gaa a a a add ad dd ad add a2 dad ad 7 | | | Third Edition yr nal IMmON With an Introduction to Twentieth-Century Music Svefan Kostka & Dorothy PayneTONAL HARMONY with an Introduction to Twentieth-Century Music Third Edition Stefan Kostka The University of Texas at Austin Dorothy Payne ‘The University of Arizona Consulting Editor in Music ALLAN W, SCHINDLER > Eastman School of Music McGraw-Hill, Ine. New York # St. Louis # San Francisco * Auckland * Bogoti * Caracas Lishon * London * Madrid * Mexico City * Milan * Montreal * New Delhi San Juan # Singapore * Sydney * Tokyo « 1 rsTonal Harmony with an Introduction to Twentieth-Century Music Copyright © 1995 by McGraw-Hill, Inc. All rights reserved. Copyright © 1989, 1984 by Alfred A. Knopf, Inc. All rights reserved. Printed in the United States of America. Exceps as permitted tunder the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form or by lany means, or stored in a data base or retrieval sysier, without the prior written permission of the publisher @ ‘This bk sri on eye, acid-ee paper conning minima | S05 oa veyed fiber wih 108, poten dik be. 1234567890 DOCIDOC 9987654 ISBN 0-07-035874-5 ‘This book was set in Baskerville by Music Book Associates, Ine The editors were Cynthia Ward and Judith R. Cornwell the production supervisor was Louise Karars ‘The cover was designed by Carol A. Couch Project supervision was done by The Tel Book R. R, Dontelley & Sons Company Was priter und binder. Library of Congress Cataloging.in- Publication Data Kostha, Stefan M. ‘Tonal harmony with an introduction to wwentieth-century music / Stefan Kostka, Dorothy Payne; consulting editor in rousi, Allan W. Schindler — Sed ed. pcm, Includes index. ISBN 007-0358745 1. Harmony. 1, Payne, Dorothy. Hl Schindler, Allan, Tide MTSO.KS5 1994 125—der0 98.4075, Contents About the Authors Preface xiii Tothe Student — xvi PART ONE: FUNDAMENTALS 1 Chapter One Elements of Pitch 3 The Keyboard and Octave Registers. 3 Notation on the Staff 4 The Major Scale 6 ‘The Major Key Signatures 9 Minor Scales 13 Minor Key Signatures 14 Seale Degree Names 18 Intervals. 19 Perfect, Major, and Minor Intervals, Augmented and Diminished Intervals 23 Inversion of Intervals. 23. Chapter Two Elements of Rhythm = 27 Rhythm 27 Durational Symbols. 27 Bestand Tempo 2&8 Meer 29 Division of the Beat 31 Simple Time Signatures 32 Compound Time Signatures 34 ‘Time Signatures Summarized 37 More on Durational Symbols 89iv Contents Chapter Three Introduction to Triads and Seventh Chords 45, Invoduetion 45 Triads 45 Seventh Chords 48 Inversions of Chords. 50. Inversion Symbols and Figured Bass 51 Recognizing Chordsin Various Textures 55 Chapter Four Diatonic Chords in Major and Minor Keys 61 Invoduction 61 The Minor Scale 61 Diatonic Triads in Major 64 Diatonic Triadsin Minor 65 Diatonie Seventh Chords in Major Diatonic Seventh Chords in Minor 69 PART TWO: DIATONIC TRIADS 75 Chapter Five Principles of Voice Leading 77 Inoduction 77 The Melodic Line 78 Notating Chords 80 Voicing Single Triad 81 Parallels 84 Chapter Six Root Position Part Writing 91 Introduction 91 Root Position Part Writing with Repeated Roots 92. Root Position Part Writing with Roowsa 4th (5th) Apart 93 Root Position Part Writing with Roots a 3rd (6th) Apart 96 Root Position Part Writing with Roots 2 9nd (7th) Apart 98 Instrumental Ranges and Transpositions 102 Chapter Seven Harmonic Progression 106 Introduction 106 Sequences and the Circle of Fifths 107 The land V Chords 110 The Chord 12 The ViChord 113, Thell Chord Ua ‘The ViUChord 115 TheIVChord 116 Common Exceptions 117 Differences in the Minor Mode 18 Conclusion 119 Chapter Eight Triads in First Inversion 125 Introduction 125 Bass Arpeggiation 126 Substituted First Inversion Triads 127 Parallel Sixth Chords 129, Part Writing First Inversion Triads 134 Chapter Nine Triads in Second Inversion 140 Introduction 40 Bass Arpeggiation and the Melodic Bass. MI ‘The Cadential SixFour M2 The Passing SixFour 144 The Pedal SixFour M46 Part Writing for Second Inversion 148 Contents>SOOOOOHCOOOS OOOH OOOOOOOHOOCOOCEE vi Contents Chapter Ten Cadences, Phrases, and Periods 152 Musical Form 152 Cadences 152 Motives and Phrases 158 Mozart: "Andie Freude” 160 Period Forms 162 Chapter Eleven Non-Chord Tones 1 174 Introduction 174 Classification of Non-Chord Tones 175 Passing Tones 176 Neighboring Tones 178 Suspensions and Revardations 179 Figured Bass Symbols 184 Embellishing a Simple Texture 185 Chapter Twelve Non-ChordTones2 190 Appoggiauas 196 Escape Tones 192 The Neighbor Group 192 Anticipations 193, The Pedal Point. 195 ‘Special Problems in the Analysis ofNon-Chord Tones 196 PART THREE: DIATONIC SEVENTH CHORDS 203. Chapter Thirteen The V7 Chord 205 Introduction 205 General Voice-Leading Considerations 206 The V7 in Root Position 207 The V7 in Three Parts 211 Other Resolutions of the V7 919 The Inverted V7 Chard 216 The V§Chord 247 The V4 Chord 218 The ViGhord 219 ‘The Approach tothe 7th 20 Chapter Fourteen The I and Vil” Chords 225 Introduction 225 The 7 Chord 226 The VU? Chord in Major 288 The VII7 Chord in Minor 230 Chapter Fifteen Other Diatonic Seventh Chords 239 The 1V7 Chord 239 The VI Chord 242 The 17 Chord 244 The IN Chord 246 Seventh Chords and the Circle-ofFifths Sequence PART FOUR: CHROMATICISM 1253 Chapter Sixteen Secondary Functions 1255 Chromaticism and Altered Chords 255 Secondary Functions 256 Secondary Dominant Chords 256 Spelling Secondary Dominants 258 Recognizing Secondary Dominants 259 Secondary Dominazts i Context 260 246 Contents vilvili Contents Chapter Seventeen Secondary Functions 2273 Secondary Leading Tone Chords 273 Spelling Secondary Leading-Tone Chords 275 Recognizing Secondary Leading-Tone Chords 275 Secondary Leading-Tone Chords in Context 277 Sequences {nvolving Secondary Functions 283 Deceptive Resolutions of Secondary Functions 287 Other Secondary Functions 288 Chapter Eighteen ‘Modulations Using Diatonic Common Chords 299 Modulation and Change of Key 299 Moduiation and Tonicization 800 Key Relationships 302 Common-Chord Modulation 305 Analyzing Common-Chord Modulation 307 Chapter Nineteen ‘Some Other Modulatory Techniques 317 Altered Chords as Common Chords 817 Sequential Modulation 318 Modulation by Common Tone 321 Monophonic Modulation $25 Direct Modulation 326 Chapter Twenty Binary and Ternary Forms 335 Formal Terminology 385 Binary Forms 335 Ternary Forms 388 Rounded Binary Forms $42 Other Formal Designs 345 PART FIVE: CHROMATICISM 2 253 Chapter Twenty-One Mode Mixture 355 Introduction 355, Borrowed Chordsin Minor 3 The Use of bé in Major 356 Other Borrowed Chords in Major 889 Modulations Involving Mode Mixture 362 Chapter Twenty-Two The Neapolitan Chord 372 Introduction 372 Conventional Use of the Neapolitan 372 Other Uses of the Neapolitan 375 Chapter Twenty-Three Augmented Sixth Chords 1 384 The Inverval of the Augmented Sixth 384 The ltlian Augmented Sixth Chord 385 The French Augmented Sixth Chord 986 ‘The German Augmented Sixth Chord 388 Other Uses of Conventional Augmented Sixth Chords Chapter Twenty-Four Augmented Sixth Chords 2 400 Introduction $00. Other Bass Positions 400 Resolutions to Other Seale Degrees. 