Some Pompeiian Musical Instruments and the Modes of Aristides Quintilianus
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
The 17-Tone Puzzle — and the Neo-Medieval Key That Unlocks It
The 17-tone Puzzle — And the Neo-medieval Key That Unlocks It by George Secor A Grave Misunderstanding The 17 division of the octave has to be one of the most misunderstood alternative tuning systems available to the microtonal experimenter. In comparison with divisions such as 19, 22, and 31, it has two major advantages: not only are its fifths better in tune, but it is also more manageable, considering its very reasonable number of tones per octave. A third advantage becomes apparent immediately upon hearing diatonic melodies played in it, one note at a time: 17 is wonderful for melody, outshining both the twelve-tone equal temperament (12-ET) and the Pythagorean tuning in this respect. The most serious problem becomes apparent when we discover that diatonic harmony in this system sounds highly dissonant, considerably more so than is the case with either 12-ET or the Pythagorean tuning, on which we were hoping to improve. Without any further thought, most experimenters thus consign the 17-tone system to the discard pile, confident in the knowledge that there are, after all, much better alternatives available. My own thinking about 17 started in exactly this way. In 1976, having been a microtonal experimenter for thirteen years, I went on record, dismissing 17-ET in only a couple of sentences: The 17-tone equal temperament is of questionable harmonic utility. If you try it, I doubt you’ll stay with it for long.1 Since that time I have become aware of some things which have caused me to change my opinion completely. -
MTO 20.2: Wild, Vicentino's 31-Tone Compositional Theory
Volume 20, Number 2, June 2014 Copyright © 2014 Society for Music Theory Genus, Species and Mode in Vicentino’s 31-tone Compositional Theory Jonathan Wild NOTE: The examples for the (text-only) PDF version of this item are available online at: http://www.mtosmt.org/issues/mto.14.20.2/mto.14.20.2.wild.php KEYWORDS: Vicentino, enharmonicism, chromaticism, sixteenth century, tuning, genus, species, mode ABSTRACT: This article explores the pitch structures developed by Nicola Vicentino in his 1555 treatise L’Antica musica ridotta alla moderna prattica . I examine the rationale for his background gamut of 31 pitch classes, and document the relationships among his accounts of the genera, species, and modes, and between his and earlier accounts. Specially recorded and retuned audio examples illustrate some of the surviving enharmonic and chromatic musical passages. Received February 2014 Table of Contents Introduction [1] Tuning [4] The Archicembalo [8] Genus [10] Enharmonic division of the whole tone [13] Species [15] Mode [28] Composing in the genera [32] Conclusion [35] Introduction [1] In his treatise of 1555, L’Antica musica ridotta alla moderna prattica (henceforth L’Antica musica ), the theorist and composer Nicola Vicentino describes a tuning system comprising thirty-one tones to the octave, and presents several excerpts from compositions intended to be sung in that tuning. (1) The rich compositional theory he develops in the treatise, in concert with the few surviving musical passages, offers a tantalizing glimpse of an alternative pathway for musical development, one whose radically augmented pitch materials make possible a vast range of novel melodic gestures and harmonic successions. -
Andrián Pertout
Andrián Pertout Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition Volume 1 Submitted in partial fulfilment of the requirements of the degree of Doctor of Philosophy Produced on acid-free paper Faculty of Music The University of Melbourne March, 2007 Abstract Three Microtonal Compositions: The Utilization of Tuning Systems in Modern Composition encompasses the work undertaken by Lou Harrison (widely regarded as one of America’s most influential and original composers) with regards to just intonation, and tuning and scale systems from around the globe – also taking into account the influential work of Alain Daniélou (Introduction to the Study of Musical Scales), Harry Partch (Genesis of a Music), and Ben Johnston (Scalar Order as a Compositional Resource). The essence of the project being to reveal the compositional applications of a selection of Persian, Indonesian, and Japanese musical scales utilized in three very distinct systems: theory versus performance practice and the ‘Scale of Fifths’, or cyclic division of the octave; the equally-tempered division of the octave; and the ‘Scale of Proportions’, or harmonic division of the octave championed by Harrison, among others – outlining their theoretical and aesthetic rationale, as well as their historical foundations. The project begins with the creation of three new microtonal works tailored to address some of the compositional issues of each system, and ending with an articulated exposition; obtained via the investigation of written sources, disclosure -
