTAIRE 117 VI.- BIBLIOGRAPHIE 210 UNIVERSITY OF OTTAWA - SCHOOL OF GRADUATE STUDIES UNIVERSITÉ D'OTTAWA ~ ÉCOLE DES GRADUÉS SIGLES ET ABREVIATIONS ALMA: Archivum Latinitatis Medii Aevi. Boèce: Boèce, De Institutione Musica. PL, t. 63. Archiv: Archiv der Gesellschaft fur altère deutsche Ges- chichte-Kunde. CS: de Coussemaker, Scriptorum de Musica, Nova séries. EL: Albert Lavignac et al; Encyclopédie de la Musique et Dictionnaire du Conservatoire, EM: Encyclopédie de la Musique. Ermisch: Hubert Ermisch, Die Chronik des Regino bis 813. GC: Willi Apel, Gregorian Chant. GH: Fr.-A. Gevaert, Histoire et théorie de la musique de l'antiquité. GS: Martin Gerbert, Scriptores ecclesiastici de musica sacra potissimum. GM: Fr.-A. Gevaert, La Mélopée dans le chant de l'Eglise latine» HDM: Willi Apel, Harvard Dictionary of Music, 15e éd. HLF: Histoire littéraire de la France, nouvelle édition. Jan: Karolus Jan, Musici Scriptores Graeci. Kurze: Fridericus Kurze, Reginonis abbatis prumiensis Chro- nikon. Manitius: Max Manitius, Geschichte der lateinischen Litera- turim Mittelalter. Mb: Marcus Meibomius, Antiquae Musicae auctores septem, grece et latine. Menge: Euclidis Phaenomena et scripta musica, edidit Henri- cus Menge. UNIVERSITY OF OTTAWA - SCHOOL OF GRADUATE STUDIES UNIVERSITÉ D'OTTAWA - ÉCOLE DES GRADUÉS SIGLES ET ABREVIATIONS vi MGG: Fr. Blume et al., Die Musik in Geschichte und Gegen- wart. MGH: Monumenta Germaniae Historica. MMA: G. Riesd, Music in the Middle Ages. NOHM: The New Oxford History of Music. PL: Migne, Patrologiae latinae cursus completus. PM: Paléographie Musicale. REA: Revue des Etudes Anciennes. REG: Revue des Etudes Grecques. RISM: Répertoire International des Sources Musicales. UNIVERSITY OF OTTAWA - SCHOOL OF GRADUATE STUDIES UNIVERSITÉ D'OTTAWA - ÉCOLE DES GRADUÉS I. AVANT-PROPOS Lorsqu'en 17Ô4 dom Martin Gerbert, prieur de l'ab­ baye de Saint-Biaise dans la Forêt Noire, publia ses Scrip­ tores Ecclesiastici de Musica sacra potissimum, il établit par le fait même les fondements de la musicologie médiévale. Pour la première fois en effet se trouvaient réunis, en trois in-quartos, selon un ordre chronologique, quelques quarante traités musicaux latins, collationés d'après les manuscrits de bibliothèques ou de monastères d'Europe cen­ trale, depuis le Ve siècle jusqu'au XlVe . Si, depuis bientôt deux siècles, le monument élevé par le savant bénédictin n'a fait que grandir, ses lacunes ou ses défauts, par contre, apparaissent aussi plus 1 Dans une belle page, Pierre Aubry (107i|-19l0) a défini la portée et la valeur de l'oeuvre de Gerbert qui, telle une carrière inépuisable, a alimenté jusqu'à ce jour tous les travaux sur l'histoire musicale du Moyen Age: "Ce qui dure le plus, ce sont les travaux où la per­ sonnalité de l'auteur se révèle le moins, ce sont les publi­ cations de textes, ce sont les fac-similés d'originaux, ce sont les instruments de travail que l'abnégation scientifi­ que de quelques-uns met entre les mains de la foule labori­ euse. Dom Gerbert (...) nous apparaît, dans son immutabili­ té, comme ces sphinx colossaux et ces pyramides de la Haute- Egypte auxquels les populations qui passaient à leurs pieds sont pu venir impunément, comme un carrière, prendre des pierres pour élever leurs demeures, sans que leur masse géante en paraisse diminuée." (P. Aubry, La musicologie mé­ diévale , Paris, 1900, p. 40.) UNIVERSITY OF OTTAWA ~ SCHOOL OF GRADUATE STUDIES UNIVERSITÉ D'OTTAWA - ÉCOLE DES GRADUÉS AVANT-PROPOS 2 clairement. Fétis, vers 1837, formulait à son égard les trois reproches suivants: 1 Gerbert n'a pas choisi les meilleurs manuscrits ou a utilisé des copies fautives; 2 il a inclus des auteurs ou des traités inutiles, et en a omis d'autres qui auraient mieux mérité d'être re­ tenus; 2 3 enfin, il a raisonné "plus en érudit qu'en musi­ cien ". P. Aubry ne retient que le premier de ces reproches et juge, non sans raison, les deux autres injustifiés. "Si Gerbert, écrit-il, n'a pas inséré ces traités, c'est vrai­ semblablement qu'il ne les connaissait pas, de même que nous avons aujourd'hui entre les mains des documents que Fétis ignorait ". Quant au troisième reproche, Aubry le juge ab­ surde: "si Fétis avait raisonné en érudit au lieu de rai­ sonner en musicien, son oeuvre serait sans doute moins ébranlée ". 