402 Resolutions to Other Chord Members 403 Other Types of Augmented Sixth Chords 405 Contents ix 391x Contents Chapter Twenty-Five Enharmonic Spellings and Enharmonic Modulations Enharmonic Speliings — 400 Enharmonic Reinterpretation 413 Enharmonic Modulations Using the MajorMinor Seventh Sonority 414 Enharmonic Moduiations Using the Diminished Seventh Chord 416 Chapter Twenty-Six #10 Further Elements of the Harmonic Vocabulary 425 Invoduction 425 The Dominaere wich a Substicuced 6th 425, The Dominant with a Raised 5th 428 Ninth, Eleventh, and Thirteenth Chords 431 ‘The Common-Tone Diminished Seventh Chord Sireteane 437 Coloristic Chord Successions 439) PART SIX: LATE ROMANTICISM ANO THE TWENTIETH CENTURY Chapter Twenty-Seven Tonal Harmony in the Late Nineteenth Century Invoduction 451 Counterpoint 452 ‘Treatment of Dominant Harmony 457 Sequence $60 Shiting Keys 463 Expanded Tonality 465, Chapter Twenty Eight An Introduction to Twentieth-Century Practices Introduction 478 Impressionism 479 433, 478 Seales 480 Chord Structure 492 Paraltelism 500 Pandiatonicism 507 SetTheory 609 The Twelve-Tone Technique 513 Total Seriafization 526 Rhythm and Meter 529 Aleatory or Chance Music 526 ‘Texture and Expanded Instrumental Resources 543 Electrowie Music 550 Appendix A Instrumental Ranges and Transpositions 557 Appendix B Answers to Self-Tests 559 indexes Index of Music Examples 659 ‘Subject Index 663. ContentsAbout the Authors Stefan Kostha holds degrees in music from the University of Colorado and the University of Texas and received his Ph.D. in music theory from the University of Wisconsin, He was a member of the faculty of the Eastman School of Music from 1969 to 1973. Since that time he has been on the faculty of the University of Texas at Austin, Dr. Kostka initiated courses in computer applications in music at both the Eastman School and the University of ‘Texas. More recently he fas specialized in courses in atonal theory and contemporary styles and techniques, interests that have led to a second. book, Materials and Technigues of Twentieth: Century Music. Dr. Kostka is active in vatious professional organizations and currently serves on the editorial board of Collage Music Symposium. Dorothy Payne presently serves as Director of the School of Music at the University of Arizona. A graduate of the Eastman School of Music, she holds bachelor’s and master’s degrees in piano performance, and a Ph.D. in music theory. Before assuming her duties in Tucson, she occupied the position of Music Department Head at the University of Connecticut, Previous faculty appointments were held at the University of Texas at Austin, the Eastman School of Music, and Pacific Lutheran University. She has been the recipient of teaching excellence awards at both the Eastman School and the University of Texas. In addition to remaining active as a performer, Payne has presented lectures and workshops on theory pedagogy at meetings of professional societies, She presently serves as an elected member of the National Association of Schools of Music Accteditation Commissio Preface Tonal Harmony with an Introduction to Twenticth-Century Music is intended for a two-year course in music theory/harmony. It offers a clear and thorough introduction to the resources and practice of Western music from the seven- teenth century to the present day. [ts concise, one-volume format and flexible approach make the book usable in a broad range of theory curricula, APPROACH The text provides students with a comprehensive but accessible and highly practical set of tools for the understanding of music. Actual musical practice is stressed more than rules or prohibitions. Principles are explained and illus- trated, and exceptions are noted. In its presentation of harmonic procedures, the text introduces students to the most common vocal and instrumental textures encountered in tonal music. Traditional four-part chorale settings are used to introduce many con- cepts, but three-part instrumental and vocal textures are also presented in iMlustrations and drill work, along with a variety of keyboard styles. To encourage the correlation of writing and performing skills, we have included musical examples in score and reduced-score formats, as well as charts on instrumental ranges and transpositions. Some of the assignments ask the student to write for small ensembles suitable for performance in class. Instructors may modify these assignments to make them most appropriate for their particular situations. PEDAGOGICAL FEATURES “The ext employs a variety of techniques to clarify underlying voice lead- ing, harmonic structure, and forma) procedures. These include textural reductions, accompanying many of the examples, which highlight choréa} motion. Our goal has been 10 elucidate tonal logic at the phrase and section level as well as from one chord to the next. Abundant musical illustrations,xiv Preface many with commentaries, serve as a springboard for class discussion and indi vidual understanding, ‘The book provides an extensive series of review material. A large portion of the text is devoted to SelfTests, consisting of studencgraded drills in chord spelling, part writing, and analysis, with suggested answers given in Appendix B, The Self-Tests can be used for in-class dril! and discussion, in preparation for the Workbook exercises, or for independent study. Periodic Checkpoints enable students to gauge their understanding of the preceding material Chapter summaries highlight the key points of each chapter. ORGANIZATION Part One (Chapters 1-4) begins the text with a thorough but concise over- view of the fundamentals of music, divided into one chapter each on pitch and rhythm. Chapters 3 and 4 introduce the student to triads and seventh chords in various inversions and textures, but without placing them yet in their tonal concent. Part Two (Chapters 5-12) opens with two chapters on the principles of voice leading, with practice limited to root position triads. Chapter 7 follows with a systematic discussion of normative harmonic progressions. Subsequent chapters deal with tiads in inversion (Chapters 8 and 9}, basic elements of musical form (Chapter 10}, and non-chord tones (Chapters Il and 12) Part Three (Chapters 13-15) is devoted entirely to diatonic seventh chords, moving from the dominant seventh in root position and inversion (Chapter 13) through the supertonic and leading-tone sevenths (Chapter 14) to the remaining diatonic seventh chords (Chapter 15) Part Four begins the study of chroxraticism with secondary functions (Chaptess 16-17} and modulation (Chapters 18-19), concluding in Chapter 20 with a discussion of binary and ternary forms. Cheomaticism continues to be the main topic in Part Five (Chapters 21-26), which covers mode mi ture, the Neapolitan, augmented sixth chords, and enharmonicism, Some further elements, ninth chords and altered dominants among them, are the subject of the final chapter of this section. Part Six, “Late Romanticism and the Twentieth Century,” begins in Chapter 27 with a discussion of the developments and extensions in tonal practice that occurred in later nineteenth-century music. The concluding chapter provides an extensive introduction to major twentieth-century practices, A SUPPLEMENTARY MATERIALS Workbook Exercises in the Workbook are closely correlated with the corresponding chapters of the text, In each chapter, the Workbook exercises begin with problems similar to those found in the Self Tests, but also incorporate more creative ypes of compositional problems for those instructors who include this type of work Cassettes ‘This third edition is accompanied by a new listening program, designe: to make it easier to hear the text and Workbook's ruumerous exarples Rect of two cassettes is available for the text (text cassettes order code: 911862-3), and one cassette is available with the Workbook (Workbook cassette order code: 911864-X), offering 400 selections in all. All examples were recorded using the same instrumentations seen in text and Workbook exampies. A headset icon, as shown at left, indicates that a piece is contained on the cassettes, Instructor's Manuat ¥¢ Instructor's Manual follows the organization of the text and provides teaching notes, a key to “objective” exercises from the Workbook, sources from the literature for part writing exercises and composition assignments, and chapter quizees. NEW TO THIS EDITION Chapter 2, “Elements of Rhythm,” has been expanded, and two new sets of exercises have been added. Because of its length, Chapter 5, “Principles of Voice Leading,” has been divided into two chapters (5 and 6) in the present edition, with an expanded discussion of instrumental ranges and transpositions at the end of the new Chapter 6. ‘The chapter on triads in first inversion is now followed immediately by the chapter on triads in second inversion. These are followed by Chapter 10, “Cadences, Phrases, and Periods,” which used to separate them. Preface xvxvi Preface