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). -
Notation Through History
Notation through History Neume Names 9th to 10th Centuries 11th to 13th Centuries Modern Notation Virga Punctum Podatus (Pes) Clivis Scandicus Climacus Torculus Porrectus Scandicus flexus Porrectus flexus Torculus Respinus Pes subpunctis Notation Symbols through History Greek Acutus Gravis Accents Neumes 6th to 13th Virga Virga centuries Jacans Punctum Mensur Maxim Longa Brevis Semibrevi Minim Semimini Fusa Semifus al a (Long) (Breve) s a ma a Notatio (Duple (Semibrev (Mini x e) m) n Long) th 13 century 14th century 15th to 17th centuri es Modern 17th to Double Whole Half Quarter Eighth Sixteent th Notatio 20 Whole- Note Note Note Note h Note centuri Note n es The Anatomy of a Note Notation English French German Italian Spanish Note note Note nota nota testa or Head tête de la note Notenkopf testina or oval capocchia Hals or asta, or Stem queue plica Notenhals gamba coda Fahne or Flag crochet uncinata or corchete Fähnchen bandiera Beam barre Balken barra barra Dot point Punkt punto puntillo punktierte nota con Dotted note pointée nota puntata Note puntillo Note Notation American British French German Italian Spanish Double Cuadrada or Double- Doppelganze or whole Breve Breve Doble ronde Doppelganzenote note Redonda Whole Ganze or Semibreve Ronde Semibreve Redonda note Ganzenote Halbe or Minima or Half note Minim Blanche Blanca Halbenote Bianca Quarter Viertel or Semiminima or Crotchet Noire Negra note Viertelnote Nera Eighth Quaver Croche Achtel or Achtelnote Croma Corchea note Sechzehntel or Sixteenth Double- Sechzehntelnote Semiquaver -
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. -
Lute Tuning and Temperament in the Sixteenth and Seventeenth Centuries
LUTE TUNING AND TEMPERAMENT IN THE SIXTEENTH AND SEVENTEENTH CENTURIES BY ADAM WEAD Submitted to the faculty of the Jacobs School of Music in partial fulfillment of the requirements for the degree, Doctor of Music, Indiana University August, 2014 Accepted by the faculty of the Jacobs School of Music, Indiana University, in partial fulfillment of the requirements for the degree Doctor of Music. Nigel North, Research Director & Chair Stanley Ritchie Ayana Smith Elisabeth Wright ii Contents Acknowledgments . v Introduction . 1 1 Tuning and Temperament 5 1.1 The Greeks’ Debate . 7 1.2 Temperament . 14 1.2.1 Regular Meantone and Irregular Temperaments . 16 1.2.2 Equal Division . 19 1.2.3 Equal Temperament . 25 1.3 Describing Temperaments . 29 2 Lute Fretting Systems 32 2.1 Pythagorean Tunings for Lute . 33 2.2 Gerle’s Fretting Instructions . 37 2.3 John Dowland’s Fretting Instructions . 46 2.4 Ganassi’s Regola Rubertina .......................... 53 2.4.1 Ganassi’s Non-Pythagorean Frets . 55 2.5 Spanish Vihuela Sources . 61 iii 2.6 Sources of Equal Fretting . 67 2.7 Summary . 71 3 Modern Lute Fretting 74 3.1 The Lute in Ensembles . 76 3.2 The Theorbo . 83 3.2.1 Solutions Utilizing Re-entrant Tuning . 86 3.2.2 Tastini . 89 3.2.3 Other Solutions . 95 3.3 Meantone Fretting in Tablature Sources . 98 4 Summary of Solutions 105 4.1 Frets with Fixed Semitones . 106 4.2 Enharmonic Fretting . 110 4.3 Playing with Ensembles . 113 4.4 Conclusion . 118 A Complete Fretting Diagrams 121 B Fret Placement Guide 124 C Calculations 127 C.1 Hans Gerle . -
Plainsound Etudes
Wolfgang von Schweinitz Plainsound Etudes FOR VIOLA SOLO Three Just Intonation Studies based on a flexible non-tempered 11-limit 31-tone scale op. 58 b 2015 for Andrew McIntosh and all violists with an interest in the sound and performance practice of microtonal just intonation PLAINSOUND MUSIC EDITION This score is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License ACCIDENTALS for microtonal just intonation EXTENDED HELMHOLTZ-ELLIS JI PITCH NOTATION The exact intonation of each pitch is written out by means of the following harmonically defined accidentals: Pythagorean series of perfect fifths, based on the open strings E e n v V ( … c g d a e … ) lowers / raises the pitch by a syntonic comma dmuU Ffow 81 : 80 = circa 21.5 cents lowers / raises the pitch by two syntonic commas cltT Ggpx circa 43 cents lowers / raises the pitch by a septimal comma < > 64 : 63 = circa 27.3 cents lowers / raises the pitch by two septimal commas • ¶ circa 54.5 cents (not used in this score) raises / lowers the pitch by an 11-limit undecimal quarter-tone 4 5 33 : 32 = circa 53.3 cents These 'Helmholtz-Ellis' accidentals for just intonation were designed in collaboration with Marc Sabat. The attached arrows for pitch alterations by a syntonic comma are transcriptions of the notation used by Hermann von Helmholtz in his book "Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik" (1863). – The annotated English translation "On the Sensations of Tone as a Physiological Basis for the Theory of Music" (published 1875/1885) was made by Alexander J. -
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 -
Music and the Making of Modern Science