2 F.-J. Fétis, Biographie universelle des musiciens, Paris, 2e éd. (1ère 1837-44) 1883-84, t. 3, art. Gerbert, p. 457-458, 1ère éd., t. 4, p. 308-309. Le troisième reproche s'adresse, il est vrai, à l'autre monumentale compilation de Gerbert, son De Cantua es musica sacra, 1774, 2 vol., plutôt qu'aux Scriptores. 3 P. Aubry, op. cit., p. 48. 4 Id., ibid., p. 54. UNIVERSITY OF OTTAWA -- SCHOOL OF GRADUATE STUDIES UNIVERSITÉ D'OTTAWA - ÉCOLE DES GRADUÉS AVANT-PROPOS 3 Le juriste français Charles-Edmond de Coussemaker (1805-1876) consacra les dernières années de sa vie à com­ pléter la collection de Gerbert et publia, de 1867 à 1876, quatre in-quartos contenant soixante-neuf nouveaux traités. Et de nos jours, une société musicologique fondée en 1945, 1'American Institute of Musicology dont le siège est à Rome, s'est donné comme tâche de publier séparément chacun de ces traités, d'après tous les manuscrits existants, en 5 les faisant précéder d'une introduction générale . C'est dans cette ligne de conduite que s'inscrit le présent travail qui a pour but l'établissement du texte, la traduction et le commentaire de l'Epistola de Armonica Institutione de Réginon de Prûm. Ce traité a déjà été publié par Gerbert , mais d'après deux manuscrits seulement, celui de Leipzig et sa copie de Bologne. Nous connaissons maintenant quatre autres manuscrits qui éclairent 5 Depuis 1950, treize vol. ont paru dans le Corpus Scriptorum de Musica. Ce sont, dans l'ordre, les traites de Jean d'Affligem, d'Aribon le Scolastique, de Jacob de Liège, de Guy d'Arezzo, de Marchette de Padoue, d'Ugolino d'Orvieto, de Philippe de Vitry et de John Hotby. 6 CS, t. 1, p. 230-247. 7 Ce sont les mss de Bruxelles, Montpellier, Metz et du Mont-Cassin. Cf. notre section sur la tradition ma­ nuscrite. UNIVERSITY OF OTTAWA - SCHOOL OF GRADUATE STUDIES UNIVERSITÉ D'OTTAWA ~ ÉCOLE DES GRADUÉS AVANT-PROPOS 4 g singulièrement la nature et la valeur de ce traité . De plus, nous avions certaines raisons de croire que Gerbert avait corrigé et retouché le texte de Réginon de façon sou­ vent arbitraire, et surtout sans toujours signaler ses cor­ rections. Cette opinion, après examen, s'est trouvée con­ firmée, ainsi qu'on le verra par l'apparat critique. Quant au Tonarius, dont l'Epistola n'est que l'in­ troduction ou la préface, de Coussemaker en a donné un fac- similé complet et définitif d'après le manuscrit de Bruxel- Q les. Un fac-similé aussi exact du Breviarium Nocturnale du manuscrit 169 de Leipzig serait éminemment souhaitable pour comparer la notation neumatique qui diffère dans ces deux manuscrits, mais cette entreprise nous est pour le moment techniquement impossible. Une traduction du traité de Réginon dans sa forme remaniée, d'après le manuscrit H 159 de Montpellier, a été faite par Théodore Nisard en 1865, mais cette très 8 Le Pr Heinrich Huschen de Bologne a formulé ré­ cemment le souhait d'une nouvelle édition du traité de Ré­ ginon en ces termes: "Eine textkritische Neuausgabe des Musiktraktats (und gegebenenfalls auch des Tonars) unter Zugrundelegung aller erhaltenen Handschriften wâre hochst wûnschenswert" (Regino von Prflm^ Historiker, Kirchen- rechtler und Musiktheoritiker.
