Description
This collection would be great for anyone who is trying to learn the music theory, and it's important for any musician.
This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/ 3.0/) license. This book was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz (http://lardbucket.org) in an effort to preserve the availability of this book.
Study Set Content:
Music Theory
v. 1.0
This is the book Music Theory (v. 1.0).
This book is licensed under a Creative Commons by-nc-sa 3.0 (http://creativecommons.org/licenses/by-nc-sa/
3.0/) license. See the license for more details, but that basically means you can share this book as long as you
credit the author (but see below), don't make money from it, and do make it available to everyone else under the
same terms.
This book was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz
(http://lardbucket.org) in an effort to preserve the availability of this book.
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per the publisher's request, their name has been removed in some passages. More information is available on this
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ii
Table of Contents
Chapter 1: The Elements of Rhythm: Sound, Symbol, and Time
................................ 9
Durational Values: Symbols Representing Time in Music....................................................................... 10
Pulse, Tempo, and Meter............................................................................................................................. 20
Music Notation Practices ............................................................................................................................ 32
Additional Information ............................................................................................................................... 43
Summary....................................................................................................................................................... 53
Chapter 2: The Elements of Pitch:Sound, Symbol, and Tone
..................................... 54
Pitch and Pitch-Class ................................................................................................................................... 55
Chromatic Alteration: Accidentals............................................................................................................. 62
The Keyboard as a Visual Tool.................................................................................................................... 67
Register Designation, The Octave, 8va, and 8vb ....................................................................................... 72
Pitch Notation: Nomenclature and Solfége ............................................................................................... 77
Moveable C-Clef; Other Clefs....................................................................................................................... 80
Summary....................................................................................................................................................... 86
Chapter 3: The Foundations Scale-Steps and Scales
................................................... 87
Scales and Scale-Steps ................................................................................................................................. 88
Heptatonic Scales: The Major Scale, The Three Forms of the Minor Scale............................................91
Solfége Revisited ........................................................................................................................................ 102
Heptatonic Scales: Introduction to Modes .............................................................................................. 106
Other Commonly Used Scales ................................................................................................................... 113
Summary..................................................................................................................................................... 120
Chapter 4: Key Sense, Key Signatures, and The Cycle of Fifths
.............................. 121
The Sense of Key: Attributes..................................................................................................................... 122
The Cycle of Fifths as a Mnemonic Device .............................................................................................. 123
Relative and Parallel Keys ......................................................................................................................... 124
Closely-Related Keys.................................................................................................................................. 125
Modes Revisited: Transposing Modes, Construction and Identification .............................................126
iii
Simple, Compound and Multiple Intervals.............................................................................................. 128
Interval Identification Procedure: The Two Evaluative Criteria .......................................................... 129
The Interval Placement Diagram ............................................................................................................. 130
Interval Inversion ...................................................................................................................................... 131
Interval Construction Procedure ............................................................................................................. 132
Interval Identification and Construction Below a Given Pitch ............................................................. 133
Introduction and Definitions .................................................................................................................... 135
The Harmonic (“Overtone”) Series .......................................................................................................... 136
Triads: Four Types, Inversion, and Basic Symbolization ....................................................................... 137
Chord Labels and Primary and Secondary Triads .................................................................................. 138
The Conditional Status of Second Inversion Triads ............................................................................... 139
Introduction to Seventh Chords: Five Basic Types................................................................................. 140
