DOCSLIB.ORG

Consonance in Music and Mathematics: Application to Temperaments and Orchestration

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Consonance in Music and Mathematics: Application to Temperaments and Orchestration Consonance in Music and Mathematics: Application to Temperaments and Orchestration Constança Martins de Castro Simas Thesis to obtain the Master of Science Degree in Mathematics and Applications Supervisor: Henrique Manuel dos Santos Silveira de Oliveira Examination Committee Chairperson: António Manuel Pacheco Pires Supervisor: Henrique Manuel dos Santos Silveira de Oliveira Member of the Committee: João Maria da Cruz Teixeira Pinto December, 2014 ii Acknowledgments I’m very glad that the process of writing this thesis led me to learn and share interesting opinions with people from different backgrounds. I want to thank my advisor for accepting and encouraging my eccentric ideas. Gladly, the brain- storming reunions contributed to this final result in the best way possible. My colleagues Ricardo Vieira Lisboa and João Carvalho were also a great help throughout this process. They gave their input while solving some mathematical problems, and sometimes just kept me company while i complained about what were the work’s issues at the moment. Carrying on to a little different background i want to thank all the musicians that helped me. Some of them by agreeing on spending their time and talent recording material and others just because of the interest they showed in helping me understand how their musical instruments worked. Namely Hen- rique Costa, Thierry Redondo, João Ferreira, Catarina Dinis, Rafaela Oliveira, Diana Santos, Natacha Fernandes, Joana Mendes, Ana Conceição, Sérgio Sousa, Aldara Medeiros e Sílvia Rocha. I want to thank specially Tiago Ramos and Rita Blanco who were always there to support me, also in the whole logistics required to record with a dozen instrumentalists in one afternoon. Great thanks also to my music analysis teacher, Pedro Figueiredo, who kept giving me some ideas to work with. Lastly, i want to thank my whole family. My cousin Tiago Simas Freire for supporting me in some musicology issues, but most of all my parents who also suffered when some things didn’t seem to be solvable, and helped me in everything they could to make me succeed. iii iv Resumo A música e a matemática são duas áreas que, ao longo do tempo, têm vindo a perder as suas ligações. Nesta tese são feitas várias abordagens à relação entre as mesmas. Uma delas mais relacionada com as afinações de escalas usadas na antiguidade, e outra com a acústica e consonância numa orquestra actual. Pitágoras estudou a relação entre os números racionais e os sons puros, procedendo depois à afinação de escalas de forma a preservá-los. Como consequência, obteve uma escala que não era uniforme em termos de consonância. Hoje em dia, os músicos convivem com uma afinação que, apesar de ser prática e extremamente uniforme, não dá valor aos sons puros. Neste estudo, serão procuradas as afinações capazes de optimizar ambos os aspectos. Para tal, criar-se-á um método computacional capaz de devolver a consonância de duas notas, num intervalo de zero a um. A segunda vertente explorada ao longo da tese, é relacionada com a orquestra e os diferentes sons que a constituem. As "cores" dos instrumentos na orquestra são diferenciadas de forma matemática. Um som produzido por um instrumento tem um espectro harmónico que lhe corresponde, definindo o seu timbre. Para obter estes espectros, serão utilizados conceitos da teoria de Fourier, mais especi- ficamente a Transformada de Fourier Discreta. Este processo parte da gravação dos instrumentos, passando pela análise das respectivas ondas sonoras na linguagem Mathematica. Palavras-chave: consonância, espectro harmónico, transformada de Fourier v vi Abstract Music and Mathematics are two fields that lost their link over time. In this thesis, we make two different approaches to the relation between them. One of the approaches relates with the tuning of scales performed in ancient times, and the other with acoustics and consonance in orchestra nowadays. Pythagoras studied the relation between rational numbers and pure sounds, tuning scales in a way that would preserve this perfect consonances. However, this turned out to have an irregular consonance in the different intervals of the scale. Nowadays, musicians deal with a tuning system that, despite being extremely practical and uniform, doesn’t value much the pure intervals. Our goal is to find a tuning sys- tem capable of optimizing the features mentioned above. Therefore, we shall develop a computational method which outputs the consonance between two musical notes, in a range from zero to one. The second matter developed along this thesis is about the orchestra and the different sounds in it. The “colors” of the instruments in the orchestra are distinguished