Load more

Recommended publications
  • Three Centuries of French Medieval Music
    THREE CENTURIES OF FRENCH MEDIEVAL MUSIC Downloaded from NEW CONCLUSIONS AND SOME NOTES. By AMEDEE GASTOUE LL the historians of our art admit that from about the third http://mq.oxfordjournals.org/ quarter of the Xlth century till the corresponding quar- A ter of the XlVth century, it was French music which dictated its laws to Europe. Monks of Limoges and Discantus singers of Notre Dame de Paris, Troubadours of the South or Trouveres of the North, such were the first masters of French music, which was to enjoy such great influence in the artistic world of the Middle Ages. The few scholars who have studied t.liia epoch, so curious, at University of Iowa Libraries/Serials Acquisitions on May 28, 2015 have generally sought to specialise in one or other of the scientific branches implied by these researches: it is to such researches that must be attributed the merit of such general views as one can hope to be able to construct on this ground. But, it must be admitted, what each of these specialists has sought to deduce in his own sphere,—or indeed, the greater part of the general views, too hasty as to the conclusions, attempted so far, whatever may have been the merit of their authors,—cannot give an exact and precise idea of the development of our art at this period. I should like to contribute, therefore, by a few special points made in this study, to laying the foundations of a work which shall view the subject as a whole, a work of which I have been preparing the details for years, with a view to publishing later on the precious remains of French music of the Middle Ages.
    [Show full text]
  • Pietro Aaron on Musica Plana: a Translation and Commentary on Book I of the Libri Tres De Institutione Harmonica (1516)
    Pietro Aaron on musica plana: A Translation and Commentary on Book I of the Libri tres de institutione harmonica (1516) Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Matthew Joseph Bester, B.A., M.A. Graduate Program in Music The Ohio State University 2013 Dissertation Committee: Graeme M. Boone, Advisor Charles Atkinson Burdette Green Copyright by Matthew Joseph Bester 2013 Abstract Historians of music theory long have recognized the importance of the sixteenth- century Florentine theorist Pietro Aaron for his influential vernacular treatises on practical matters concerning polyphony, most notably his Toscanello in musica (Venice, 1523) and his Trattato della natura et cognitione de tutti gli tuoni di canto figurato (Venice, 1525). Less often discussed is Aaron’s treatment of plainsong, the most complete statement of which occurs in the opening book of his first published treatise, the Libri tres de institutione harmonica (Bologna, 1516). The present dissertation aims to assess and contextualize Aaron’s perspective on the subject with a translation and commentary on the first book of the De institutione harmonica. The extensive commentary endeavors to situate Aaron’s treatment of plainsong more concretely within the history of music theory, with particular focus on some of the most prominent treatises that were circulating in the decades prior to the publication of the De institutione harmonica. This includes works by such well-known theorists as Marchetto da Padova, Johannes Tinctoris, and Franchinus Gaffurius, but equally significant are certain lesser-known practical works on the topic of plainsong from around the turn of the century, some of which are in the vernacular Italian, including Bonaventura da Brescia’s Breviloquium musicale (1497), the anonymous Compendium musices (1499), and the anonymous Quaestiones et solutiones (c.1500).
