WHAT IS the CIRCLE of FIFTHS? WHO FIRST USED
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Rediscovering Frédéric Chopin's "Trois Nouvelles Études" Qiao-Shuang Xian Louisiana State University and Agricultural and Mechanical College, [email protected]
Louisiana State University LSU Digital Commons LSU Doctoral Dissertations Graduate School 2002 Rediscovering Frédéric Chopin's "Trois Nouvelles Études" Qiao-Shuang Xian Louisiana State University and Agricultural and Mechanical College, [email protected] Follow this and additional works at: https://digitalcommons.lsu.edu/gradschool_dissertations Part of the Music Commons Recommended Citation Xian, Qiao-Shuang, "Rediscovering Frédéric Chopin's "Trois Nouvelles Études"" (2002). LSU Doctoral Dissertations. 2432. https://digitalcommons.lsu.edu/gradschool_dissertations/2432 This Dissertation is brought to you for free and open access by the Graduate School at LSU Digital Commons. It has been accepted for inclusion in LSU Doctoral Dissertations by an authorized graduate school editor of LSU Digital Commons. For more information, please [email protected]. REDISCOVERING FRÉDÉRIC CHOPIN’S TROIS NOUVELLES ÉTUDES A Monograph Submitted to the Graduate Faculty of the Louisiana State University and Agricultural and Mechanical College in partial fulfillment of the requirements for the degree of Doctor of Musical Arts in The School of Music by Qiao-Shuang Xian B.M., Columbus State University, 1996 M.M., Louisiana State University, 1998 December 2002 TABLE OF CONTENTS LIST OF EXAMPLES ………………………………………………………………………. iii LIST OF FIGURES …………………………………………………………………………… v ABSTRACT …………………………………………………………………………………… vi CHAPTER 1. INTRODUCTION…………………………………………………………….. 1 The Rise of Piano Methods …………………………………………………………….. 1 The Méthode des Méthodes de piano of 1840 -
James Clerk Maxwell
James Clerk Maxwell JAMES CLERK MAXWELL Perspectives on his Life and Work Edited by raymond flood mark mccartney and andrew whitaker 3 3 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries c Oxford University Press 2014 The moral rights of the authors have been asserted First Edition published in 2014 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2013942195 ISBN 978–0–19–966437–5 Printed and bound by CPI Group (UK) Ltd, Croydon, CR0 4YY Links to third party websites are provided by Oxford in good faith and for information only. -
On Modulation —
— On Modulation — Dean W. Billmeyer University of Minnesota American Guild of Organists National Convention June 25, 2008 Some Definitions • “…modulating [is] going smoothly from one key to another….”1 • “Modulation is the process by which a change of tonality is made in a smooth and convincing way.”2 • “In tonal music, a firmly established change of key, as opposed to a passing reference to another key, known as a ‘tonicization’. The scale or pitch collection and characteristic harmonic progressions of the new key must be present, and there will usually be at least one cadence to the new tonic.”3 Some Considerations • “Smoothness” is not necessarily a requirement for a successful modulation, as much tonal literature will illustrate. A “convincing way” is a better criterion to consider. • A clear establishment of the new key is important, and usually a duration to the modulation of some length is required for this. • Understanding a modulation depends on the aural perception of the listener; hence, some ambiguity is inherent in distinguishing among a mere tonicization, a “false” modulation, and a modulation. • A modulation to a “foreign” key may be easier to accomplish than one to a diatonically related key: the ear is forced to interpret a new key quickly when there is a large change in the number of accidentals (i.e., the set of pitch classes) in the keys used. 1 Max Miller, “A First Step in Keyboard Modulation”, The American Organist, October 1982. 2 Charles S. Brown, CAGO Study Guide, 1981. 3 Janna Saslaw: “Modulation”, Grove Music Online ed. L. Macy (Accessed 5 May 2008), http://www.grovemusic.com. -
Theory Placement Examination (D
SAMPLE Placement Exam for Incoming Grads Name: _______________________ (Compiled by David Bashwiner, University of New Mexico, June 2013) WRITTEN EXAM I. Scales Notate the following scales using accidentals but no key signatures. Write the scale in both ascending and descending forms only if they differ. B major F melodic minor C-sharp harmonic minor II. Key Signatures Notate the following key signatures on both staves. E-flat minor F-sharp major Sample Graduate Theory Placement Examination (D. Bashwiner, UNM, 2013) III. Intervals Identify the specific interval between the given pitches (e.g., m2, M2, d5, P5, A5). Interval: ________ ________ ________ ________ ________ Note: the sharp is on the A, not the G. Interval: ________ ________ ________ ________ ________ IV. Rhythm and Meter Write the following rhythmic series first in 3/4 and then in 6/8. You may have to break larger durations into smaller ones connected by ties. Make sure to use beams and ties to clarify the meter (i.e. divide six-eight bars into two, and divide three-four bars into three). 