The chapter entitled “Levels uf Harmony,” has been withdrawn from this edition, However, teachers interested in obtaining copies of this chapter from the second edition may do so by writing to McGraw-Hill Explanations and discussions have been improved and clarified through oul, with additional examples and SelF-Tests. There have been some ‘ermminology, such as the substitution of “major ring to chord quality. minor adjustments in t minor seventh” for “dominant seventh” when ref New summaries have been added to the end of each chapter to assist the student in reviewing the material The Workbook contains « number of new analytical exercises. The Instructor's Manual has been expanded considerably. Each chapter now includes a chapter quiz (ia some cases more than one) which the instructor may duplicate and use in class. Most exciting, pethaps, is the availability in recorded form of many of the musical examples in the third edition. These recordings are, in most cases, of fine student musicians, and they should add considerably to the effectiveness of this text. ACKNOWLEDGMENTS Many colleagues and friends provided assistance and encouragement during the development of the first edition of this text, notably Professors Douglass Green, Jerry Grigadean, and Janet McGaughey. Reviewers of the manuscript contributed many helpful! suggestions; our sincere thanks are extended to Judith Allen, University of Virginia; Michael Arenson, University of Delaware; 'B, Glenn Chandler, Cenwcal Connecticut State College; Herbert Colvin, Baylor University; Charles Mligel, Southern Lllinois University; Roger Foltz, University of Nebraska, Omaha; Albert G. Huetteman, University of Massachusetts; William Hussey, University of Texas at Austin; Hanley Jackson, Kansas State University; Marvin Johnson, University of Alabama; Frank Lorince, West Virginia University; William L. Maxson, Eastern Washington University; Leonard Ot, University of Missouri; John Pozdro, University of Kansas, Jeffrey L. Prater, Towa State University; Russell Riepe, Southwest Texas State University; Wayne Scott, University of Colorado; Richard Soule, University of Nevada; James Stewart, Ohio University; William Toutant, California State University at Northridge; and John D. White, University of Florida. We are also grateful to those who contributed to the development of the second edition: Richard Bass, University of Connecticut; James Bennighof, Baylor University; Richard Devore, Kent State University; Lora Gingerich, Ohio State University; Kent Kennan, University of Texas at Austin; James W. Krehbiel, Eastern Dlinois University; Frank Lorince, West Vieginia University (retired); Donald Para, Western Michigan University; Marian Petersen, University of Missouri at Kansas Gity; Donald Peterson, University of Tennessee; and John Pozdro, University of Kansas. Contributors to the third edition include Shirley Bean, University of Missouri, Kansas City; Brian Berlin, University of Texas at Austin; Horace Boyer, University of Massachusetts; Polly Brecht, Middle Tennessee State University; ohn Buccheri, Northwestern University; Arthur Campbell, St. Olaf College; Lisa Derry, Western Michigan University; David Foley, Ball State University; Douglass Green, University of Texas at Austin; Andrew Grobengieser, University of Texas at Austin; Thom Hutcheson, Middle Tennessee State University; Robert Judd, California State University, Fresno; William Pelto, Ithaca College; H. Lee Riggins, Bowling Green State University, Lynne Rogers, University of Texas at Austin; and Judith Solomon, Texas Christian University Finally, we would express gratitude to Mary Robertson for her love and inspiration, and to Bill Penn for his unfailing encouragement. Stefan Kostka Dorothy Payne Prface vit4000000000000 0000000000 OEEECO To the Student HARMONY IN WESTERN MUSIC One thing that distinguishes Western art music from many other kinds of music is its preoccupation with harmony. In other words, just about any piece that you are apt to perform will involve more than one person playing br singing different notes at the same time-oF, in the case of a keyboard player, more than one finger pushing down keys. There are exceptions, of course, such as works for unaccompanied flute, violin, and so on, but an implied harmonic background is often still apparent to the ear in such pieces. ~ In general, the music from cultures other than our own European-American culture is concerned ess widh harmony than with other aspects of music Complexities of rhythm or subUleties of melodic variation, for example, might serve as the focal point in a particular musical culture. Even in our ‘own music, some compositions, such as those for nonpitched percussion instruments, may be said to have little or no harmonic content, but they are the exception. If harmony is so important in our music, it might be a good idea if we agreed on a definition of it. What does the expression sing in harmony mean to you? It probably conjures up impressions of something on the order of a barbershop quartet, or a chorus, or maybe just two people singing a song, one with the melody, the other one singing the harmony. Since harmony began historically with vocal music, this is a reasonable way to begin formu- lating a definition of harmony. In all of these examples, our conception of harmony involves more than one person singing at once, and the harmony is the sound thar the combined voices produce. Harmony is the sound that results when two oF more pitches are performed simi neously. Ii the vertical aspect of music, produced by the combination of the compo- nents of the horizontal aspect. ‘While this book deals with harmony and with chords, which are little samples takert out of the harmony, it would be a good idea to keep in mind that musical lines (vocal or instrumental) produce the harmony, not the reverse. to Sing through the four parts in Example 1. The soprano and tenor lines are the most melodic. The actual melody being harmonized is in the soprano, while the tenor follows its contour for a while and then ends with an eighth. note figure of its own. The bass line is strong and independent but less metodic, while the alto part is probably the least distinctive of all. These four relatively independent lines combine to create harmony, with chords occur- ring at the rate of approximately one per beat. Example 1, Bach, “Heralich licb hab! ich dich, o Hers” a The relationship between the vertical and horizontal aspects of music is a subtle one, however, and it has fluctuated ever since the beginnings of har- mony (about the ninth century). At times the emphasis has been almost entirely on independent horizontal Jines, with liele attention paid to the resulting chords—a tendency easily seen in the twentieth century. At other times the independence of the lines has been weakened or is absent entirely. In Example 2 the only independent lines are the sustained bass note and the melody (highest notes). The other lines merely double the melody at various intervals, creating a very nontraditional succession of chords. Example 2, Debussy, “La Cathédrale engloutie,” from Preludes, Book 1 Somore sane dureté i Student xixxx To the Student TONAL HARMONY DEFINED primarily is usually eal ‘The kind of harmony that this book deals wi tonal harmony. The term refers to the harmonic siyle of music composed, during the period from about 1650 to about 1900. This would inelude such composers as Purcell, Bach, Handel, Haydn, Mozart, Beethoven, Schubert, ‘Schumann, Wagner, Brahms, Tchaikovsky, and alt of their contemporaries. Much of today’s popular music is based on tonal harmony, just as Bach’s music was, which means that both types have a good deal in common. First, both make use of a tonal center, a pitch class* that provides a center of gravity Second, both types of music make use almost exclusively of major and minor scales. Third, both use chords that are tertian in structure. Terlian means “built of thirds,” so a tertian chord might be C-E-G, a nontertian one C-FB. Fourth, and very important, is that the chords