Sixth Chords
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The Group-Theoretic Description of Musical Pitch Systems
The Group-theoretic Description of Musical Pitch Systems Marcus Pearce [email protected] 1 Introduction Balzano (1980, 1982, 1986a,b) addresses the question of finding an appropriate level for describing the resources of a pitch system (e.g., the 12-fold or some microtonal division of the octave). His motivation for doing so is twofold: “On the one hand, I am interested as a psychologist who is not overly impressed with the progress we have made since Helmholtz in understanding music perception. On the other hand, I am interested as a computer musician who is trying to find ways of using our pow- erful computational tools to extend the musical [domain] of pitch . ” (Balzano, 1986b, p. 297) Since the resources of a pitch system ultimately depend on the pairwise relations between pitches, the question is one of how to conceive of pitch intervals. In contrast to the prevailing approach which de- scribes intervals in terms of frequency ratios, Balzano presents a description of pitch sets as mathematical groups and describes how the resources of any pitch system may be assessed using this description. Thus he is concerned with presenting an algebraic description of pitch systems as a competitive alternative to the existing acoustic description. In these notes, I shall first give a brief description of the ratio based approach (§2) followed by an equally brief exposition of some necessary concepts from the theory of groups (§3). The following three sections concern the description of the 12-fold division of the octave as a group: §4 presents the nature of the group C12; §5 describes three perceptually relevant properties of pitch-sets in C12; and §6 describes three musically relevant isomorphic representations of C12. -
Jazz Harmony Iii
MU 3323 JAZZ HARMONY III Chord Scales US Army Element, School of Music NAB Little Creek, Norfolk, VA 23521-5170 13 Credit Hours Edition Code 8 Edition Date: March 1988 SUBCOURSE INTRODUCTION This subcourse will enable you to identify and construct chord scales. This subcourse will also enable you to apply chord scales that correspond to given chord symbols in harmonic progressions. Unless otherwise stated, the masculine gender of singular is used to refer to both men and women. Prerequisites for this course include: Chapter 2, TC 12-41, Basic Music (Fundamental Notation). A knowledge of key signatures. A knowledge of intervals. A knowledge of chord symbols. A knowledge of chord progressions. NOTE: You can take subcourses MU 1300, Scales and Key Signatures; MU 1305, Intervals and Triads; MU 3320, Jazz Harmony I (Chord Symbols/Extensions); and MU 3322, Jazz Harmony II (Chord Progression) to obtain the prerequisite knowledge to complete this subcourse. You can also read TC 12-42, Harmony to obtain knowledge about traditional chord progression. TERMINAL LEARNING OBJECTIVES MU 3323 1 ACTION: You will identify and write scales and modes, identify and write chord scales that correspond to given chord symbols in a harmonic progression, and identify and write chord scales that correspond to triads, extended chords and altered chords. CONDITION: Given the information in this subcourse, STANDARD: To demonstrate competency of this task, you must achieve a minimum of 70% on the subcourse examination. MU 3323 2 TABLE OF CONTENTS Section Subcourse Introduction Administrative Instructions Grading and Certification Instructions L esson 1: Sc ales and Modes P art A O verview P art B M ajor and Minor Scales P art C M odal Scales P art D O ther Scales Practical Exercise Answer Key and Feedback L esson 2: R elating Chord Scales to Basic Four Note Chords Practical Exercise Answer Key and Feedback L esson 3: R elating Chord Scales to Triads, Extended Chords, and Altered Chords Practical Exercise Answer Key and Feedback Examination MU 3323 3 ADMINISTRATIVE INSTRUCTIONS 1. -
An Analysis and Performance Considerations for John