Other Common Trichords and Seventh Chords...................................................................................... 141
Larger Chord Structures: Upper Dominant Discords and Non-Dominant Upper Extensions............142
Basic Chord Symbolization ....................................................................................................................... 143
Chapter 7: Basic Analytical Techniques: The Four Parameters
.............................. 144
The Purpose of Analysis ............................................................................................................................ 145
Tonal Music: Expectation and Iteration .................................................................................................. 146
Roman Numeral Analysis (RNA) ............................................................................................................... 147
The Figured Bass Tradition and its Use in Analysis ............................................................................... 148
Categories of Chord Progressions: Expectations in Tonal Harmony.................................................... 149
Definition and the Sense of Closure in Music ......................................................................................... 151
Melodic Cadences....................................................................................................................................... 152
Final (Conclusive) and Non-Final (Inconclusive) Cadences................................................................... 153
Harmonic Cadence Types .......................................................................................................................... 154
Procedure for Evaluating and Identifying Cadences.............................................................................. 155
Chapter 9: Melodic Elaboration I: Non-Harmonic Activity
...................................... 156
Non-Harmonic (Non-Chord) Tones .......................................................................................................... 157
Types of NHT .............................................................................................................................................. 158
Procedure for Evaluating and Identifying NHT ...................................................................................... 159
The Suspension Figure .............................................................................................................................. 160
iv
Chapter 10: Harmonic Elaboration I: Seventh Chords
.............................................. 161
Origins of Seventh Chords as Non-Harmonic Activity........................................................................... 162
Expected (Typical) Use of Seventh Chords.............................................................................................. 163
Evaluating Seventh Chords in Contrast with Non-Harmonic Origins .................................................. 164
Other Uses of Seventh Chords .................................................................................................................. 165
Chapter 11: Chromaticism: Evaluating Tone Outside of the Prevailing Key
Essential versus Inessential Chromaticism ............................................................................................. 167
Modulation and Tonicization: Similarities and Contrasts..................................................................... 168
Modulation: Attributes and Closely Related Keys .................................................................................. 169
Types of Modulation: Common Chord, Direct (Phrase), Chromatic, Remote, Chain ..........................170
Tonicization: Applied Chords or Secondary Functions.......................................................................... 171
Introduction to Altered Chords: Mode Mixture ..................................................................................... 172
Chapter 12: Formal Organization: Small Part Forms
................................................ 173
Form as a Meta-Rhythm ............................................................................................................................ 174
The Motive: The Irreducible Creative Gesture........................................................................................ 175
Expansion: Sub-Phrase, Phrase, Period, Double Period ......................................................................... 176
Phrase Extension and Phrase Elision ....................................................................................................... 177
Small Homophonic Part Forms: Binary, Ternary and Rounded Binary ...............................................178
Expansion and Magnification: Textbook Models of Larger Forms ....................................................... 179
Chapter 13: Concise Forms: Composing in the Vernacular Style
........................... 180
Characteristics of Tonal Melody............................................................................................................... 181
Common Chord Progressions ................................................................................................................... 182
Argot, Jargon, and Slang in Popular Song ............................................................................................... 183
Typical Formal Patterns ............................................................................................................................ 184
The Blues..................................................................................................................................................... 185
Chapter 14: The Four-Voiced Setting: The Chorale and The Chorale Setting
Introduction and Purpose of Study.......................................................................................................... 187
SATB Chorale Style .................................................................................................................................... 188
Proscriptions and Prescriptions: Adherence to the Style...................................................................... 189
Active Tones, Voice Range, Doubling, Position ...................................................................................... 190
Chapter 15: Voice-Leading Procedures: A Positive Learning Approach