2 Sample Graduate Theory Placement Examination (D. Bashwiner, UNM, 2013) V. Triads and Seventh Chords A. For each of the following sonorities, indicate the root of the chord, its quality, and its figured bass (being sure to include any necessary accidentals in the figures). For quality of chord use the following abbreviations: M=major, m=minor, d=diminished, A=augmented, MM=major-major (major triad with a major seventh), Mm=major-minor, mm=minor-minor, dm=diminished-minor (half-diminished), dd=fully diminished. Root: Quality: Figured Bass: B. -
Many of Us Are Familiar with Popular Major Chord Progressions Like I–IV–V–I
Many of us are familiar with popular major chord progressions like I–IV–V–I. Now it’s time to delve into the exciting world of minor chords. Minor scales give flavor and emotion to a song, adding a level of musical depth that can make a mediocre song moving and distinct from others. Because so many of our favorite songs are in major keys, those that are in minor keys1 can stand out, and some musical styles like rock or jazz thrive on complex minor scales and harmonic wizardry. Minor chord progressions generally contain richer harmonic possibilities than the typical major progressions. Minor key songs frequently modulate to major and back to minor. Sometimes the same chord can appear as major and minor in the very same song! But this heady harmonic mix is nothing to be afraid of. By the end of this article, you’ll not only understand how minor chords are made, but you’ll know some common minor chord progressions, how to write them, and how to use them in your own music. With enough listening practice, you’ll be able to recognize minor chord progressions in songs almost instantly! Table of Contents: 1. A Tale of Two Tonalities 2. Major or Minor? 3. Chords in Minor Scales 4. The Top 3 Chords in Minor Progressions 5. Exercises in Minor 6. Writing Your Own Minor Chord Progressions 7. Your Minor Journey 1 https://www.musical-u.com/learn/the-ultimate-guide-to-minor-keys A Tale of Two Tonalities Western music is dominated by two tonalities: major and minor. -
Cadence in Music Version 1.9: Oct 4, 2007 12:24 Pm GMT-5
Connexions module: m12402 1 Cadence in Music Version 1.9: Oct 4, 2007 12:24 pm GMT-5 Catherine Schmidt-Jones This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License ∗ Abstract A cadence is a place in a piece of music that feels like a stopping or resting point. In tonal music, cadences are classied by their chord progressions. Cadence in Music A cadence is any place in a piece of music that has the feel of an ending point. This can be either a strong, denite stopping point - the end of the piece, for example, or the end of a movement or a verse - but it also refers to the "temporary-resting-place" pauses that round o the ends of musical ideas within each larger section. A musical phrase1, like a sentence, usually contains an understandable idea, and then pauses before the next idea starts. Some of these musical pauses are simply take-a-breath- type pauses, and don't really give an "ending" feeling. In fact, like questions that need answers, many phrases leave the listener with a strong expectation of hearing the next, "answering", phrase. Other phrases, though, end with a more denite "we've arrived where we were going" feeling. The composer's expert control over such feelings of expectation and arrival are one of the main sources of the listener's enjoyment of the music. Like a story, a piece of music can come to an end by simply stopping, but most listeners will react to such abruptness with dissatisfaction: the story or music simply "stopped" instead of "ending" properly. -
Unified Music Theories for General Equal-Temperament Systems
Unified Music Theories for General Equal-Temperament Systems Brandon Tingyeh Wu Research Assistant, Research Center for Information Technology Innovation, Academia Sinica, Taipei, Taiwan ABSTRACT Why are white and black piano keys in an octave arranged as they are today? This article examines the relations between abstract algebra and key signature, scales, degrees, and keyboard configurations in general equal-temperament systems. Without confining the study to the twelve-tone equal-temperament (12-TET) system, we propose a set of basic axioms based on musical observations. The axioms may lead to scales that are reasonable both mathematically and musically in any equal- temperament system. We reexamine the mathematical understandings and interpretations of ideas in classical music theory, such as the circle of fifths, enharmonic equivalent, degrees such as the dominant and the