built on the various scale degrees relate to one another and to the tonal center in fairly complex ways. Because each chord tends to have more or iess standard roles, of functions, within a key, this characteristic is sometimes referred to as functional harmony. The details of these relationships between chords will be discussed more fully in the text; but to get an idea of what it’s all about, play the chord of Example 3 on the piano-f Example 3. = Play it several times, Arpeggiate it up and down. The “function” of this chord is clear, isn’t it? Somehow, you know a lot about this chord without having to read a book about it. Play it again, and listen to where the chord “wants” to go. Then play Example 4, which will seem to follow Example 3 perfectly. This is an example of what is meant by the relationships between chords in tonal harmony and why we sometimes use the term functional harmony. ‘itch clas: Notes an octave apart or enharmonicaly equivalent belong to the same pitch cas (all Cis Bs, and DY, or example), There ace eel pitch clases al ‘ityou cannot arrange 1 be a a piano while reading this book, Ly to play rough the examples just before ot right afer reading a particular secuon or chapter. Reading about mic without hearing ‘tis wot only dll i's uninformative To the Student Example 4. be == Tonal harmony is not limited to the period 1650-1900. It began evolving long before 1650, and itis still around today. Turn on your radio, go to a nightclub, listen to the canned music in the supermarket—it's almost all tonal harmony. Then why do we put the demise of tonal harmony at 1900? Because from about that time, most composers of “serious,” or “legitimate,” or “concert” music have been more interested in nontonal harmony than in tonal harmony. This does not mean that tonal harmony ceased to exist in the real world or in music of artistic merit, Also, itis important to realize that not all music with a tonal center makes use of functional harmony—especially a good deal of the music of the twentieth century—music by composers such as Bartok and Hindemith, for example. From our discussion we can formulate this definition of tonal harmony: crony refers to music with a tonal center, based on major and/or minor using tertian chords that are related to one another and to the tonal center in various ways, USING THIS TEXT ‘The information in this text is organized in the traditional chapter format, but there are several additional features of which you should be aware. Self Tests All chapters contain one or more such sections. These Self-Tests contain questions and drill material for use in independent study or classroom discus- sion. Suggested answers to all Self-Test problems appear in Appendix B. In many cases more than one correct answer is possible, but only one answer will be given in Appendix B. If you are in doubt about the correctness of your answer, ask your instructor, xxivexii To the Student Exercises After each Self-Test section, we refer to a group of Exercises to be found in the Workbook. Most of the Workbook Exercises will be similar to those in the preceding Self-Test, so refer to the Self-Test if you have questions con- cerning completion of the Exercises. However, the Workbook will also often contain more creative compositional problems than appeared in the Self-Test, since it would be impossible to suggest “answers” to such problems if they were used as SelFTests Checkpoints You will occasionally encounter a Checkpoint section, These are intended to jog your memory and to help you review what you have just read. No angwers are given to Checkpoint questions, PART FundamentalsCHAPTER a Elements of Pitch ‘THE KEYBOARD AND OCTAVE REGISTERS Pitch in music refers to the highness or lowness of a sound. Pitches are nnained by using the first seven letters of the alphabet: A, B, CG, D, E, F, and G, We will approach the notation of pitch by relating this pitch alphabet .o the keyboard, using C’s as an example. The C nearest the middle of the keyboard is called middle C or C4, Higher C’s (moving toward the right on the keyboard) are named C5, C6, and so on. Lower C's (moving left) are named C3, C2, and CI. All the C's on the piano are labeled in Example 1-1. i Example 1-1. LLAEVER STNee eee eae aera middle ¢ From any C up to or down to the next C is called an octave. All the pitches from one C up to, but not including, the next Care said to be in the same octave register. As Example 1-2 illustrates, the white key above C4 would be named D4, because it is in the same octave register, but the white key below C4 would be named B3. poeeeeeeeooeoweweowooweoosewersA Elements of Pitch Example 1-2. ma NOTATION ON THE STAFF Our system of musical notation is similar to a graph in which tim indicated on the X axis and pitch is shown on the ¥ axis. Ja Example 1-3 R occurs hefore S in time and is higher thaa S in pitch, Example 1-3. y R s A siaff is used in music to indicate the precise pitch desired. A staff consists of five lines and four spaces, but it may be extended indefinitely through the use of ledger lines (Ex. 1-4) Example 1-4. Ledge tines sat{ =e ns A dlef must appear at the beginning of the staff in order to indicate which pitches are to be associated with which lines and spaces. The three clefs cormmonly used today are shown in Example 1-5, and the position of C4 in each is illustrated. Notice that the G clef appears in either of two positions, Notation on the Staff 5 Example 1-5. Genesic name: G clef Falef Cater Coke Speciicmme: Treble clef Bawdlef — Altodet Tenor eet Cf on co a The clefs in Example 1-5 are shown in the positions that are in common use today, but you may occasionally find them placed differently on the staff in some editions. Wherever they appear, the design of the G clef circles G4, the dots of the F clef surround F3, and the C clef is centered on C4, The grand staff is a combination of two staves joined by @ brace, with the top and bottom staves using treble and bass clefs, respectively. Various pitches are notated and labeled on the grand staff in Example 1-6, Pay special attention to the way in which the ledger lines are used on the grand staff. For instance, the notes C4 and A3 appear twice in Example 1-6, once in rela- 11 t0 the top staff and once in relation to the bottom staff. Example 1-6. Feces as SELF-TEST 1-1 (Answers begin, on page 559.) ‘A. Name the pitches in the blanks provided, using the correct octave register designations. EEE EEE© Blements of Pitch B, Noate the indicated pitches on the staff in the correct octave. EXERCISE 1-1. See Workbook. TE MAJOR SCALE ‘The major scale is a specific pattern of small steps (catled half steps) and larger ones (called whole steps) encompassing an octave. A half siep is the distance from a key on the piano to the very next key, white or black. Using only the white keys on the piano keyboard, there are two half steps in each octave (Ex. 1-7) wa The Major Scale 7 A whole step skips the very next key and goes instead to the following one. Using only the white keys on the piano keyboard, there are five whole steps in each octave (Ex. 1-8) Example 1-8. Pio oid step step step stepstep, ‘The major scale pattern of whole and half steps is the same as that found fon the white keys from any C up to the next C. {n the diagrain below, the numbers with carats above them (1, 2, etc.) are scale degree numbers for the C major scale.* You can see from this diagram that half steps in the major scale occur only between scale degrees 3.and 4 and? and i. Notice also that the major scale can be thought of as two identical, four-note patterns separated by a whole step. ~~ a 1 % 1 % AAA ANA DE F GA B CG 8 5 4 mo "Throughout this book we wil refer to major seles with uppercase euers—for example, A major ‘or A~and mir scales with lowerease leners-for example, ior orB Elements of Pitch octave, as in Example sxamnine the steps on the white keys of a G-to-G If we examine the steps on the white key ample eps that 0% 1-9, we do not find the same pattern of whole and half steps in the C-to-C octave. In order o play a G major scale, we would need to skip the F key and play the black key that is between F and G, We will label that key with an accidental, a symbol that raises or lowers a pitch by a half or whole step. All the possible accidentals are listed in this table. Symbol Name bjfeet * Double sharp Raise a whole step : Sharp Raise a half step 4 Natural Cancel a previous accidental > Flat Lower a half step » Double flat Lower a whole step Example 1-9. VVVVV rye tia We can make our G scale conform to the major scale pattern by adding one accidental, in this case a sharp. 