DOCSLIB.ORG

Music and the Making of Modern Science

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
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. This simile is singularly exact. For Ophelia is quite essential to the play, she is very charming — and a little mad. ” 1 If in the story of science mathematics takes the part of Ophelia, music might be compared with Horatio, Hamlet ’ s friend and companion who helps investigate the ghost, discusses what may lie beyond their philosophies, sings the sweet prince to his rest, and tells his story. This book will examine some significant moments in the relationship of music to science, especially those in which prior developments in music affected subsequent aspects of natural science. By investigating this direction of influence, we question the common presupposition that, however beguiling, music is conceptually derivative or secondary compared to other modes of thought or perception — an effect, rather than a cause. The examples considered in this book show the larger intellectual and cultural dimensions of music as a force in its own right. By virtue of its special position in Greek natural philosophy, music occupied the perfect position to mediate between idealized mathematical objects and the world of experience. 2 Based on these ancient models, the continuing structures of learning mandated music ’s ensuing centrality as the “hinge ” discipline connecting arithmetic, geometry, and the sensual world. This both reflected and moved the profound alterations that surrounded the birth of the “new philosophy ” during the sixteenth and seventeenth centuries. My main contention is that, in whatever directions its interventions tended, from ancient until modern times music so deeply and persistently affected the making of science over so many historical vicissitudes that we should tell their stories jointly. Our awareness of how exactly music entered into the story can enlarge and deepen our understanding of the human and intellectual dimensions of science. In so doing, we may draw more closely together the study of “ aural culture” and symbolic structures hitherto considered separate. This rapprochement calls for an enriched exploration of the felt dimensions of scientific experience, considered as a fully human activity vividly engaged with perception, feeling, and thought. 3 2 Introduction As Horatio has ties to both Hamlet and Ophelia, music touches both natural philosophy and mathematics. Accordingly, we will examine several critical shifts of understanding in both these domains. Chapter 1 describes the most consequential move of all: ancient Greek natural philosophy connected music with mathematics and astronomy within a fourfold study, the quadrivium . This alliance involved both experiment and theory, and hence positioned music at the frontier between the worlds of physical sensation and ideal forms. During the subsequent fifteen centuries, music retained its central place among the mathematical sciences, an essential component of what became “ liberal education, ” which explicitly continued a program the Pythagoreans began, Plato systematized, and Boethius transmitted to the West. These ancient developments are important not merely as historical background, buried as hidden sediment under the surface of modernity, but as continually active and reemergent forces that shaped and continue to shape “modern ” science and mathematics. Chapter 2 considers the status of these forces as they seemed to a preeminent fourteenth- century natural philosopher. Nicole Oresme used musical concepts as important elements in his reexamination of the cosmos, its possible cycles, and their relation to arithmetic and geometry. The case of Oresme shows how significant musical issues were well before the advent of the “new philosophy” of the sixteenth century. Oresme ’s contact with the “ new music ” ( ars nova ) led him to refute the simplest versions of cosmic harmony and to propose radical new alternatives that depend on the tension between arithmetic and geom- etry. The underlying musical and cosmological considerations allow us to deduce his own unstated conclusion in favor of geometry. Disputes about the order of the planets had profound musical and cosmological implica- tions, especially on the growing controversy over whether the seemingly immovable Earth could be understood to move, as the Pythagoreans held. Though he had presented strong arguments in favor of this view, Oresme himself finally accepted the geocentric account. Chapter 3 investigates the role of music in this cosmological controversy as it came to a head in the fifteenth century. The problem of a seemingly immovable yet moving center such as the Earth parallels the musical problem of changing the usually fixed modal center of a composition. Despite its proverbial impossibility, the theorist Heinrich Glarean drew attention to just such a shift of mode in Josquin des Prez ’ s motet De profundis . If so, music might show how the immovable could move, after all. Indeed, harmony became the defin- ing issue on which Copernicus and those following him phrased their arguments about the new cosmology. Musicians followed this controversy closely; in his 1588 polemic for a revival of ancient musical practice, Vincenzo Galilei was among the first Italians to defend the heliocentric view, many years before his celebrated son Galileo took up this cause, again under the banner of harmony. Several decades before