subdominant, and the leading tone, and endow them with meaning outside of the 12-TET system. In the process of deriving scales, we create various kinds of sequences to describe facts in music theory, and we name these sequences systematically and unambiguously with the aim to facilitate future research. - 1 - 1. INTRODUCTION Keyboard configuration and combinatorics The concept of key signatures is based on keyboard-like instruments, such as the piano. If all twelve keys in an octave were white, accidentals and key signatures would be meaningless. Therefore, the arrangement of black and white keys is of crucial importance, and keyboard configuration directly affects scales, degrees, key signatures, and even music theory. To debate the key configuration of the twelve- tone equal-temperament (12-TET) system is of little value because the piano keyboard arrangement is considered the foundation of almost all classical music theories. -
Electrophonic Musical Instruments
G10H CPC COOPERATIVE PATENT CLASSIFICATION G PHYSICS (NOTES omitted) INSTRUMENTS G10 MUSICAL INSTRUMENTS; ACOUSTICS (NOTES omitted) G10H ELECTROPHONIC MUSICAL INSTRUMENTS (electronic circuits in general H03) NOTE This subclass covers musical instruments in which individual notes are constituted as electric oscillations under the control of a performer and the oscillations are converted to sound-vibrations by a loud-speaker or equivalent instrument. WARNING In this subclass non-limiting references (in the sense of paragraph 39 of the Guide to the IPC) may still be displayed in the scheme. 1/00 Details of electrophonic musical instruments 1/053 . during execution only {(voice controlled (keyboards applicable also to other musical instruments G10H 5/005)} instruments G10B, G10C; arrangements for producing 1/0535 . {by switches incorporating a mechanical a reverberation or echo sound G10K 15/08) vibrator, the envelope of the mechanical 1/0008 . {Associated control or indicating means (teaching vibration being used as modulating signal} of music per se G09B 15/00)} 1/055 . by switches with variable impedance 1/0016 . {Means for indicating which keys, frets or strings elements are to be actuated, e.g. using lights or leds} 1/0551 . {using variable capacitors} 1/0025 . {Automatic or semi-automatic music 1/0553 . {using optical or light-responsive means} composition, e.g. producing random music, 1/0555 . {using magnetic or electromagnetic applying rules from music theory or modifying a means} musical piece (automatically producing a series of 1/0556 . {using piezo-electric means} tones G10H 1/26)} 1/0558 . {using variable resistors} 1/0033 . {Recording/reproducing or transmission of 1/057 . by envelope-forming circuits music for electrophonic musical instruments (of 1/0575 . -
An Exploration of the Relationship Between Mathematics and Music
An Exploration of the Relationship between Mathematics and Music Shah, Saloni 2010 MIMS EPrint: 2010.103 Manchester Institute for Mathematical Sciences School of Mathematics The University of Manchester Reports available from: http://eprints.maths.manchester.ac.uk/ And by contacting: The MIMS Secretary School of Mathematics The University of Manchester Manchester, M13 9PL, UK ISSN 1749-9097 An Exploration of ! Relation"ip Between Ma#ematics and Music MATH30000, 3rd Year Project Saloni Shah, ID 7177223 University of Manchester May 2010 Project Supervisor: Professor Roger Plymen ! 1 TABLE OF CONTENTS Preface! 3 1.0 Music and Mathematics: An Introduction to their Relationship! 6 2.0 Historical Connections Between Mathematics and Music! 9 2.1 Music Theorists and Mathematicians: Are they one in the same?! 9 2.2 Why are mathematicians so fascinated by music theory?! 15 3.0 The Mathematics of Music! 19 3.1 Pythagoras and the Theory of Music Intervals! 19 3.2 The Move Away From Pythagorean Scales! 29 3.3 Rameau Adds to the Discovery of Pythagoras! 32 3.4 Music and Fibonacci! 36 3.5 Circle of Fifths! 42 4.0 Messiaen: The Mathematics of his Musical Language! 45 4.1 Modes of Limited Transposition! 51 4.2 Non-retrogradable Rhythms! 58 5.0 Religious Symbolism and Mathematics in Music! 64 5.1 Numbers are God"s Tools! 65 5.2 Religious Symbolism and Numbers in Bach"s Music! 67 5.3 Messiaen"s Use of Mathematical Ideas to Convey Religious Ones! 73 6.0 Musical Mathematics: The Artistic Aspect of Mathematics! 76 6.1 Mathematics as Art! 78 6.2 Mathematical Periods! 81 6.3 Mathematics Periods vs. -
Chapter 21 on Modal Mixture