1 1 *# Lolo & KAKANRALDA G A BC DE FOG i 6 9 4 5 6 47 i The Major Key Signatures. 9 ‘The scale is written on the staff in Example 1-10. Example 1-10. Notice that when we write or say the names of notes and accidentals, we put the accidental last (as in Ff or F-sharp), but in staff notation the accidental, always precedes the note that it modifies (as in Ex. 1-10) THE MAJOR KEY SIGNATURES ‘One way to learn the major scales is by means of the pattern of whole and half steps discussed in the previous section. Another is by memorizing the key signatures associated with the various scales. The term fey is used in music to identify the first degree of a scale. For instance, the key of G major refers to the major scale that begins on G. A key signature is a pattern of sharps or flats that appears at the beginning of a staff and indicates that certain notes are to be consistently raised or lowered. There are seven key signatures using sharps. In each case, the name of the major key can be found by going up a half step from the last sharp (Ex. 1-11) Example 1-11. major 1 aarp Qaharps Sharps sharps Sharps ‘sharps 7 sharps10 Elements of Pitch ‘There are also seven key signatures using flats. Except for the key of F major, the name of the major key is the same as the name of the nextto-ast flat (Ex. 1-12) Example 1-12. eesioe || Bomajor |] emer | Aboujor | obmalor || Gomajor a so 1 fat 2a 3a te 5a 6 fa You may have noticed that there are three pairs of major keys that would sound exactly the sime—that is, they would be played on the very same keys of de piano keyboard. B major Cb major Ft major Gb major Gf major Db major Notes that are spelled differently but sound the same are said to be enkar monic; so B major and Cb majeac, for example, are enharmonic keys. If two major keys are not enharmonic, then they are transpositions of each other. To transpose means to write or play music in some key other than the original The key signatures in Examples 1-11 and 1-12 musi be memorized—not only the number of accidentals involved, but also their order and placement upon the staff. Notice that the pattern of placing the sharps on the staff changes at the fifth sharp for both the treble and the bass clefS. Try repeating the order of accidentals for sharps (FCGDAEB) and for flats (BEADGCF) until you feet confident with them, Some people find it easier to memorize key signatures if they visualize a ile of fifths, which is a diagram somewhat like the face of a clock. Reading clockwise around the circle of fifths below, you will see that each new key begins on 5 (the fifth scale degree) of the previous key. as ahh RMR RN The Major Key Signatures 11 SELF-TEST 1-2 (Answers begia on page 560.) A. Notate the specified scales using accidentals, not key signatures. Show the placement of whole and half steps, as in the example. , Cpesior bot LK Bemajoe De majorMinor Seales 13 12 Elements of Pitch Amalon EXERCISE 1-2. See Workbook. major ~ MINOR SCALES Musicians traditionally memorize and practice three minor scale forma tions, although they are not used with equal frequency, as we shall see in a Jater chapter. One of these is the natural minor scale. You can see from the illustration below that the natural minor scale is like a major scale with low. ered §,6, and " B, Identify these major key signatures. C major cop lkl)r c falple — 9: —<— ote Scale degree io 3)4 8 fells} i a - 7 ~— eo vajor natural minor © D Eb) F G |ab||py © jr mar mor mijor mor mar mae mh m r z a 7 5 . 7 Another minar scale type is the harmonic minor scale, which can be thought of as major with lowered § and 6. C. Notte the specitied key signacuces - C major cp —— = = Seale degree i maior Demajor © Femsjor — Bomajor—Bmajor © Comajor—Dinajor © Gmajor Rg eo ano aw charmonic minor =D eo] D. Fill in the blanks. The third type of minor scale is the melodic minor scale, which has an Key signature Name ofkey Key signature Name ofey | cating form and a descending fom, The ascending form, shown below, 1, Three flats major 8. Bb major : 2. Seven sharps ___ major 9. One sharp __ major b Cmajor c plelr cg ape 3. D major 10. Five flats _—_ major i Seale degree 334/43 6 3 3 4. One flat — major NW. Fé major § cascending melodic minor CG D |kb] F G A B GC 5B Ab major 12. Co major i & —— Basler 1S, Four sharps —mser : t The descending form of the melodic minor scale is the same as the natural 7. Six fais __ major 4A major minor scale, prime mtr44 Elements of Pitch : sd in Example 1-18. The scale “The three minor scale types are surnmariged in Example 118. The s dearest iller from the major ave circled. Notice the arrows used in Fee nee aeipthe melodie minor scale in order to distinguish the 7 TF EXERCISE 1-6. See Workbook. rete pny rte nyse Inversion of Interovls 23 AUGMENTED AND DIMINISHED INTERVALS tia perfect or a major interval is made a half step larger without changing the numerical name, the interval becomes augmented labbrevineed sa perfect or a minor interval is made a half step smaller without changing its numerical name, it becomes diminished (abbreviated ®). Th relationships are summarized below, There is no such thing as a diminished unison. Doubly augmented and doubly diminished intervals are possible, but they seldom veeur,Tilone ns term used for the +4 oF its enharmonic equivatent, the °% INVERSION GF INTERVALS the botiom pitch above zhe cop one; for example, the interval D-Acowec to AD. When we invert an interval, che new numerical name is always different from the old one. The new mumterical name can be ealeubared by subtracting the old numerical name from 9, Constant value of 9 9 9 9 9 9 Minus old mumericname 2-9 4 5 6 7 Equalsnewnumericname 7 § 5 4 3 You can see that an inverted 2nd becomes a 7th, a Srd becomes @ 6th, and, so on (Ex. 1-22)24 Blements of Pitch Example 1-22. = 2 7 “The modifies also changes when an interval is inverted, with the excepuon of perfect intervals Oia modifier [a | Mle] + |e [ew modifier |) m[e |? | + fulness of inversion, suppose you wanted to know ‘G3. Invert the m6 down to a M3 up, as in Example find that the answer fs B2. ‘Asan example of the use what nove lies a m6 below 1-23, transpose the B3 down an Sve, and you Example 1-23. ‘as with scales, is necessary for any serious musician id with tion for your further study. As you did w nd flow various intervals sound and feel Fluency with intervals, and will provide a solid foun scales, you will benefit from finding out how vari on a musical instrument. ‘One exercise you can do (y of the chromatic scale in rand: asa sharped note and once as a o and below each note. Work for speed, using your ear jou can think of others) is to write out the notes fom order, Include each black key twice—once flatied note. Then play some interval above to correct yourself at ipa toe i SUMMARY Pitch in music refers to the highness or lowness of a sound, Particular pitches are named by using the musical alphabet, consisting of the letters A through G, at which point the alphabet starts over. From one letter up or down to its next occurrence is called an octave, while the space from any Cup to the next B is called an octave register. Octave registers are numbered, with the lowest C on the piano keyboard designated as C1. The G nearest the middle of the piano keyboard is called middle Gor C4, Pitches are notated on the staff, an arrangement of five lines and four spaces that can be extended through the use of ledger lines. A staff always begins with one of several clef, which determine exactly what pitch