Vincenzo Galilei ’ s surprising avowal, music influenced funda- mental changes in the concept of number. Though irrational quantities had long been excluded from arithmetic and harmonics, sixteenth-century musical theory and practice Introduction 3 called for irrational and rational quantities on an equal footing. Chapter 4 discusses three central figures in this story: the German mathematician Michael Stifel, who was the first person to use the phrase “ irrational numbers ” in the course of his exposition of music, but who then hesitated to grant those numbers full reality; Girolamo Cardano, celebrated physician-polymath, who gave such quantities even greater significance in his musical writings; and Nicola Vincentino, a composer obsessed with reviving ancient Greek quarter tones who found himself in need of what he called “ irrational proportions ” to define these unfamiliar intervals. Each of these three men was involved with practical music to a degree correlated with their respective reliance on irrational numbers. Johannes Kepler, more than anyone, incorporated music into the foundations of his innovative astronomy. Chapter 5 relates his interest in musical practice to his novel approach to its theory, which moved him to reject algebraic results that contradicted musical experience. Kepler ’ s search for cosmic polyphony points to Orlando di Lasso ’ s In me transierunt as a moving expression of the “ song of the Earth, ” down to the melodic spelling of the Earth ’s song. Kepler presents both cosmos and music as essentially alive and erotically active, based on his sexual understanding of numbers. The pervasive dis- sonance of the cosmic harmonies reflects the throes of war and eros. Like Oresme, Kepler realized the essential incompleteness of the cosmic music, which may never reach a final cadence, a universal concord on which the world-music could fittingly end. Kepler treats this as an indication of divine infinitude, inscribed in the finite cosmos. Ren é Descartes began his career writing about music, which affected his innovative natural philosophy throughout its development. Chapter 6 reads his correspondence with Marin Mersenne as tracing the interaction between musical, mathematical, and philosophi-
Load more

Recommended publications
  • What the Renaissance Knew Piero Scaruffi Copyright 2018
    What the Renaissance knew Piero Scaruffi Copyright 2018 http://www.scaruffi.com/know 1 What the Renaissance knew • The 17th Century – For tens of thousands of years, humans had the same view of the universe and of the Earth. – Then the 17th century dramatically changed the history of humankind by changing the way we look at the universe and ourselves. – This happened in a Europe that was apparently imploding politically and militarily, amid massive, pervasive and endless warfare – Grayling refers to "the flowering of genius“: Galileo, Pascal, Kepler, Newton, Cervantes, Shakespeare, Donne, Milton, Racine, Moliere, Descartes, Spinoza, Leibniz, Locke, Rubens, El Greco, Rembrandt, Vermeer… – Knowledge spread, ideas circulated more freely than people could travel 2 What the Renaissance knew • Collapse of classical dogmas – Aristotelian logic vs Rene Descartes' "Discourse on the Method" (1637) – Galean medicine vs Vesalius' anatomy (1543), Harvey's blood circulation (1628), and Rene Descartes' "Treatise of Man" (1632) – Ptolemaic cosmology vs Copernicus (1530) and Galileo (1632) – Aquinas' synthesis of Aristotle and the Bible vs Thomas Hobbes' synthesis of mechanics (1651) and Pierre Gassendi's synthesis of Epicurean atomism and anatomy (1655) – Papal unity: the Thirty Years War (1618-48) shows endless conflict within Christiandom 3 What the Renaissance knew • Decline of – Feudalism – Chivalry – Holy Roman Empire – Papal Monarchy – City-state – Guilds – Scholastic philosophy – Collectivism (Church, guild, commune) – Gothic architecture 4 What
    [Show full text]
  • Classical and Modern Diffraction Theory
    Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 Classical and Modern Diffraction Theory Edited by Kamill Klem-Musatov Henning C. Hoeber Tijmen Jan Moser Michael A. Pelissier SEG Geophysics Reprint Series No. 29 Sergey Fomel, managing editor Evgeny Landa, volume editor Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 Society of Exploration Geophysicists 8801 S. Yale, Ste. 500 Tulsa, OK 74137-3575 U.S.A. # 2016 by Society of Exploration Geophysicists All rights reserved. This book or parts hereof may not be reproduced in any form without permission in writing from the publisher. Published 2016 Printed in the United States of America ISBN 978-1-931830-00-6 (Series) ISBN 978-1-56080-322-5 (Volume) Library of Congress Control Number: 2015951229 Downloaded from http://pubs.geoscienceworld.org/books/book/chapter-pdf/3701993/frontmatter.pdf by guest on 29 September 2021 Dedication We dedicate this volume to the memory Dr. Kamill Klem-Musatov. In reading this volume, you will find that the history of diffraction We worked with Kamill over a period of several years to compile theory was filled with many controversies and feuds as new theories this volume. This volume was virtually ready for publication when came to displace or revise previous ones. Kamill Klem-Musatov’s Kamill passed away. He is greatly missed. new theory also met opposition; he paid a great personal price in Kamill’s role in Classical and Modern Diffraction Theory goes putting forth his theory for the seismic diffraction forward problem.