AN ANALYSIS AND PERFORMANCE CONSIDERATIONS FOR JOHN HARBISON’S CONCERTO FOR OBOE, CLARINET, AND STRINGS by KATHERINE BELVIN (Under the Direction of D. RAY MCCLELLAN) ABSTRACT John Harbison is an award-winning and prolific American composer. He has written for almost every conceivable genre of concert performance with styles ranging from jazz to pre-classical forms. The focus of this study, his Concerto for Oboe, Clarinet, and Strings, was premiered in 1985 as a product of a Consortium Commission awarded by the National Endowment of the Arts. The initial discussions for the composition were with oboist Sara Bloom and clarinetist David Shifrin. Harbison’s Concerto for Oboe, Clarinet, and Strings allows the clarinet to finally be introduced to the concerto grosso texture of the Baroque period, for which it was born too late. This document includes biographical information on John Harbison including his life and career, compositional style, and compositional output. It also contains a brief history of the Baroque concerto grosso and how it relates to the Harbison concerto. There is a detailed set-class analysis of each movement and information on performance considerations. The two performers as well as the composer were interviewed to discuss the commission, premieres, and theoretical/performance considerations for the concerto. INDEX WORDS: John Harbison, Concerto for Oboe, Clarinet, and Strings, clarinet concerto, oboe concerto, Baroque concerto grosso, analysis and performance AN ANALYSIS AND PERFORMANCE CONSIDERATIONS FOR JOHN HARBISON’S CONCERTO FOR OBOE, CLARINET, AND STRINGS by KATHERINE BELVIN B.M., Tennessee Technological University, 2004 M.M., University of Cincinnati, 2006 A Dissertation Submitted to the Graduate Faculty of The University of Georgia in Partial Fulfillment of the Requirements for the Degree DOCTOR OF MUSICAL ARTS ATHENS, GEORGIA 2009 © 2009 Katherine Belvin All Rights Reserved AN ANALYSIS AND PERFORMANCE CONSIDERATIONS FOR JOHN HARBISON’S CONCERTO FOR OBOE, CLARINET, AND STRINGS by KATHERINE BELVIN Major Professor: D. -
“Chordal Command”
Musician Transformation Training “CHORDAL COMMAND” This training will cover key insights and techniques you must understand in order to get the most out of the “Chord County” program, which covers Chordal Command concepts. Chords rule in contemporary music and having a deep understanding of how to build and manipulate them is the key to excelling to higher heights. From the most basic chords to complex voicings, this resource will equip you with the formulas and shortcuts to master them all! Enjoy! -Pg 1- © 2010. HearandPlay.com. All Rights Reserved Introduction In this guide, we’ll be starting with triads and what I call the “FANTASTIC FOUR.” Then we’ll move on to shortcuts that will help you master extended chords (the heart of contemporary playing). After that, we’ll discuss inversions (the key to multiplying your chordal vocaluary), primary vs secondary chords, and we’ll end on voicings and the difference between “voicings” and “inversions.” But first, let’s turn to some common problems musicians encounter when it comes to chordal mastery. Common Problems 1. Lack of chordal knowledge beyond triads: Musicians who fall into this category simply have never reached outside of the basic triads (major, minor, diminished, augmented) and are stuck playing the same chords they’ve always played. There is a mental block that almost prohibits them from learning and retaining new chords. Extra effort must be made to embrace new chords, no matter how difficult and unusual they are at first. Knowing the chord formulas and shortcuts that will turn any basic triad into an extended chord is the secret. -
Generalized Interval System and Its Applications