Music and the Making of Modern Science Music and the Making of Modern Science Peter Pesic The MIT Press Cambridge, Massachusetts London, England © 2014 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. MIT Press books may be purchased at special quantity discounts for business or sales promotional use. For information, please email [email protected]. This book was set in Times by Toppan Best-set Premedia Limited, Hong Kong. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Pesic, Peter. Music and the making of modern science / Peter Pesic. pages cm Includes bibliographical references and index. ISBN 978-0-262-02727-4 (hardcover : alk. paper) 1. Science — History. 2. Music and science — History. I. Title. Q172.5.M87P47 2014 509 — dc23 2013041746 10 9 8 7 6 5 4 3 2 1 For Alexei and Andrei Contents Introduction 1 1 Music and the Origins of Ancient Science 9 2 The Dream of Oresme 21 3 Moving the Immovable 35 4 Hearing the Irrational 55 5 Kepler and the Song of the Earth 73 6 Descartes ’ s Musical Apprenticeship 89 7 Mersenne ’ s Universal Harmony 103 8 Newton and the Mystery of the Major Sixth 121 9 Euler: The Mathematics of Musical Sadness 133 10 Euler: From Sound to Light 151 11 Young ’ s Musical Optics 161 12 Electric Sounds 181 13 Hearing the Field 195 14 Helmholtz and the Sirens 217 15 Riemann and the Sound of Space 231 viii Contents 16 Tuning the Atoms 245 17 Planck ’ s Cosmic Harmonium 255 18 Unheard Harmonies 271 Notes 285 References 311 Sources and Illustration Credits 335 Acknowledgments 337 Index 339 Introduction Alfred North Whitehead once observed that omitting the role of mathematics in the story of modern science would be like performing Hamlet while “ cutting out the part of Ophelia. -
MTO 12.3: Duffin, Just Intonation in Renaissance Theory and Practice
Volume 12, Number 3, October 2006 Copyright © 2006 Society for Music Theory Ross W. Duffin ABSTRACT: Just intonation has a reputation as a chimerical, theoretical system that simply cannot work in practice. This is based on the assessment of most modern authorities and supported by misgivings expressed during the Renaissance when the practice was supposedly at its height. Looming large among such misgivings are tuning puzzles printed by the 16th-century mathematician, Giovanni Battista Benedetti. However, Renaissance music theorists are so unanimous in advocating the simple acoustical ratios of Just intonation that it seems clear that some reconciliation must have occurred between the theory and practice of it. This article explores the basic theory of Just intonation as well as problematic passages used to deny its practicability, and proposes solutions that attempt to satisfy both the theory and the ear. Ultimately, a resource is offered to help modern performers approach this valuable art. Received June 2006 Introduction | Theoretical Background | Benedetti's Puzzles | Problematic Passages | Is Just Tuning Possible? A New Approach | Problem Spots in the Exercises | Rehearsal Usage | Conclusion Introduction The idea . that one can understand the ratios of musical consonances without experiencing them with the senses is wrong. Nor can one know the theory of music without being versed in its practice. [1] So begins the first of two letters sent by the mathematician Giovanni Battista Benedetti to the composer Cipriano de Rore in 1563. Subsequently publishing the letters in 1585,(1) Benedetti was attempting to demonstrate that adhering to principles of Just intonation, as championed most famously by Gioseffo Zarlino,(2) would, in certain cases, cause the pitch of the ensemble to migrate. -
An Application of Calculated Consonance in Computer-Assisted Microtonal Music
University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2013-12-23 An Application of Calculated Consonance in Computer-Assisted Microtonal Music Burleigh, Ian George Burleigh, I. G. (2013). An Application of Calculated Consonance in Computer-Assisted Microtonal Music (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/24833 http://hdl.handle.net/11023/1225 doctoral thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY An Application of Calculated Consonance in Computer-Assisted Microtonal Music by Ian George Burleigh A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE INTERDISCIPLINARY DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF COMPUTER SCIENCE and SCHOOL OF CREATIVE AND PERFORMING ARTS | MUSIC CALGARY, ALBERTA DECEMBER, 2013 © Ian George Burleigh 2013 Abstract Harmony (the audible result of varied combinations of simultaneously sounding tones) ought to, for the most part, sound pleasing to the ear. The result depends, among other factors, on a proper choice of the pitches for the tones that form harmonious chords, and on their correct intonation during musical performance. This thesis proposes a computational method for calculation of relative consonance among groups of tones, and its possible practical applications in machine-assisted arrangement of tones, namely the choice of tone pitches and their microtonal adjustment.