    [Show full text]
  • La Caccia Nell'ars Nova Italiana
    8. Iohannes Tinctoris, Diffinitorium musice. Un dizionario Il corpus delle cacce trecentesche rappresenta con «La Tradizione Musicale» è una collana promossa di musica per Beatrice d’Aragona. A c. di C. Panti, 2004, ogni probabilità uno dei momenti di più intenso dal Dipartimento di Musicologia e Beni Culturali pp. LXXIX-80 e immediato contatto tra poesia e musica. La viva- dell’Università di Pavia, dalla Fondazione Walter 9. Tracce di una tradizione sommersa. I primi testi lirici italiani cità rappresentativa dei testi poetici, che mirano Stauffer e dalla Sezione Musica Clemente Terni e 19 tra poesia e musica. Atti del Seminario di studi (Cre mona, alla descrizione realistica di scene e situazioni im- Matilde Fiorini Aragone, che opera in seno alla e 20 febbraio 2004). A c. di M. S. Lannut ti e M. Locanto, LA CACCIA Fonda zione Ezio Franceschini, con l’intento di pro- 2005, pp. VIII-280 con 55 ill. e cd-rom mancabilmente caratterizzate dal movimento e dalla concitazione, trova nelle intonazioni polifo- muovere la ricerca sulla musica vista anche come 13. Giovanni Alpigiano - Pierluigi Licciardello, Offi - niche una cassa di risonanza che ne amplifica la speciale osservatorio delle altre manifestazioni della cium sancti Donati I. L’ufficio liturgico di san Do nato di cultura. «La Tradizione Musicale» si propone di of- portata. L’uso normativo della tecnica canonica, de- Arezzo nei manoscritti toscani medievali, 2008, pp. VIII-424 NELL’ARS NOVA ITALIANA frire edizioni di opere e di trattati musicali, studi 8 finita anch’essa ‘caccia’ o ‘fuga’, per l’evidente me- con ill. a colori monografici e volumi miscellanei di alto valore tafora delle voci che si inseguono, si dimostra 16.
    [Show full text]
  • Musical Techniques
    Musical Techniques Musical Techniques Frequencies and Harmony Dominique Paret Serge Sibony First published 2017 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address: ISTE Ltd John Wiley & Sons, Inc. 27-37 St George’s Road 111 River Street London SW19 4EU Hoboken, NJ 07030 UK USA www.iste.co.uk www.wiley.com © ISTE Ltd 2017 The rights of Dominique Paret and Serge Sibony to be identified as the authors of this work have been asserted by them in accordance with the Copyright, Designs and Patents Act 1988. Library of Congress Control Number: 2016960997 British Library Cataloguing-in-Publication Data A CIP record for this book is available from the British Library ISBN 978-1-78630-058-4 Contents Preface ........................................... xiii Introduction ........................................ xv Part 1. Laying the Foundations ............................ 1 Introduction to Part 1 .................................. 3 Chapter 1. Sounds, Creation and Generation of Notes ................................... 5 1.1. Physical and physiological notions of a sound .................. 5 1.1.1. Auditory apparatus ............................... 5 1.1.2. Physical concepts of a sound .......................... 7 1.1.3.
    [Show full text]
  • Philippe Le Chancelier Et Son Oeuvre
    Université de Poitiers École doctorale SHES CESCM – UMR CNRS 6223 Anne-Zoé RILLON-MARNE PHILIPPE LE CHANCELIER ET SON ŒUVRE : ETUDE SUR L’ELABORATION D’UNE POETIQUE MUSICALE Volume I Thèse de Doctorat de Musicologie Sous la direction du Pr. Olivier CULLIN Poitiers 2008 2 Remerciements La thèse de doctorat est un travail long et solitaire mais il ne se fait pas dans la solitude. L’encadrement, les échanges dont j’ai pu profiter tout au long de ces années m’ont été d’un grand soutient intellectuel et moral. Mes premières pensées vont à Olivier Cullin, professeur à l’Université de Tours, qui a su, dans sa tâche de directeur de thèse, mêler exigence, confiance et encouragements. Par ses conseils, ses corrections et son écoute attentive, il a nettement contribué à faire exister ce travail. Il cultive et parvient à transmettre une curiosité qui fait de la recherche un véritable plaisir. J’adresse également ma reconnaissance à Nigel Wilkins qui encadra mes premiers pas à l’Université en dirigeant mes mémoires de maîtrise et DEA à la Sorbonne. Je remercie également très chaleureusement ceux qui m’ont aidée, écoutée ou lue malgré leurs emplois du temps bien remplis. Je pense principalement à Nicole Bériou et Gilbert Dahan. L’intérêt qu’ils ont porté à mon travail m’a permis de prendre confiance et donné l’occasion de présenter certains aspects de mes recherches à diverses occasions. L’entraide et la solidarité entre doctorants m’ont également été d’un grand soutien. Je me souviens des discussions avec mes amis, membres de l’ « équipe », docteurs ou futurs docteurs Séverine, Guillaume, Christelle ou encore Margaret.