Introduction and Purpose of Study.......................................................................................................... 192
Root Position Triads: Root Motion and Prescribed Procedures ............................................................ 193
Root Position Triads: Conditional Procedures ........................................................................................ 194
Triads in Inversion: Prescribed Procedures ............................................................................................ 195
Complete Procedural Table....................................................................................................................... 196
v
Chapter 16: “Emulative” Composition
......................................................................... 197
Introduction and Purpose of Study.......................................................................................................... 198
Realizing Simple Figured Bass in SATB.................................................................................................... 199
Realizing Simple Figured Bass in Keyboard Style................................................................................... 200
Procedure for Harmonizing a Given Melody .......................................................................................... 201
Chapter 17: Melodic Elaboration II Adding NHT to a Basic Setting
Enhancing a Setting using Appropriate Embellishment........................................................................ 203
Restrictions................................................................................................................................................. 204
The Suspension Figure: Review and Construction Procedure .............................................................. 205
Cadential Elaboration ................................................................................................................................ 206
Other NHT................................................................................................................................................... 207
Chapter 18: Harmonic Elaboration II: Adding Seventh Chords to a Basic
Setting
Review and Common Use of Seventh Chords.......................................................................................... 209
Tendency Tones ......................................................................................................................................... 210
Resolution of Seventh Chords: General Procedures for Voice Leading................................................211
Special Resolution Procedures ................................................................................................................. 212
Chapter 19: Appendix A: Common Musical Terms
.................................................... 213
Chapter 20: Appendix B: Upper Dominant Discords and Non-Dominant Upper
Extensions
Chapter 21: Appendix C: Generalized “Textbook” Models of Larger Forms
Chapter 22: Appendix D: Realizing Chord Changes and Some Typical Jazz Chord
Voicings
vi
About the Author
Mark Andrew Cook
Mark Andrew Cook serves as Director for Music Theory
and Composition at Shepherd University. He is also a
member of the Jazz Studies Faculty. Prior to his
appointment at Shepherd, he served as a member of the
Music Theory Faculty and was the Jazz Ensemble
Director at The Catholic University of America.
Additionally, he served as an Adjunct Music Theory
Instructor at Towson University. He also taught Music Theory, Jazz Studies, History
and Applied subjects at Montgomery College. He served as the Director of Jazz
Ensembles and Wind Ensemble, and as Music Director and Conductor for The
Montgomery College Symphony Orchestra. In addition to teaching at Shepherd
University, Dr. Cook is Guest Lecturer in Music Theory and Composition at The
Barbara Ingram School for the Arts.
He received his B.M.ed. from the Peabody Institute of the Johns Hopkins University,
and both his Master’s degree and Ph.D. in Music Theory from The Catholic
University of America, his dissertation being an analysis (proportional organization
and set analysis) of Paul Hindemith’s symphony
Die Harmonie der Welt
.
He is an active composer and performer in both the Classical and Jazz styles and has
many performing and recording credits.
1
Acknowledgments
The author would like to thank the following colleagues who have reviewed the text
and provided comprehensive feedback and suggestions for improving the material:
• Kurtis Adams, Shepherd University
• Laura Renninger, Shepherd University
• David Gonzol, Shepherd University
• Scott Beard, Shepherd University
• Chris Vadala, University of Maryland, College Park
• William Hollin, The Barbara Ingram School for the Arts
• Scott Benford, Washington County (MD) Public Schools
• Michael Thorsen, Principal, The Barbara Ingram School for the Arts
• Paul Garvin Taylor, The Catholic University of America
• Steven Strunk, The Catholic University of America
• Lawren Diana Hill
In addition, a select group of instructors assisted the development of this material
by actually using it in their classrooms. Their input, along with their students’
feedback, has provided us critical confirmation that the material is effective in the
classroom:
2
Dedication
In Memoriam
Dr. Robert Wayne Ricks
He always compelled me to “take a closer look and let the Music tell its own story.”
3
Foreword
This text is primarily designed to serve as a textbook for a college-level music
theory fundamentals course. However, it also has the flexibility to serve equally
well for a typical core curriculum college-level Music Theory I or Harmony I course.
Our goal is to deliver sufficient information to enable the student to be able to
evaluate and analyze select music from the literature as quickly as is practical.
Secondly, we seek to provide sufficient instruction to enable a student to begin
writing music as quickly as is practical.
In order to develop a complete argument, it is important that the student
understand that this text “assumes a blank slate.” No prior knowledge on the part
of the student is assumed.
In order to give Instructors greater flexibility we have intentionally provided
content that may exceed the course objectives in some institutions. We anticipate
that instructors may want to adjust the material in the text to match their current
course content, or adjust their courses to make use of all of the content in this text.