Generalized Interval System and Its Applications Minseon Song May 17, 2014 Abstract Transformational theory is a modern branch of music theory developed by David Lewin. This theory focuses on the transformation of musical objects rather than the objects them- selves to find meaningful patterns in both tonal and atonal music. A generalized interval system is an integral part of transformational theory. It takes the concept of an interval, most commonly used with pitches, and through the application of group theory, generalizes beyond pitches. In this paper we examine generalized interval systems, beginning with the definition, then exploring the ways they can be transformed, and finally explaining com- monly used musical transformation techniques with ideas from group theory. We then apply the the tools given to both tonal and atonal music. A basic understanding of group theory and post tonal music theory will be useful in fully understanding this paper. Contents 1 Introduction 2 2 A Crash Course in Music Theory 2 3 Introduction to the Generalized Interval System 8 4 Transforming GISs 11 5 Developmental Techniques in GIS 13 5.1 Transpositions . 14 5.2 Interval Preserving Functions . 16 5.3 Inversion Functions . 18 5.4 Interval Reversing Functions . 23 6 Rhythmic GIS 24 7 Application of GIS 28 7.1 Analysis of Atonal Music . 28 7.1.1 Luigi Dallapiccola: Quaderno Musicale di Annalibera, No. 3 . 29 7.1.2 Karlheinz Stockhausen: Kreuzspiel, Part 1 . 34 7.2 Analysis of Tonal Music: Der Spiegel Duet . 38 8 Conclusion 41 A Just Intonation 44 1 1 Introduction David Lewin(1933 - 2003) is an American music theorist. -
Music Content Analysis : Key, Chord and Rhythm Tracking In
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by ScholarBank@NUS MUSIC CONTENT ANALYSIS : KEY, CHORD AND RHYTHM TRACKING IN ACOUSTIC SIGNALS ARUN SHENOY KOTA (B.Eng.(Computer Science), Mangalore University, India) A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF COMPUTER SCIENCE NATIONAL UNIVERSITY OF SINGAPORE 2004 Acknowledgments I am grateful to Dr. Wang Ye for extending an opportunity to pursue audio research and work on various aspects of music analysis, which has led to this dissertation. Through his ideas, support and enthusiastic supervision, he is in many ways directly responsible for much of the direction this work took. He has been the best advisor and teacher I could have wished for and it has been a joy to work with him. I would like to acknowledge Dr. Terence Sim for his support, in the role of a mentor, during my first term of graduate study and for our numerous technical and music theoretic discussions thereafter. He has also served as my thesis examiner along with Dr Mohan Kankanhalli. I greatly appreciate the valuable comments and suggestions given by them. Special thanks to Roshni for her contribution to my work through our numerous discussions and constructive arguments. She has also been a great source of practical information, as well as being happy to be the first to hear my outrage or glee at the day’s current events. There are a few special people in the audio community that I must acknowledge due to their importance in my work. -
8.1.4 Intervals in the Equal Temperament The
8.1 Tonal systems 8-13 8.1.4 Intervals in the equal temperament The interval (inter vallum = space in between) is the distance of two notes; expressed numerically by the relation (ratio) of the frequencies of the corresponding tones. The names of the intervals are derived from the place numbers within the scale – for the C-major-scale, this implies: C = prime, D = second, E = third, F = fourth, G = fifth, A = sixth, B = seventh, C' = octave. Between the 3rd and 4th notes, and between the 7th and 8th notes, we find a half- step, all other notes are a whole-step apart each. In the equal-temperament tuning, a whole- step consists of two equal-size half-step (HS). All intervals can be represented by multiples of a HS: Distance between notes (intervals) in the diatonic scale, represented by half-steps: C-C = 0, C-D = 2, C-E = 4, C-F = 5, C-G = 7, C-A = 9, C-B = 11, C-C' = 12. Intervals are not just definable as HS-multiples in their relation to the root note C of the C- scale, but also between all notes: e.g. D-E = 2 HS, G-H = 4 HS, F-A = 4 HS. By the subdivision of the whole-step into two half-steps, new notes are obtained; they are designated by the chromatic sign relative to their neighbors: C# = C-augmented-by-one-HS, and (in the equal-temperament tuning) identical to the Db = D-diminished-by-one-HS. Corresponding: D# = Eb, F# = Gb, G# = Ab, A# = Bb. -
A Proposal for the Inclusion of Jazz Theory Topics in the Undergraduate Music Theory Curriculum