    [Show full text]
  • Selected Correspondence of Descartes
    Selected Correspondence of Descartes René Descartes Copyright © Jonathan Bennett 2017. All rights reserved [Brackets] enclose editorial explanations. Small ·dots· enclose material that has been added, but can be read as though it were part of the original text. Occasional •bullets, and also indenting of passages that are not quotations, are meant as aids to grasping the structure of a sentence or a thought. Every four-point ellipsis . indicates the omission of a brief passage that has no philosophical interest, or that seems to present more difficulty than it is worth. (Where a letter opens with civilities and/or remarks about the postal system, the omission of this material is not marked by ellipses.) Longer omissions are reported between brackets in normal-sized type. —The letters between Descartes and Princess Elisabeth of Bohemia, omitted here, are presented elsewhere on this website (but see note on page 181).—This version is greatly indebted to CSMK [see Glossary] both for a good English translation to work from and for many explanatory notes, though most come from AT [see Glossary].—Descartes usually refers to others by title (‘M.’ for ‘Monsieur’ or ‘Abbé’ or ‘Reverend Father’ etc.); the present version omits most of these.—Although the material is selected mainly for its bearing on Descartes as a philosopher, glimpses are given of the colour and flavour of other sides of his life. First launched: April 2013 Correspondence René Descartes Contents Letters written in 1619–1637 1 to Beeckman, 26.iii.1619........................................................1
    [Show full text]
  • 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.
    [Show full text]
  • The Science of String Instruments
    The Science of String Instruments Thomas D. Rossing Editor The Science of String Instruments Editor Thomas D. Rossing Stanford University Center for Computer Research in Music and Acoustics (CCRMA) Stanford, CA 94302-8180, USA [email protected] ISBN 978-1-4419-7109-8 e-ISBN 978-1-4419-7110-4 DOI 10.1007/978-1-4419-7110-4 Springer New York Dordrecht Heidelberg London # Springer Science+Business Media, LLC 2010 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer ScienceþBusiness Media (www.springer.com) Contents 1 Introduction............................................................... 1 Thomas D. Rossing 2 Plucked Strings ........................................................... 11 Thomas D. Rossing 3 Guitars and Lutes ........................................................ 19 Thomas D. Rossing and Graham Caldersmith 4 Portuguese Guitar ........................................................ 47 Octavio Inacio 5 Banjo ...................................................................... 59 James Rae 6 Mandolin Family Instruments........................................... 77 David J. Cohen and Thomas D. Rossing 7 Psalteries and Zithers .................................................... 99 Andres Peekna and Thomas D.
    [Show full text]
  • Founding a Family of Fiddles
    The four members of the violin family have changed very little In hundreds of years. Recently, a group of musi- cians and scientists have constructed a "new" string family. 16 Founding a Family of Fiddles Carleen M. Hutchins An article from Physics Today, 1967. New measmement techniques combined with recent acoustics research enable us to make vioUn-type instruments in all frequency ranges with the properties built into the vioHn itself by the masters of three centuries ago. Thus for the first time we have a whole family of instruments made according to a consistent acoustical theory. Beyond a doubt they are musically successful by Carleen Maley Hutchins For three or folti centuries string stacles have stood in the way of practi- quartets as well as orchestras both cal accomplishment. That we can large and small, ha\e used violins, now routinely make fine violins in a violas, cellos and contrabasses of clas- variety of frequency ranges is the re- sical design. These wooden instru- siJt of a fortuitous combination: ments were brought to near perfec- violin acoustics research—showing a tion by violin makers of the 17th and resurgence after a lapse of 100 years— 18th centuries. Only recendy, though, and the new testing equipment capa- has testing equipment been good ble of responding to the sensitivities of enough to find out just how they work, wooden instruments. and only recently have scientific meth- As is shown in figure 1, oiu new in- ods of manufactiu-e been good enough struments are tuned in alternate inter- to produce consistently instruments vals of a musical fourth and fifth over with the qualities one wants to design the range of the piano keyboard.