is represented by each line or space. A grand siaff consists of two staves joined by a brace, with a treble clef on the top staff and a bass clef on the bottom staff. The major scale consists of a particular acrangement of whole steps and half steps. Most major scales also have a parallel minor scale that. ‘begins on the same note but that lowers scale degrees 3, 6, and 7 by a half step. This form of the minor is called the natural minor scale. The harmonic minor scale lowers only scale degrees $ and 6 of its parallel major, while the melodic minor scale lowers seale degree 5 when ascending and scale degrees 5, 6 and7 when descending. Every scale has an associated hey signature, consisting of zero to seven sharps or flats arranged in a particular way on the staff. There are 15 ey signatures in all, with one major and one minor scale associated with each, Major and minor keys that share the same key signature are said 10 be relative keys. The notes of a scale are all assigned scale degree names, which vary only slightly between major and minor. Enharmonic notes or keys sound the same but are spelied differently. To transpose ‘music means to play it in another key. ‘The difference between any two pitches is called an interval A harmonic interval separates pitches that are sounded simultaneously, while a melodic interval separates pitches that are sounded in succes- sion. Intervals are defined by means of a numerical name and a modifier that precedes it. These modifiers include the terms perfect, ‘major, minor, augmented, and diminished. To invert an interval, put the lower note above the upper one (or the reverse). The numerical name and modifier of an inverted interval can be predicted using the method explained in this chapter. Swnmary 2526 Elements of Pitch SELF-TEST 1-6 (Answers begin on page 562.) Label each interval, A, Most of the intervals below are either augmented or diminished B, Label what each interval becomes when itis inverted. 5.°5 becomes 1. Pd becomes 2. M7 becomes 6. m2 becomes 3. +2 becomes 7. m6 becomes 4. M3 becomes 8. +6 becomes C. Notate the specified interval below the given note, (You may find it helpful to invert the interval first in some cases.) Ps ™ 8 sue 128 4567 EXERCISE 1-6. See Workbook. iat gag CHAPTER N Elements of Rhythm RHYTHM This chapter is concerned with the time aspect of music—how sounds are Hotated so that they witl occur at a predictable moment and in a predeter. iNned pauern. Risthm is general term used to refer to the time aspect of ‘music, as contrasted with the pitch aspect. DURATIONAL SYMBOLS Durations are notated by using symbols that are organized so that each symbol is twice the duration of the next shorter symbol and half the dace Hon of the next longer symbol. The table below lists a number of these symbols Value | Note a) Breve [Horo 1-1 Whole nae Quarter Eighth Sixteenth, 2728 Elements of Rhytlon anew duration that is equal to their sum. A dot always adds to the duration one-half the value of the note, rest, or dot that precedes it. For example, dead d)and du = 4__2) When notated on the staff, a dot is never placed on a staff line. It the notehead itself is on a staff fine, the dot is put to the right of the note but in the space above it. BEAT AND TEMPO “The beats the basic pulse of a musical passage. To determine the beat of a passage you are listening to, tap your foot to the music or try to imagine the way a conductor would conduct the passage—the conductor's arm move- ment. The resulting steady pulse is called the beat, and the rate at which the beats occur is called the lempo. ‘A composer commonly specifies the tempo of a passage by one of two methods—sometimes by both, The first method uses words, often in Italian, to describe the tempo. Halian English German French Grave Solemn Schwer Lourd Largo Broad Breit Large Lento Slow Langsam Lent Adagio Slow Langsam Lent ‘Andante Moderately slow Gehend Allan Moderato Moderate Massig Modéré Allegretto Moderately fast. -Erwas bewegt Un peu animé Allegro Fast Schnell Animé Vivace Lively Lebhaft Vit Presto Very fast Bilig Vite ‘The second method is more exact, since it shows precisely how many beats are to occur in the space of one minute. For example, if the desired ternpo would result in seventy-wo quarter notes in one minute, the tempo indica tion would be J = 72 or M.M. d= 72. The M.M. stands for Maelzel's metronome, after Johann Maelzel, who widely promoted the device during the early nineteenth century. Ha i AE METER Beats tend to be grouped into patterns that are consistent throughout a passage; the pattern of beats is called the meter. Groups of two, three, and four beats are the most common, although other meters occur, Incidentally, 2 group of four beats could often also be interpreted as two groups of wo beats each, and vice versa. Ip any case, the groups of beats are called measures (abbreviated m. or mm.), and in notation the end of a measure is always indicated by a vertical line through the staff called a bar line. The words duple, tiple, and quadruple are used to refer to the number of beats in each measure, so we have duple meter, triple meter, and quadruple meter. These terms are summarized below, along with the pattern of stresses usually found in cach meter (referred to as metric accent) Grouping Meter type | Metric accent pescern “Tworbeat measure | Duple | Strong.weak Three-beat measure | Triple Strong-weake-weak Fourbeat measure | Quadruple | Strong-weak-less strong-weak ‘As you might imagine, most marches are in duple meter, since people have two feet, while contemporary popular music tends to be in duple or quadru- ple meter. Walizes are always in triple meter, as are a number of traditional songs such as “Amazing Grace” and “Scarborough Fair.” The meter of many passages is clear and easily identified, but in other cases the meter may be 2zabiguous. For example, sing "Take Me Out to the Ball Game” quite slowly while you tap your foot or conduct, then decide upon the meter type. Now sing it again, but very fast. The first time you probably felt the meter was triple, but at a faster tempo you should have identified the meter as duple (or quadruple). Between those extreme tempos are more moderate tempos, which two listeners might interpret in different ‘ways—one hearing a faster triple meter, the other a slower duple meter. Both, listeners would be correct, because identifying meter is a matter of inter pretation rather than of right and wrong. Meter 2930 Elements of Rhythm SELF-TEST 2-1 (Answers begin on page 563.) A. Show how many notes or rests of the shorter duration would be required to equal the longer duration. 9 10. n. 12. Boe ee 13, 67, 4. hbase 15. ah, 16. B. Sing aloud each of the songs listed below. Then identify the meter type of each, using the terms duplr, tiple, and quadruple. 1. "Silent Night” (slow tempo) 2. “Jingle Bells” 3. "America the Beautiful” __ 4. “Seventy-Six Trombones” __ 5. “Home on the Range” C. Scale review, Given the key and the s melodic minor form for each minor key. le degree, supply the note name. Assume the | enter enh acta alii Division of the Beat ex fe 2 BL a 1 De 6 ae be 26 3 woe 4 aa Bb MAbs 7 4B: 3 12 FRB 5g 13, bb 5 6 ct we 6 7. Be: 5 15. 