University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Masters Theses Graduate School 8-2016 A Proposal for the Inclusion of Jazz Theory Topics in the Undergraduate Music Theory Curriculum Alexis Joy Smerdon University of Tennessee, Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Part of the Music Education Commons, Music Pedagogy Commons, and the Music Theory Commons Recommended Citation Smerdon, Alexis Joy, "A Proposal for the Inclusion of Jazz Theory Topics in the Undergraduate Music Theory Curriculum. " Master's Thesis, University of Tennessee, 2016. https://trace.tennessee.edu/utk_gradthes/4076 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Alexis Joy Smerdon entitled "A Proposal for the Inclusion of Jazz Theory Topics in the Undergraduate Music Theory Curriculum." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Master of Music, with a major in Music. Barbara A. Murphy, Major Professor We have read this thesis and recommend its acceptance: Kenneth Stephenson, Alex van Duuren Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) A Proposal for the Inclusion of Jazz Theory Topics in the Undergraduate Music Theory Curriculum A Thesis Presented for the Master of Music Degree The University of Tennessee, Knoxville Alexis Joy Smerdon August 2016 ii Copyright © 2016 by Alexis Joy Smerdon All rights reserved. -
Nonatonic Harmonic Structures in Symphonies by Ralph Vaughan Williams and Arnold Bax Cameron Logan [email protected]
University of Connecticut OpenCommons@UConn Doctoral Dissertations University of Connecticut Graduate School 12-2-2014 Nonatonic Harmonic Structures in Symphonies by Ralph Vaughan Williams and Arnold Bax Cameron Logan [email protected] Follow this and additional works at: https://opencommons.uconn.edu/dissertations Recommended Citation Logan, Cameron, "Nonatonic Harmonic Structures in Symphonies by Ralph Vaughan Williams and Arnold Bax" (2014). Doctoral Dissertations. 603. https://opencommons.uconn.edu/dissertations/603 i Nonatonic Harmonic Structures in Symphonies by Ralph Vaughan Williams and Arnold Bax Cameron Logan, Ph.D. University of Connecticut, 2014 This study explores the pitch structures of passages within certain works by Ralph Vaughan Williams and Arnold Bax. A methodology that employs the nonatonic collection (set class 9-12) facilitates new insights into the harmonic language of symphonies by these two composers. The nonatonic collection has received only limited attention in studies of neo-Riemannian operations and transformational theory. This study seeks to go further in exploring the nonatonic‟s potential in forming transformational networks, especially those involving familiar types of seventh chords. An analysis of the entirety of Vaughan Williams‟s Fourth Symphony serves as the exemplar for these theories, and reveals that the nonatonic collection acts as a connecting thread between seemingly disparate pitch elements throughout the work. Nonatonicism is also revealed to be a significant structuring element in passages from Vaughan Williams‟s Sixth Symphony and his Sinfonia Antartica. A review of the historical context of the symphony in Great Britain shows that the need to craft a work of intellectual depth, simultaneously original and traditional, weighed heavily on the minds of British symphonists in the early twentieth century. -
Describing Species
DESCRIBING SPECIES Practical Taxonomic Procedure for Biologists Judith E. Winston COLUMBIA UNIVERSITY PRESS NEW YORK Columbia University Press Publishers Since 1893 New York Chichester, West Sussex Copyright © 1999 Columbia University Press All rights reserved Library of Congress Cataloging-in-Publication Data © Winston, Judith E. Describing species : practical taxonomic procedure for biologists / Judith E. Winston, p. cm. Includes bibliographical references and index. ISBN 0-231-06824-7 (alk. paper)—0-231-06825-5 (pbk.: alk. paper) 1. Biology—Classification. 