through a mathematical procedure. A sound produced by an instrument is defined by its harmonic spectrum, representing its timbre. To derive these spectra, we shall use concepts from Fourier theory, specially the Discrete Fourier Transform. This process is initiated with the recording of instrument sounds in an anechoic chamber, and then completed with the analysis of the soundwaves using the Mathematica language. Keywords: consonance, harmonic spectrum, Fourier transform vii viii Contents Acknowledgments........................................... iii Resumo.................................................v Abstract................................................. vii List of Tables.............................................. xi List of Figures............................................. xiv 1 Introduction 1 1.1 Organization...........................................2 2 State-of-the-art 3 2.1 What is sound?..........................................3 2.2 What is consonance?......................................6 2.3 Soundwaves and Fourier Analysis...............................8 2.3.1 Wave equation and the Beats phenomenon......................8 2.3.2 Fourier Series......................................9 2.3.3 Fourier Transform.................................... 10 3 Computing consonance 12 3.1 Recording orchestral instruments................................ 13 3.2 Calculation of the frequency spectra.............................. 13 3.3 A program to compute consonance............................... 17 3.3.1 1st step: Grouping frequencies............................. 17 3.3.2 2nd step: Notion of timbre in the program....................... 17 3.3.3 3rd step: Critical Bandwidth............................... 18 4 Temperaments 22 4.1 Pythagorean Tuning....................................... 24 4.2 Just Intonation.......................................... 25 4.3 Meantone Temperaments.................................... 26 4.4 Equal Temperament....................................... 28 4.5 Consonance calculations and results for each Temperament................. 30 ix 5 Timbres and Consonance in the Orchestra 33 5.1 Strings............................................... 34 5.1.1 Violin........................................... 36 5.1.2 Viola............................................ 39 5.1.3 Cello............................................ 39 5.2 Woodwinds............................................ 41 5.2.1 Flute............................................ 43 5.2.2 Oboe........................................... 44 5.2.3 Clarinet.......................................... 46 5.2.4 Bassoon.......................................... 47 5.3 Brass............................................... 49 5.3.1 Trumpet.......................................... 51 5.3.2 French Horn....................................... 52 5.3.3 Trombone......................................... 53 5.3.4 Tuba............................................ 54 5.4 Percussion............................................ 56 5.5 Consonance analysis of orchestral excerpts.......................... 60 5.5.1 Weight function of a harmonic spectrum........................ 60 5.5.2 Wagner’s Tristan chord................................. 61 5.5.3 Beethoven’s fifths in the 9th symphony......................... 64 5.5.4 Clarinet and oboe, the most consonant dissonance.................. 65 6 Conclusions 66 6.1 Future Work............................................ 67 Bibliography 70 7 Appendix 71 x List of Tables 2.1 Ratios of the most important intervals.............................7 4.1 Ratios of the intervals in a Pythagorean chromatic scale................... 25 4.2 Ratios of the intervals in a Just chromatic scale........................ 26 4.3 Ratios of the intervals in an Equal chromatic scale...................... 29 4.4 Consonance in all the temperaments with weight g(x) .................... 31 4.5 Consonance in all the temperaments with weight from Figure 4.9.............. 32 5.1 Values of zeros for Bessel functions [Benson, 2007]...................... 58 5.2 Consonances in the notes of the Tristan chord ob-oboes/ cl-clarinets/ bas-bassoons/ cel-celli 62 5.3 Consonances of a minor second in the clarinet and the oboe................ 65 xi xii List of Figures 2.1 Rhythmic cells..........................................4 2.2 Beethoven’s 5th symphony...................................4 2.3 Beethoven’s 5th symphony...................................5 2.4 Violin’s sound wave.......................................5 2.5 Flute’s soundwave........................................6 2.6 Harmonic Spectrum of C....................................6 3.1 WAV sound on Mathematica .................................. 13 3.2 Function to create the list of points for plotting the frequency spectrum........... 15 3.3 ListPlot of the coordinates calculated for the Frequency Spectrum.............