    [Show full text]
  • 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
    [Show full text]
  • This Electronic Thesis Or Dissertation Has Been Downloaded from the King’S Research Portal At
    This electronic thesis or dissertation has been downloaded from the King’s Research Portal at https://kclpure.kcl.ac.uk/portal/ Insular sources of thirteenth-century polyphony and the significance of Notre Dame. Losseff, Nicola The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without proper acknowledgement. END USER LICENCE AGREEMENT Unless another licence is stated on the immediately following page this work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ You are free to copy, distribute and transmit the work Under the following conditions: Attribution: You must attribute the work in the manner specified by the author (but not in any way that suggests that they endorse you or your use of the work). Non Commercial: You may not use this work for commercial purposes. No Derivative Works - You may not alter, transform, or build upon this work. Any of these conditions can be waived if you receive permission from the author. Your fair dealings and other rights are in no way affected by the above. Take down policy If you believe that this document breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 09. Oct. 2021 -1- INSULAR SOURCES OF THIRTEENTH-CENTURY POLYPHONY AND THE SIGNIFICANCE OF NOTRE DAME Nicola Losseff Submitted for the degree of Doctor of Philosophy at King's College, London, 1993 1LoNDgt UNW.
    [Show full text]
  • On the Bimodular Approximation and Equal Temperaments
    On the Bimodular Approximation and Equal Temperaments Martin Gough DRAFT June 8 2014 Abstract The bimodular approximation, which has been known for over 300 years as an accurate means of computing the relative sizes of small (sub-semitone) musical intervals, is shown to provide a remarkably good approximation to the sizes of larger intervals, up to and beyond the size of the octave. If just intervals are approximated by their bimodular approximants (rational numbers defined as frequency difference divided by frequency sum) the ratios between those intervals are also rational, and under certain simply stated conditions can be shown to coincide with the integer ratios which equal temperament imposes on the same intervals. This observation provides a simple explanation for the observed accuracy of certain equal divisions of the octave including 12edo, as well as non-octave equal temperaments such as the fifth-based temperaments of Wendy Carlos. Graphical presentations of the theory provide further insights. The errors in the bimodular approximation can be expressed as bimodular commas, among which are many commas featuring in established temperament theory. Introduction Just musical intervals are characterised by small-integer ratios between frequencies. Equal temperaments, by contrast, are characterised by small-integer ratios between intervals. Since interval is the logarithm of frequency ratio, it follows that an equal temperament which accurately represents just intervals embodies a set of rational approximations to the logarithms (to some suitable base) of simple rational numbers. This paper explores the connection between these rational logarithmic approximations and those obtained from a long-established rational approximation to the logarithm function – the bimodular approximation.
    [Show full text]
  • Behind the Mirror Revealing the Contexts of Jacobus's Speculum
    Behind the Mirror Revealing the Contexts of Jacobus’s Speculum musicae by Karen Desmond A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Music New York University May, 2009 ___________________________ Edward H. Roesner © Karen Desmond All Rights Reserved, 2009 DEDICATION For my family iv ACKNOWLEDGMENTS I would like to thank my advisor, Edward Roesner, for his unfaltering support throughout this process, for his thoughtful suggestions regarding lines of inquiry, and his encyclopedic knowledge of the field. I would like to thank Stanley Boorman and Gabriela Iltnichi for their friendship and expertise, and their critical eye in their careful reading of many drafts of my work. For their assistance during my research trip to Belgium, I must mention Monsieur Abbé Deblon and Christian Dury at the Archives de l’Evêché, Liège, Paul Bertrand at the Archives de l’Etat, Liège, Philippe Vendrix for his kind hospitality, and to Barbara Haggh-Huglo for her tips and advice in advance of my trip, and for also reading a final draft of this dissertation. I would also like to thank Margaret Bent and Ruth Steiner for help during the early stages of my doctoral research, and Suzanne Cusick for her reading of the final draft. Finally, heartfelt thanks are due to my husband, Insup; my two sons, Ethan and Owen; and my parents, John and Chris, who have been steadfast in their encouragement of this endeavor. v ABSTRACT This study addresses the general question of how medieval music theory participated in the discourse of the related disciplines of philosophy, natural science and theology.