2. Species. I. Title. QH83.W57 1999 570'.1'2—dc21 99-14019 Casebound editions of Columbia University Press books are printed on permanent and durable acid-free paper. Printed in the United States of America c 10 98765432 p 10 98765432 The Far Side by Gary Larson "I'm one of those species they describe as 'awkward on land." Gary Larson cartoon celebrates species description, an important and still unfinished aspect of taxonomy. THE FAR SIDE © 1988 FARWORKS, INC. Used by permission. All rights reserved. Universal Press Syndicate DESCRIBING SPECIES For my daughter, Eliza, who has grown up (andput up) with this book Contents List of Illustrations xiii List of Tables xvii Preface xix Part One: Introduction 1 CHAPTER 1. INTRODUCTION 3 Describing the Living World 3 Why Is Species Description Necessary? 4 How New Species Are Described 8 Scope and Organization of This Book 12 The Pleasures of Systematics 14 Sources CHAPTER 2. BIOLOGICAL NOMENCLATURE 19 Humans as Taxonomists 19 Biological Nomenclature 21 Folk Taxonomy 23 Binomial Nomenclature 25 Development of Codes of Nomenclature 26 The Current Codes of Nomenclature 50 Future of the Codes 36 Sources 39 Part Two: Recognizing Species 41 CHAPTER 3. -
AUTOHARPAUTOHARP 1 SHADRACH PRODUCTIONS, Denver, Colorado USA Chords Aplenty
Chords Aplenty CChordshords AAplentyplenty C G C F D B E A A C D G C E F B C B F How to choose GREAT chords to play the music you love on diatonic and chromatic AUTOHARPAUTOHARP 1 SHADRACH PRODUCTIONS, Denver, Colorado USA Chords Aplenty ©2013 Lucille Reilly. All rights reserved. No part of this work may be reproduced mechanically or electronically, or photocopied without prior permission in writing from the publisher, except for brief quotations included in critical reviews. Shadrach Productions supports the purchase, not the unauthorized repro- duction, of visual and audio works generated by all musicians, composers, authors, and artists in order to propagate the arts for years to come. We encourage you, your friends and colleagues to do the same. First printing: September 2013. Published by: Shadrach Productions P.O. Box 7338 Denver, CO 80207-0338 USA www.thedulcimerlady.com Printed with pride in the USA by Frederic Printing, Aurora, Colorado. ISBN: 978-0-9895233-0-1 Library of Congress Control Number: 2013909918 Cover design, page design, typesetting, illustrations, and music typography by Lucille Reilly. Editor: Sarah Christmyer Back cover photo: Ian Serff To place orders, please visit www.thedulcimerlady.com. Companion MIDI files are available The symbol “8” at the beginning of a tune or music example means you can hear it on a MIDI file. All MIDI files may be obtained from www.thedulcimerlady.com. ii Chords Aplenty TABLE OF CONTENTS Introduction ....................................................................................................... -
Reharmonizing Chord Progressions
Reharmonizing Chord Progressions We’re going to spend a little bit of time talking about just a few of the techniques which you’ve already learned about, and how you can use these tools to add interest and movement into your own chord progressions. CHORD INVERSIONS If a song that you’re playing stays on the same chord for several beats, it can begin to sound stagnant if you play the same chord voicing over and over. One of the things you can do to add movement into the chord progression is to stay on the same chord but choose a different inversion of that chord. For instance, if you have 2 consecutive measures where the 1(Major) chord forms the harmony, try playing the first measure using 1 in root position and start the next measure by changing to a 1 over 3 (in other words, use a first inversion 1 chord). In modern chord notation, we’d write this as C/E. Or, if you don’t want to change the bass note– you can at least try using a different ‘voicing’ of the chord: instead of (from bottom to top note) C, G, E, C you might try C, C, G, E or C, G, E, G. For a guitarist, this may mean just playing the chord in a different position. For a keyboardist, you may have to consider which note names are doubled and whether the spacing between notes is closer or farther apart. SUBSTITUTE CHORDS OF SIMILAR QUALITY One of the things we’ve talked about previously is that certain chords in any given key sound ‘at rest’ and certain chords sound with a great deal of tension and feel like they ‘need to resolve’ to a place of rest.