Load more

Recommended publications
  • 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]
  • HOW to BUY a BASSOON by Wendal Jones
    HOW TO BUY A BASSOON By Wendal Jones Most people think the bassoon is the most unique wind instrument of all. Unmistakable in sound and appearance, it is more easily recognized than the other woodwinds. The flute, clarinet, oboe and saxophone families are comprised of several different sizes but each family generally has the same look, from small to large, yet none look remotely like the bassoon. A close relative of the bassoon, the contra-bassoon is twice as big, so it must be doubled up a couple of times so that the instrument may be held more easily. Although there are miniature bassoons that have gained some popularity in Europe, they are used mainly for teaching very young players who cannot manage to hold or finger a regular bassoon, let alone a contra-bassoon. There is no sizable repertoire for these small instruments and they are unknown in orchestras or bands. For the most part, the bassoon is an ensemble instrument with an occasional solo passage providing just the right touch (oftentimes humorous) to a composition. The bassoon is also known for its plaintive voice in the orchestra. Solo passages like those found in the slow movement of Tchaikovski's Fifth Symphony and several in Scheherazade by Rimsky-Korsakov come to mind here. The bassoon is found in the symphony orchestra, concert bands, and in chamber music groups and there are some dazzling concerto soloists, too. The instrument is not generally found in jazz bands, although there have been some wonderful jazz bassoon soloists in the second half of the 20th century, notably Stuart McKay of Florida.
    [Show full text]
  • 18Th Century Quotations Relating to J.S. Bach's Temperament
    18 th century quotations relating to J.S. Bach’s temperament Written by Willem Kroesbergen and assisted by Andrew Cruickshank, Cape Town, October 2015 (updated 2nd version, 1 st version November 2013) Introduction: In 1850 the Bach-Gesellschaft was formed with the purpose of publishing the complete works of Johann Sebastian Bach (1685-1750) as part of the centenary celebration of Bach’s death. The collected works, without editorial additions, became known as the Bach- Gesellschaft-Ausgabe. After the formation of the Bach-Gesellschaft, during 1873, Philip Spitta (1841-1894) published his biography of Bach.1 In this biography Spitta wrote that Bach used equal temperament 2. In other words, by the late 19 th century, it was assumed by one of the more important writers on Bach that Bach used equal temperament. During the 20 th century, after the rediscovery of various kinds of historical temperaments, it became generally accepted that Bach did not use equal temperament. This theory was mainly based on the fact that Bach titled his collection of 24 preludes and fugues of 1722 as ‘Das wohltemperirte Clavier’, traditionally translated as the ‘Well-Tempered Clavier’ . Based on the title, it was assumed during the 20 th century that an unequal temperament was implied – equating the term ‘well-tempered’ with the notion of some form of unequal temperament. But, are we sure that it was Bach’s intention to use an unequal temperament for his 24 preludes and fugues? The German word for ‘wohl-temperiert’ is synonymous with ‘gut- temperiert’ which in turn translates directly to ‘good tempered’.
    [Show full text]
  • Harmonic Series for Clarinets by Allen Cole
    Harmonic Series for Clarinets by Allen Cole The primary notes of the clarinet go from low E to throat Bb. Each of these pitches has a particular number of vibrations per second, or frequency. By applying pressure to the reed, we can make it vibrate a various multiples of that frequency. These other, higher frequencies are called harmonics. When the fundamental frequency is doubled, the pitch rises one octave to its second harmonic. This is what happens when you press the octave key on a saxophone, oboe or bassoon. The clarinet's physical structure causes it not to sound octaves or other even-numbered harmonics, so its pitch rises in much longer, less even leaps. Because the clarinet does not overblow octaves and other even-numbered harmonics, its high note fingerings can seem confusing at first. Below are the fundamental notes from which the altissimo fingerings are derived. Practice moving between the different registers to help develop your embouchure & fingers. Chalemeau register - This is the bottom register, where the instrument's natural sound is heard. This pitch is called the fundamental. This register is named for the folk instrument that later became the clarinet. Clarion register - Press your left thumb on the register key and go up a 12th to the notes with the clear, trumpet-like sound that gave the clarinet its name. This is the third harmonic, or three times the frequency of the fundamental pitch. Altissimo register - Vent the "E" tone hole by sliding or removing your left index finger. For pitches "D" and above, put your right pinkie on the pinkie Eb key.