CHAPTER21 Modal Mixture Much music of the late eighteenth and early nineteenth centuries commonly employs a type of chromaticism that cannot be said to derive from applied functions and tonicization. In fact, the chromaticism often appears to be nonfunctional-a mere coloring of the melodic and harmonic surface of the music. Listen to the two phrases of Example 21.1. The first phrase (mm. 1-8) contains exclusively diatonic harmonies, but the second phrase (mm. 11-21) is full of chromaticism. This creates sonorities, such as the A~-major chord in m. 15, which appear to be distant from the underlying F-major tonic. The chromatic harmonies in mm. 11-20 have been labeled with letter names that indicate the root and quality of the chord. EXAMPLE 21.1 Mascagni, "A casa amici" ("Homeward, friends"), Cavalleria Rusticana, scene 9 418 CHAPTER 21 MODAL MIXTURE 419 These sonorities share an important feature: All but the cadential V-I are members of the parallel mode, F minor. Viewing this progression through the lens of F minor reveals a simple bass arpeggiation that briefly tonicizes 420 THE COMPLETE MUSICIAN III (A~), then moves to PD and D, followed by a final resolution to major tonic in the major mode. The Mascagni excerpt is quite remarkable in its tonal plan. Although it begins and ends in F major, a significant portion of the music behaves as though written in F minor. This technique of borrowing harmonies from the parallel mode is called modal mixture (sometimes known simply as mixture). We have already encountered two instances of modal mixture. -
Orientalism As Represented in the Selected Piano Works by Claude Debussy
Chapter 4 ORIENTALISM AS REPRESENTED IN THE SELECTED PIANO WORKS BY CLAUDE DEBUSSY A prominent English scholar of French music, Roy Howat, claimed that, out of the many composers who were attracted by the Orient as subject matter, “Debussy is the one who made much of it his own language, even identity.”55 Debussy and Hahn, despite being in the same social circle, never pursued an amicable relationship.56 Even while keeping their distance, both composers were somewhat aware of the other’s career. Hahn, in a public statement from 1890, praised highly Debussy’s musical artistry in L'Apres- midi d'un faune.57 Debussy’s Exposure to Oriental Cultures Debussy’s first exposure to oriental art and philosophy began at Mallarmé’s Symbolist gatherings he frequented in 1887 upon his return to Paris from Rome.58 At the Universal Exposition of 1889, he had his first experience in the theater of Annam (Vietnam) and the Javanese Gamelan orchestra (Indonesia), which is said to be a catalyst 55Roy Howat, The Art of French Piano Music: Debussy, Ravel, Fauré, Chabrier (New Haven, Conn.: Yale University Press, 2009), 110 56Gavoty, 142. 57Ibid., 146. 58François Lesure and Roy Howat. "Debussy, Claude." In Grove Music Online. Oxford Music Online, http://www.oxfordmusiconline.com/subscriber/article/grove/music/07353 (accessed April 4, 2011). 33 34 in his artistic direction. 59 In 1890, Debussy was acquainted with Edmond Bailly, esoteric and oriental scholar, who took part in publishing and selling some of Debussy’s music at his bookstore L’Art Indépendeant. 60 In 1902, Debussy met Louis Laloy, an ethnomusicologist and music critic who eventually became Debussy’s most trusted friend and encouraged his use of Oriental themes.61 After the Universal Exposition in 1889, Debussy had another opportunity to listen to a Gamelan orchestra 11 years later in 1900. -
Consonance and Dissonance in Visual Music Bill Alves Harvey Mudd College
Claremont Colleges Scholarship @ Claremont All HMC Faculty Publications and Research HMC Faculty Scholarship 8-1-2012 Consonance and Dissonance in Visual Music Bill Alves Harvey Mudd College Recommended Citation Bill Alves (2012). Consonance and Dissonance in Visual Music. Organised Sound, 17, pp 114-119 doi:10.1017/ S1355771812000039 This Article is brought to you for free and open access by the HMC Faculty Scholarship at Scholarship @ Claremont. It has been accepted for inclusion in All HMC Faculty Publications and Research by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. Organised Sound http://journals.cambridge.org/OSO Additional services for Organised Sound: Email alerts: Click here Subscriptions: Click here Commercial reprints: Click here Terms of use : Click here Consonance and Dissonance in Visual Music Bill Alves Organised Sound / Volume 17 / Issue 02 / August 2012, pp 114 - 119 DOI: 10.1017/S1355771812000039, Published online: 19 July 2012 Link to this article: http://journals.cambridge.org/abstract_S1355771812000039 How to cite this article: Bill Alves (2012). Consonance and Dissonance in Visual Music. Organised Sound, 17, pp 114-119 doi:10.1017/ S1355771812000039 Request Permissions : Click here Downloaded from http://journals.cambridge.org/OSO, IP address: 134.173.130.244 on 24 Jul 2014 Consonance and Dissonance in Visual Music BILL ALVES Harvey Mudd College, The Claremont Colleges, 301 Platt Blvd, Claremont CA 91711 USA E-mail: [email protected] The concepts of consonance and dissonance broadly Plato found the harmony of the world in the Pythag- understood can provide structural models for creators of orean whole numbers and their ratios, abstract ideals visual music.