7 EXERCISE 2-1. See Workbook. DIVISION OF THE BEAT In most musical passages we hear durations that are shorter than the beat. We call these shorter durations divisions of the beat. Beats generally divide either into two equal parts, called simple beat, or into three equal parts, called compound beat. Be careful not to confuse beat type, which refers to bow the beat divides (simple or compound), with meter type, which refers to how the measure divides (duple, triple, or quadruple). The common beat and meter types can be combinétwith cach other in six possible ways. Meter Beat Duple Triple Quadruple Simple | Simple ‘Simple Simple duple wwiple quadruple Compound | Compound | Compound Compound | gape triple quadruple For example, sing “Take Me Out to the Ball Game” quickly in dupe meter, as you did in the discussion of meter on page 29. You can hear that the beats divide into thirds, so this is an example of compound duple. Do the same with “I Don’t Know How to Love Him’ (from jesus Christ Superstar) or “Around Her Neck She Wore a Yellow Ribbon,” and you will find that both are simple duple (or simple quadruple), 3182 Elements of Rhythm SELF-TEST 2-2 (Answers begin on page 564.) Sing aloud each of the songs listed below. Then identify the beat and meter types of each, using the terms simple duple, and so on. 1. “Auld Lang Syne” 2. "Pop Goes the Weasel” 3. “Silent Night” 4. “Jingle Bells” 6. “Seventy Six Trombones” SIMPLE TIME SIGNATURES [A time signature is a symbol that tells the performer how many beats will occur in each measure, what note value will represent the beat, and whether the beat is simple or compound. A time signature for simple beat has , 3, or 4s the top number. The top number indicates the number of beats in the measure; the bottom number indicates the beat note (2= 4, 4=4,8= 4, and so on). Some typical simple time signatures are listed in the following table. ume | Bets por | Beat | Dison Time denture | ate’ | nate | tba A [2 fd ad om wlefefele jaya a 8 ° Simple Time Signatures Example 2-1 illustrates how some of the songs we have been considering might be notated. The beat values were chosen arbitrarily “Jingle Bells,” for example, could also be notated correctly in 3 or jor any other simple duple time signature Example 2-1 Jingle Bele” = “america the Beaulifa ‘Home on the Range SELF-TEST 2-3 (Answers begin on page 564.) A. Fill in the blanks, Beat and Beat | Division | Time meer ype roe | ofthe at — | signature 1. Simple duple J 4, | Simple quadruple 5. |simpiewpe | 3334 Elements of Rhythnw i Compound Time Signatures 35 Beats per | Beat | Division of B. Renotate the excerpts from Example 2-1 using the specified time signatures. measure | note | the beat Time signature 1.8 Jingle Betts 8 2 | 4) 7 i 2.4 “America the Beautiful” efajiid EXERCISE 2-3. See Workbook. { ib 8 d| J 3.} “Home on the Range” COMPOUND TIME SIGNATURES ! | e s [i] 7 J If the beat divides into three equal parts, as in compound beat, the note value representing the beat will be a dotted value, as shown below. 1 R 4 Beat | Division of | rote | the beat Td i" Example 22 illustrates some familiar tunes that use compound beat. As [ before, the choice of the actual beat note is an arbitrary one. : 1.| 47 yer) A| FA Example 2.2. “Take Me Out to the Ball Game” “Down n the Valley” Hig “Pop Goes the Wesel" Dotted values present a problem where time signatures are concerned. For example, if there are two beats per measure, and the beat note is #:, what would the time signature be? $y? 429? axdse? There is no easy solution, and the method that survives today is the source of much confusion concerning ‘compound beat. Simply stated, a compound time signature informs the musician of the nuniber of divisions of the beat contained in a measure and 1 wwhat the division duration is. This means that the top number of a compound time signature will be 6, 9, or 12, because ovo beats times three divisions equals six, three beats times three divisions equals nine, and four beats times three divisions equals qwelve. Some examples are given in the tabie below. tt en terete se36 Elements of Rhythm You can see from this discussion that compound time signatures do not follow the rule, so often learned by the student musician, that “the top number \ells how many beats are in a measure, and the bottom number tells what, note gets the beat.” Of course, there are some pieces in §, for example, that really do have six beats t0 the measure, but such a piece is not really in com> pound duple. A measure of § performed in six does not sound like compound duple; instead, it sounds like two measures of simple tiple, or 3. In com- Pound duple, the listener must hear two compound beats to the measure, not six simpfe beats. In the same way, a slow work notated in 3 might be conducted in four, which would seem to the listener to be simple quadruple, In both cases, the usual division value has become the beat value soe TITTY scone 8 £72) IT t soe FDTD scons 89 TF T2434 ‘The reverse also occurs—that is, the usual beat value sometimes becomes the actual division value. For instance, a fast waltz or scherzo is almost always notited as simple triple, usually as 7. But the aural effect is of one beat per measure, for which we might use the term compound single. If you didn’t know the metric convention of such pieces, you would probably assume on hearing them that they were in compound duple, because the measures (end to group in pairs. | | L Time Signatures Summarized 37 SELF-TEST 2-4 (Answers begin on page 564.) A. Fill in the blanks, Bevend om 1. [compoundaipe 2 i ‘Compound quadruple B, Renotate the excerpts from Example 2-2 using the specified time signatures, 1. § “Take Me Out to the Ball Game” 2. $ Down in the Valley” “Pop Goes the Weasel” EXERCISE 2-4. See Workbook. ‘TIME SIGNATURES SUMMARIZED ‘There are two types of beat, simple and compound, and three common meters, duple, triple, and quadruple, which can be combined in a total of six ways. For each of these six combinations there is a number that will always appear as the top part of the time signature.38 Elements of Riythm waco | Beat type | Duple | Triple | Quadruple 3 4 coneeinafe | 8 |__| Simple 2 Atisener can usualy recognize the beat and meter ypes ofa passage without the music, Therefore, you can usually say what the top number of the hat duple and quadruple are often indistinguish~ hne bottom number of the time signature is, mber representing a note value seeing time signature is (except U able). However, to know what t you have to look at the music, since any nar ‘can be used for any meter. Bottom | Simple beat | Compound beat amber | duration | duration 1 fa 2 - ey eyele slope |? 3B Remember that the bottom number of a time signature (the leftmost column in the table above) stands for the beat value in a simple time signature and the division value in a compound time signature More on Durational Symbols MORE ON DURATIONAL SYMBOLS When rhythms are notated, itis customary to use beams, ties, and dots in such a way that the metric accent is emphasized rather than obscured. Several incorrect and correct examples are notated below. iD) imam BLAH $1) Tb. JAN BAAS 6) 0A 7 Of course, its correct to notate rhythms so as 10 obscure the metric accent when that is the desired result. Syncopations (rhythmic figures that stress normally weak beats or divisions) are frequently notated in that way, as below. tli ds dds ols More involved figures, such as the following, are especially common in twentieth-century music. Gl TIT 8-8-8 A grouplet refers to the division of an undotted value into some number of equal parts other than two, four, eight, and so on, or the division of a dotted value into some number of equal parts other than three, six, twelve, and so on, as you can see below. 3940 Elements of Rhythm Orginal Grospte J | EDD an Fone 1 (70 “| Ofall the possibilities, the superimposition of triplets on a simple beat is the ‘most common. ‘When a single-stem note is notated on the staff, the stem should go up if the note is below the middle line and down if the note is above the middle line, A note on the middle line may theoretically have its stem point in cither direction, but most professional copyists consistently put a downward stem on notes that occur on the middle line (Ex. 28) Example 2-3. 