    [Show full text]
  • The Bass Clarinetist's Pedagogical Guide to Excerpts
    THE BASS CLARINETIST’S PEDAGOGICAL GUIDE TO EXCERPTS FROM THE WIND BAND LITERATURE Britni Cheyenne Bland, B.M., M.M Dissertation Prepared for the Degree of DOCTOR OF MUSICAL ARTS UNIVERSITY OF NORTH TEXAS August 2015 APPROVED: Kimberly Cole Luevano, Major Professor John C. Scott, Committee Member Debbie Rohwer, Committee Member John Holt, Chair of the Department of Instrumental Studies Benjamin Brand, Director of Graduate Studies James Scott, Dean of the College of Music Costas Tsatsoulis, Interim Dean of the Toulouse Graduate School Bland, Britni Cheyenne. The Bass Clarinetist’s Pedagogical Guide to Excerpts from the Wind Band Literature. Doctor of Musical Arts (Performance) August 2015, 44 pp., 14 musical examples, 7 figures, 20 references. Student clarinet performers often encounter bass clarinet for the first time in a high school or university wind ensemble, so it is logical for clarinet pedagogues to encourage and assist their students in learning this wind band literature. In addition to becoming familiar with this oft performed repertoire, students will develop a set of specialized bass clarinet skills that one cannot learn on soprano clarinet. These skills include increased air capacity and support, timbre consistency in differing registers, intonation tendencies of the lower instrument, voicing flexibility, right hand thumb dexterity for keys that do not exist on soprano clarinet, technical facility for eleven pinky keys (as opposed to the seven pinky keys on a typical soprano clarinet0, and effective altissimo fingerings. The purpose, then, of this document is to provide a performance guide for select bass clarinet solo excerpts from the wind band literature and to provide supplemental exercises intended to help students acquire the specialized bass clarinet skill set they will need in order to perform the selected excerpts successfully.
    [Show full text]
  • Flexible Tuning Software: Beyond Equal Temperament
    Syracuse University SURFACE Syracuse University Honors Program Capstone Syracuse University Honors Program Capstone Projects Projects Spring 5-1-2011 Flexible Tuning Software: Beyond Equal Temperament Erica Sponsler Follow this and additional works at: https://surface.syr.edu/honors_capstone Part of the Computer and Systems Architecture Commons, and the Other Computer Engineering Commons Recommended Citation Sponsler, Erica, "Flexible Tuning Software: Beyond Equal Temperament" (2011). Syracuse University Honors Program Capstone Projects. 239. https://surface.syr.edu/honors_capstone/239 This Honors Capstone Project is brought to you for free and open access by the Syracuse University Honors Program Capstone Projects at SURFACE. It has been accepted for inclusion in Syracuse University Honors Program Capstone Projects by an authorized administrator of SURFACE. For more information, please contact [email protected]. Flexible Tuning Software: Beyond Equal Temperament A Capstone Project Submitted in Partial Fulfillment of the Requirements of the Renée Crown University Honors Program at Syracuse University Erica Sponsler Candidate for B.S. Degree and Renée Crown University Honors May/2011 Honors Capstone Project in _____Computer Science___ Capstone Project Advisor: __________________________ Dr. Shiu-Kai Chin Honors Reader: __________________________________ Dr. James Royer Honors Director: __________________________________ James Spencer, Interim Director Date:___________________________________________ Flexible Tuning Software: Beyond Equal
    [Show 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.