    [Show full text]
  • Sagittal a Microtonal Notation System
    Sagittal A Microtonal Notation System by George D. Secor and David C. Keenan Introduction George Secor began development of the Sagittal (pronounced “SAJ-i-tl”) notation system in August 2001. In January 2002 he presented what he had developed to the Yahoo group tuning and offered to consider suggestions for improvements. At that stage the system could notate the equal temperaments with 17, 19, 22, 29, 31, 41, and 72 divisions per octave. Little did he know that he had provided a unifying symbolic principle which would ultimately be developed into a system capable of notating almost any conceivable microtonal tuning. In the early stages of the discussion, one idea that surfaced repeatedly was that a set of symbols indicating prime-number commatic alterations to tones in a Pythagorean series might be used to notate both rational intervals (e.g. just intonation) and equal divisions of the octave. Similar ideas had previously been proposed by Hermann Helmholtz, Alexander Ellis, Carl Eitz, Paul Rapoport, Daniel Wolf, Joe Monzo, and others1, but these had never been implemented in a performance notation to such an extent as was being discussed. As a first step, Gene Ward Smith suggested that it would be desirable that there be no more than one comma symbol per prime number, and a selection of 19-limit commas was tentatively identified to define the semantics of the notation. David Keenan enthusiastically observed that these commas came in an assortment of sizes that made the objective theoretically feasible, but he also realized that devising a set of distinct and recognizable symbols suitable for a performance notation was not going to be a simple matter.
    [Show full text]
  • Inhaltsverzeichnis Vorwort Und Einleitung I. Die Lehre Vom Organum Und Biskant Von Der Musica Enchiriadis Bis Zur Ars Nova Um 13
    Inhaltsverzeichnis Vorwort und Einleitung 11 I. Die Lehre vom Organum und Biskant von der Musica Enchiriadis bis zur Ars nova um 1325 14 Kap. 1: Bas Alte Organum 14 Musica Enchiriadis 14 Scolica Enchiriadis 19 Bamberger Bialog über das Organum, Bialog I 23 Bialog II 25 Kölner Traktat 26 Schlettstädter Traktat 27 Pariser Traktat 27 Guido von Arezzo, Micrologus, Kap. 18 und 19 über das Organum 32 Guglielmo Roffredi, Summa musicae artis /Cap. IX, Be diaphonia7 36 Kap. 2: Bas frühe und spätere Neue Organum 37 Johannes Affligemensis (Cotto), Be musica cum tonario, Kap. 23, Be diaphonia, id est organo 37 Mailänder Traktat Ad Organum faciendum, Prosa­ teil 38 Mailänder Traktat Ad Organum faciendum, Vers- teil 40 Berliner Traktat A (Nebenfassung des Mailänder Traktats Ad Organum facien­ dum) 42 Berliner Traktat B (Nebenfassung des Mailänder Traktats Ad Organum facien­ dum) ^3 Brügger Version des Mailänder Traktats Ad Orga­ num faciendum 45 Organumtraktat von Montpellier 46 Organumtraktat von St. Martial (A. de Lafage- Traktat) 48 Liber Musicae (Londoner oder Schneider-Traktat) 49 Kap. 3: Bie Klangschrittlehre - Traktate der Gruppe A 50 Item de cursu animadvertendum est, Si discantus fuerit cum cantu et cantus remittatur (im Liber musicae, Londoner oder Schneider-Traktat) 52 Incipit titulus artis cuj non deserit vox vene- randus, Tres sunt principales consonantie 53 Omnis homo qui uult bene organi^are primitus debet 54 Incipit regula approbata. uidelicet pro tono possunus reddere semiton(i)um 56 Si cantus ascendit duas uoces, et Organum inci­ pit (Organumtraktat des Pseudo-Guido de Caroli loco) 56 http://d-nb.info/880241004 _ H.
    [Show full text]
  • FD2020 Full-Proceedngs-160920-V3
    Proceedings of the 36th Annual Meeting of the International Society for Psychophysics Fechner Day 2020 {Online} October 19-22, 2020 1 Published by the International Society for Psychophysics, 2020. Cover Image: Markus Spiske Cover design: Jordan Richard Schoenherr Title: Proceedings of the 36th Annual Meeting of the International Society for Psychophysics Fechner Day 2020 Edited by Jordan Richard Schoenherr, Timothy Hubbard, William Stine, and Craig Leth-Steensen for the International Society for Psychophysics. All papers are considered nonarchival, representing working papers of the authors. The International Society for Psychophysics does not hold any rights to the works contained herein which remain the intellectual property of the authors. Please contact the authors listed in the respective extended abstracts or papers for further details. Table of Contents Table of Contents ....................................................................................................... 3 Preface ......................................................................................................................... 4 Schedule ....................................................................................................................... 6 Abstracts and Papers ................................................................................................. 9 3 Preface Welcome to the 36th Annual Conference of the International Society for Psychophysics, Fechner Day 2020! As a member of the Executive Committee, I am pleased to welcome
    [Show full text]