2 SS Beams are used to connect durations shorter than a quarter note when the durations occur within the same beat. The stem direction of beamed notes is decided by the note that is farthest from the middle line. That is, if the note that is farthest from che middle line is below it, then all the stems that are to be beamed together will point upward (Ex. 2-4) isn Saisie on Example 2-4. SUMMARY Rhythm refers (0 the time aspect of music, as contrasted with the pitch aspect. The relative duration of a musical sound is specified by a durational symbol such as a whole note, half note, and so forth. One or more dots may follow a durational syrobol, each one adding to the duration one-half the value of the note or dot that precedes it; a tie connects two notes, creating a value equal to their sum, Most durational symbols use stems, and there are conventions of notation regarding the direction of the stems. Beams are often used to group together {but not to tie) durations shorter than a quarter-note. ‘The basic pulse of a musical passage is Called the beat, and the Lempo is the rate at which the beats occur. The general tempo may be indi- cated by one of many terms in English or other languages, or it may be specified more exactly by a metronome marking. Beats usually group into patterns of two, three, or four beats, referred to as duple, ple, and quadruple meters. Associated with each ameter is its own pactern of metric accents. Beats in any meter usually divide into two equal parts (simple beat) or three equal parts (compound beat), giving rise to such terms as “triple simple” and “duple com pound.” A groupletis used when a beat divides in a way that is contrary to the prevailing division of the beat. A time signature is a symbol that tells the performer the beat and meter types and what note value will represent the beat. A listener can identify the beat and meter types just by listening to the music, but not the note value that represents the beat, The beat values for simple time signatures are always undotted notes, while those for compound time signatures are always dotted notes, Summary 4442 Elements of Rhythm SELF-TEST 2-5 (Answers begin on page 565.) A. Fillin the blanks. —o | sazen rote ete . i a lemme | | : i a T 4. Compound duple did | + ; 5 J | 5 fm| ” B, Each measure below is incomplete. Add one or more rests to the end of each to complete the measure. AIT) | 4.ib 2. | 2eLTA | 6444 | 384 | efdidad | G. Provide the best time signature for each exercise. In some cases more than one correct, answer may be possibte. wot d Jd 2d 121 3 J 41 6 a— SITE 5. Jd TD. | FATAL fil Elements of Rhytlon 43 D. Fach passage below is notated so that placement of the beats is obscured in some fashion, Rewrite each one to clarify the beat placement. This may involve breaking some of the long notes into tied shorter notes or rebeaming groups of notes. veld JISTI I ¢ 24d TNs | iid Jd) 38l MFRS | sbALAIG| Bo on ao E, Add stems as required. 1. Each duration is a quarter note. se= —— 2. Each duration is an eighth note. Beam them in groups of three, F. Listen to a recording of the beginning of each of the five movements of Beethoven's Symphony No. 6, Op. 68, and identify the beat and meter types of each. Then name three time signatures that could have been used to notate the movement, (Note that movements I and V begin with slow intrectuctions; wait until the allegro portions before making any decision.) Movement Beat type Meter type Possible time sigmatures44 Elements of Rlythm G. Scale review. Given the scale degree, the note, and whether the key is major or minor supply the name of the key. Assume melodic minor for all minor key examples. ex. 6 is C# in_@ minor . 1. Gis Be in minor 8. 5 is Bb in major 2. Bis Bo in___ major 9. 18 is GE in minor 3, 17 is BA in minor 10. 5 is C in major 4. 6 is Fe in major 11. 3 is Bb in minor 5. 4 is Eb in major 12, 47 is Ein minor 6 5 is G in minor 13, 7 is Dt in major 7. 6 ie Bo in___ major 14, 3 is Bb in major H. Interval review, Notate the speci 1 2 3 ‘4 5 6 7 8 9 Ms I. Interval review, Notate the specified interval below the given note, 1 2 3 ‘ 5 5 7 8 ° mo 6 ° we Ps m2 EXERCISE 2-5. See Workbook. cetctnmmti nates i Introduction to Triads and Seventh Chords CHAPTER a INTRODUCTION In this chapter we begin working with chords, the basic vocabulary of tonal harmony. We wil! not be concerned at this stage with how chords are used compositionally or even what kinds of chords occur in the major and minor modes, although we will get to these topics soon enough. First we have to learn how to spell the more common chord types and how to recognize them in various contexts TRIADS In “To the Student” (pp. xvii-xxit), we explained that tonal harmony makes use of fertian (built of rds) chords. The fundamental tertian sonority is the triad, a three-note chord consisting of a 5th divided into two superimposed 3rds. There are four possible ways to combine major and minor 3rds to produce a tertian triad. c Fons [2m [m0 iS 138 135 i3s ‘The names and abbreviations for these four triad types are given in Example 1. Example 3-1. augmented major ‘minor diminished o wy (om) eC) 45roenth Chords 46 Introduction to Triads and § Play these triads at the piano and compare the way they sound. You might be able to guess from listening 10 them thae in conal music the major and mk nor triads are found the most often, the augmented the least often. There are also names (in addition to note names) for the members ofa triad (EX. 8-2) Example 3-2. Suudy the preceding diagram and examples very carefully before going on. CHECKPOINT 1 Which triad rypes contain a m3 as the bottom interval? As the top interval? 2. Which triad types contain a M3 as the top interval? As the bottom interval? 3. Which triad types contain a PS bewween the root and the 5th? a%5? a +5? SELF-TEST 3-1 (Answers begin on page 567.) A. Spell the triad, given the root and type. (As with keys, upper-case letters indicate major and lowercase letters indicate minor; augmented triads are represented by upper-case letters followed by a “s,” and diminished by lower-case leurs followed by a “°") 1 be _—_ TA 2£ ad Bg 9. Ge 4 fe 10.8 Be 11. ab 6 De 12. ct NB ean hie Triads 47 B, Notate che triad, given the root and type. . Fill in the blanks xm - 2 3 & & 6 2 B&B 9 10, Fifth Fo ot CEB mid DOA G@ Root Bho BO Fo ‘Type + om om + M & Me om mM. D. Given the chord quality and one member of the triad, notate the remainder of the triad, with the root as the lowest tone. ™ ’ 2 3 4 5 6 7 ‘it root fiteh oot fits ‘ied ied EXERCISE 3-1. See Workbook.Introduction to Triads and Seventh Chords 42 Induction To Seventh Chords 49° SEVENTH CHORDS ! SELF-TEST 3-2 (Answers begin on page 568.) Itwe extend a estan triad by adding another 3rd on top ofthe 5th of the arin she result isa four-note chord. Because the interval between this added i A. Identify the type of each seventh chord, using the abbreviations given in aie dnd the root is some kind of 7sh (major, minor, or diminished), chords | (M7, Mind. meg, 7,°7). hhord, using the abbreviations gi Example 3-3 Of this sorate called seventh chords | eae jould be possible to use more than one kind of 7th with each \ tried pe, there are many more seventh-chord types than wiad types. How- seen uel harmony commonly makes use of only five seventh-chord types Ex. 33) Below each chord in Example 3-3 you will find the commonly {Rx tame for each chord and the symbol used as an abbreviation. Be sure to play Example 8-8 to familinsize yourself with the sound of these chords os 1 2 3 4 5 ° ; Example 3-3. Type of chord major seventh rajorminor seventh minor seventh symbol: a Men? 7 i ™ : 2 3 ‘ 5 6 7 Constrsction nar sind nar triad minor iad tnajoe 28 imino 38 singe 7th ' ‘ Meat ” M7 Mo? 7 ” ” halt diminihed seventh nine sevens diinihed tind diminished ind ‘me Simmined hh i i Quite soon we will begin composition exercises using triads. While seventh . Given the seventh chord quality and one member of the chord, notate the rest of the chords will not be used in composition exercises for some time, you chord. " he rest of the nevertheless be able to start becoming familiar with them from an analytical | standpoint through examples and analysis assignments i ° : 2 3 4 5 6 7 MECKPOINT ‘hid of seeihal "oof idol ithot " wenthof idol CHECKPO! i Mt * Min’? te or ee 1. Which seventh-chord types have a diminished triad on the bottom? ord ype u tom *? 0 " 2 8 4 6 2, Which ones have a M3 between the Sth and the 7th of the chord? 3. Which ones have a m3 between the 3rd and the 5th of the chord? : e verenthof —fogtof ” Githot thot rootef — sevegrhor ” fithof hid ot 4, Which ones contain at least one P5? Which contain two? Mm? " m M7 7 ” m Mind