    [Show full text]
  • The Earliest Music for Bass Clarinet Pdf
    THE EARLIEST BASS CLARINET MUSIC (1794) AND THE BASS CLARINETS BY HEINRICH AND AUGUST GRENSER Albert R. Rice C.I.R.C.B. - International Bass Clarinet Research Center THE EARLIEST BASS CLARINET MUSIC (1794) AND THE BASS CLARINETS BY HEINRICH AND AUGUST GRENSER by Albert R. Rice For many years the bass clarinets by Heinrich Grenser and August Grenser made in 1793 and 1795 have been known. What has been overlooked is Patrik Vretblad’s list of a concert including the bass clarinet performed in 1794 by the Swedish clarinetist Johann Ignaz Strenensky.1 This is important news since it is the earliest documented bass clarinet music. All other textbooks and studies concerning the bass clarinet fail to mention this music played in Sweden. Although it is not definitely known what type of bass clarinet was played, evidence suggests that it was a bassoon-shaped bass clarinet by Heinrich Grenser. This article discusses the Stockholm court’s early employment of full time clarinetists; its players and music, including the bass clarinet works; the bass clarinets by Heinrich and August Grenser; and conclusions. Stockholm Court Orchestra Stockholm’s theater court orchestra employed seven clarinetists during the eighteenth century, including the famous composer and clarinetist Bernhard Henrik Crusell: Christian Traugott Schlick 1779-1786 August Heinrich Davidssohn 1779-1799 Georg Christian Thielemann 1785-1812 Carl Sigimund Gelhaar 1785-1793 Johann Ignaz Stranensky 1789-18052 Bernhard Henrik Crusell 1793-1834 Johan Christian Schatt 1798-18183 In 1779, Schlick and Davidssohn appeared as extra players at the Stockholm theater in a concert of the music academy.
    [Show full text]
  • Mathematics and Music
    Mathematics and Music What? Archytas, Pythagoras Other Pythagorean Philosophers/Educators: Mathematics The Quadrivium (“study of the unchangeable”) Number Magnitude Arithmetic Music Geometry Astronomy numbers at numbers in magnitudes magnitudes rest motion at rest in motion 1 Physics of Sound and Musical Tone y 2 Pressure 1 0 -5 -2.5 0 2.5 5 x Time -1 -2 Pitch: frequency of wave = number of cycles per second (Hz) higher pitch more cycles per second skinnier waves on graph Volume: amplitude of wave = difference between maximum pressure and average pressure higher volume taller waves on graph Timbre: quality of tone = shape of wave 2 Musical Scale: (increasing pitch = frequency) C→D→E→F→G→A→B→C→… Notes between: C# D# F# G# A# bbb bbb bbb bbb bbb or D E G A B 12-note Musical Scale (Chromatic Scale): b b C→ C#→ D→ Ebb→ E→ F→ F#→ G→ G#→A→Bbb→B→C→… Musical Intervals: Interval Name Examples 2nd 2 half steps C→D, E → F# 3rd 4 half steps G→B, B → D# 5th 7 half steps G→D, B → F# # # Octave 12 half steps C1→C2, F 2→ F 3 Harmonics ( Partials ) Multiply Frequency Interval Example by Produced C1=fundamental 2 1 octave C2 3 1 octave + perfect 5th G2 (2% sharp) 4 2 octaves C3 5 2 octaves + major 3rd E3 (14% flat) 6 2 octaves + perfect 5th G3 (2% sharp) bbbb 7 2 octaves + dominant 7th B 3 (32% flat) 8 3 octaves C4 9 3 octaves + whole step D4 (4% sharp) 10 3 octaves + major 3rd E4 (14% flat) 3 When a musical instrument is played, the harmonics appear at different amplitudes --- this creates the different timbres.