    [Show full text]
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • August 1909) James Francis Cooke
    Gardner-Webb University Digital Commons @ Gardner-Webb University The tudeE Magazine: 1883-1957 John R. Dover Memorial Library 8-1-1909 Volume 27, Number 08 (August 1909) James Francis Cooke Follow this and additional works at: https://digitalcommons.gardner-webb.edu/etude Part of the Composition Commons, Ethnomusicology Commons, Fine Arts Commons, History Commons, Liturgy and Worship Commons, Music Education Commons, Musicology Commons, Music Pedagogy Commons, Music Performance Commons, Music Practice Commons, and the Music Theory Commons Recommended Citation Cooke, James Francis. "Volume 27, Number 08 (August 1909)." , (1909). https://digitalcommons.gardner-webb.edu/etude/550 This Book is brought to you for free and open access by the John R. Dover Memorial Library at Digital Commons @ Gardner-Webb University. It has been accepted for inclusion in The tudeE Magazine: 1883-1957 by an authorized administrator of Digital Commons @ Gardner-Webb University. For more information, please contact [email protected]. AUGUST 1QCQ ETVDE Forau Price 15cents\\ i nVF.BS nf//3>1.50 Per Year lore Presser, Publisher Philadelphia. Pennsylvania THE EDITOR’S COLUMN A PRIMER OF FACTS ABOUT MUSIC 10 OUR READERS Questions and Answers on the Elements THE SCOPE OF “THE ETUDE.” New Publications ot Music By M. G. EVANS s that a Thackeray makes Warrington say to Pen- 1 than a primer; dennis, in describing a great London news¬ _____ _ encyclopaedia. A MONTHLY JOURNAL FOR THE MUSICIAN, THE THREE MONTH SUMMER SUBSCRIP¬ paper: “There she is—the great engine—she Church and Home Four-Hand MisceUany Chronology of Musical History the subject matter being presented not alpha¬ Price, 25 Cent, betically but progressively, beginning with MUSIC STUDENT, AND ALL MUSIC LOVERS.
    [Show full text]
  • Descartes' Optics
    Descartes’ Optics Jeffrey K. McDonough Descartes’ work on optics spanned his entire career and represents a fascinating area of inquiry. His interest in the study of light is already on display in an intriguing study of refraction from his early notebook, known as the Cogitationes privatae, dating from 1619 to 1621 (AT X 242-3). Optics figures centrally in Descartes’ The World, or Treatise on Light, written between 1629 and 1633, as well as, of course, in his Dioptrics published in 1637. It also, however, plays important roles in the three essays published together with the Dioptrics, namely, the Discourse on Method, the Geometry, and the Meteorology, and many of Descartes’ conclusions concerning light from these earlier works persist with little substantive modification into the Principles of Philosophy published in 1644. In what follows, we will look in a brief and general way at Descartes’ understanding of light, his derivations of the two central laws of geometrical optics, and a sampling of the optical phenomena he sought to explain. We will conclude by noting a few of the many ways in which Descartes’ efforts in optics prompted – both through agreement and dissent – further developments in the history of optics. Descartes was a famously systematic philosopher and his thinking about optics is deeply enmeshed with his more general mechanistic physics and cosmology. In the sixth chapter of The Treatise on Light, he asks his readers to imagine a new world “very easy to know, but nevertheless similar to ours” consisting of an indefinite space filled everywhere with “real, perfectly solid” matter, divisible “into as many parts and shapes as we can imagine” (AT XI ix; G 21, fn 40) (AT XI 33-34; G 22-23).
    [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]
  • The Tuning Fork: an Amazing Acoustics Apparatus
    FEATURED ARTICLE The Tuning Fork: An Amazing Acoustics Apparatus Daniel A. Russell It seems like such a simple device: a U-shaped piece of metal and Helmholtz resonators were two of the most impor- with a stem to hold it; a simple mechanical object that, when tant items of equipment in an acoustics laboratory. In 1834, struck lightly, produces a single-frequency pure tone. And Johann Scheibler, a silk manufacturer without a scientific yet, this simple appearance is deceptive because a tuning background, created a tonometer, a set of precisely tuned fork exhibits several complicated vibroacoustic phenomena. resonators (in this case tuning forks, although others used A tuning fork vibrates with several symmetrical and asym- Helmholtz resonators) used to determine the frequency of metrical flexural bending modes; it exhibits the nonlinear another sound, essentially a mechanical frequency ana- phenomenon of integer harmonics for large-amplitude lyzer. Scheibler’s tonometer consisted of 56 tuning forks, displacements; and the stem oscillates at the octave of the spanning the octave from A3 220 Hz to A4 440 Hz in steps fundamental frequency of the tines even though the tines of 4 Hz (Helmholtz, 1885, p. 441); he achieved this accu- have no octave component. A tuning fork radiates sound as racy by modifying each fork until it produced exactly 4 a linear quadrupole source, with a distinct transition from beats per second with the preceding fork in the set. At the a complicated near-field to a simpler far-field radiation pat- 1876 Philadelphia Centennial Exposition, Rudolph Koenig, tern. This transition from near field to far field can be seen the premier manufacturer of acoustics apparatus during in the directivity patterns, time-averaged vector intensity, the second half of the nineteenth century, displayed his and the phase relationship between pressure and particle Grand Tonometer with 692 precision tuning forks ranging velocity.
    [Show full text]