    [Show full text]
  • Stanley Hasty: His Life and Teaching Elizabeth Marie Gunlogson
    Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2006 Stanley Hasty: His Life and Teaching Elizabeth Marie Gunlogson Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF MUSIC STANLEY HASTY: HIS LIFE AND TEACHING By ELIZABETH MARIE GUNLOGSON A treatise submitted to the College of Music in partial fulfillment of the requirements for the degree of Doctor of Music Degree Awarded: Fall Semester, 2006 Copyright @ 2006 Elizabeth M. Gunlogson All Rights Reserved The members of the Committee approve the Treatise of Elizabeth M. Gunlogson defended on November 10, 2006. ______________________ Frank Kowalsky Professor Directing Treatise ______________________ Seth Beckman Outside Committee Member ______________________ Patrick Meighan Committee Member The Office of Graduate Studies has verified and approved the above named committee members. ii To Stanley and June Hasty iii ACKNOWLEDGEMENTS First and foremost I would like to thank Stanley and June Hasty for sharing their life story with me. Your laughter, hospitality and patience throughout this whole process was invaluable. To former Hasty students David Bellman, Larry Combs, Frank Kowalsky, Elsa Ludewig- Verdehr, Tom Martin and Maurita Murphy Mead, thank you for your support of this project and your willingness to graciously share your experiences with me. Through you, the Hasty legacy lives on. A special thanks to the following people who provided me with valuable information and technical support: David Coppen, Special Collections Librarian and Archivist, Sibley Music Library (Eastman School of Music); Elizabeth Schaff, Archivist, Peabody Institute/Baltimore Symphony Orchestra; Nicole Cerrillos, Public Relations Manager, Pittsburgh Symphony Orchestra; Tom Akins, Archivist, Indianapolis Symphony Orchestra; James Gholson, Professor of Clarinet, University of Memphis; Carl Fischer Music Publishing; and Annie Veblen-McCarty.
    [Show full text]
  • Introduction: the Ingredients of a Masterpiece
    Music Survey Courses: Approaches to Teaching Introduction: The Ingredients of a Masterpiece By Daniel N. Thompson In the sciences, research receives its justification and its support-despite all the lip service to 'pure' knowledge-from the exploitable discoveries or patents to which it may lead. In the humanities, research receives its justification­ despite all the lip service to the advancement of learning-from its applicabil­ ity to teaching. [172J -Robert Scholes Introduction Perhaps because I practice the discipline of ethnomusicology, I believe that the study of music can justifiably include the study of any aspect of musical behavior, including the study of the teaching of music as well as the study of the teaching about music. l With this in mind, some time ago I had the idea that it would be an interesting departure for Current Musi­ cology to examine the teaching of music survey courses, with particular at­ tention paid to "masterpieces" courses-of the type that constitutes the music component of Columbia's undergraduate Core Curriculum (partic­ ularly because the teaching of the Core survey course is the endeavor most commonly shared among the music department's professors and graduate­ student instructors). I wanted views from outside Columbia-indeed, from outside the re­ search university setting-as well, so I solicited articles from scholar­ administrators at a conservatory and at a liberal arts college. I am there­ fore pleased to present, in this special section of Current Musicology #65, the viewpoints of Peter Rojcewicz, from The Juilliard School in Manhattan, and of Sean Williams, from The Evergreen State College in Olympia, Washington.
    [Show full text]
  • Music Theory Contents
    Music theory Contents 1 Music theory 1 1.1 History of music theory ........................................ 1 1.2 Fundamentals of music ........................................ 3 1.2.1 Pitch ............................................. 3 1.2.2 Scales and modes ....................................... 4 1.2.3 Consonance and dissonance .................................. 4 1.2.4 Rhythm ............................................ 5 1.2.5 Chord ............................................. 5 1.2.6 Melody ............................................ 5 1.2.7 Harmony ........................................... 6 1.2.8 Texture ............................................ 6 1.2.9 Timbre ............................................ 6 1.2.10 Expression .......................................... 7 1.2.11 Form or structure ....................................... 7 1.2.12 Performance and style ..................................... 8 1.2.13 Music perception and cognition ................................ 8 1.2.14 Serial composition and set theory ............................... 8 1.2.15 Musical semiotics ....................................... 8 1.3 Music subjects ............................................. 8 1.3.1 Notation ............................................ 8 1.3.2 Mathematics ......................................... 8 1.3.3 Analysis ............................................ 9 1.3.4 Ear training .......................................... 9 1.4 See also ................................................ 9 1.5 Notes ................................................
    [Show full text]