4
Preface
The manner in which music theory has been traditionally taught is now in a state of
flux. Originally, the study of music theory was designed to acquaint the music
student or knowledgeable amateur with the composer’s working materials in
“Classical” music roughly spanning the 17th- through the 19th Centuries.
The role of music theory has expanded far beyond this mandate: theory training
now incorporates greater or lesser explanations of music after 1900, music before
1600, idiomatic Jazz practices, elements of World Music, and Popular Song idioms.
Such an expansion of means and methods in learning and teaching the fundamental
language of music presents a formidable and almost daunting challenge: what to
teach, how to teach it, and in what sequence?
Additionally, music theory has become a favored required Arts elective in College
and University curricula, and most music programs have a developmental music
theory class to address the needs of under-prepared music majors. Often, music
theory is required companion material for private instruction as well.
This textbook seeks to address these multiple needs: to serve as a basic to moderate
text for the typical fundamentals of music course and to serve as an introductory
text for those interested in acquiring a rudimentary knowledge of the language of
music.
The text also provides supplemental information, such as chord symbolization,
aspects of Jazz harmony, vernacular song form and its attributes, and so on. Usually
when this material is added to existing texts, it is incomplete and delivered in a
manner that reflects only limited real-world experience.
This author is fortunate to have had extensive experience as a teacher of music
theory at the college and university level, as a teacher of AP music theory in an Arts
Magnet high school, as a teacher of the Jazz idiom, as a practicing Classical and Jazz
musician, and as a composer in many styles.
Therefore the scope of this text is to:
5
• Provide clear and concise explanations regarding the basic language of
music;
• Address appropriate subject matter for use by the instructor of college-
level introductory/developmental theory courses, as well as typical
Music Theory I courses;
• Add other relevant information, usually acquired informally by the
student outside the classroom;
• Support each learning objective or skill set with reinforcement in the
form of exercises;
• Prepare the student for a continuing study of music theory at
intermediate to advanced levels.
The format of the text and its scope will easily adapt itself to any of these
circumstances for the instructor or for the student. The modular approach and the
complete flexibility in terms of the online access and individualized customization
enhance the facility with which the text may be employed.
For example, a typical Fundamentals class may not require an examination of the
SATB style and part-writing procedures. In contrast, these would be critical skills
for a Music Theory I course. The Instructor can freely choose what material suits a
given need without resorting to an additional text. The multiple methods of access,
electronically and in print, offer both instructor and student an elastic approach to
the subject matter.
Introduction
A Definition of Music
In it’s broadest possible sense, music is defined as “organized sound.” This open-
ended and safe definition is coherent regardless of era, style, culture, or the
mechanics of musical organization. Each successive historical era produces
musically artistic expressions of its own time, its own musical aura. The study of
Music Theory is the means by which we investigate this.
A Definition of Music Theory
Music Theory is the study of music and its organizational characteristics. We define
and examine aspects of music:
• How do we perceive music aurally?
• How do we experience music aesthetically and?
• How do we symbolize music visually?
Preface
6
We learn to associate sound with symbol (or notation), so to increase our ability to
perceive music at levels of increasing depth and comprehension, both
experientially and analytically.
The Purpose of Music Theory
The study of the language of music yields three unshakeable tenets:
• We learn to analyze music in order to gain an understanding of the
how great composers create. We use it as a “window” into their minds,
if you will;
• We learn to analyze music in order to deepen our own understanding,
either as musicians or consumers of this form of artistic expression.
• We employ the knowledge gained in the study of music to stimulate
and enhance our own creativity.
Among the community of musicians, the greater our comprehension, the more
sublime our interpretation. This creates a more meaningful experience for our
audience. This is the ultimate focus of the study of music.
As consumers, the more we understand about music, the more refined is our ability
to intelligently evaluate what we enjoy. It is the intelligent consumer of Art who is
the greatest supporter of Art.
The Means by which We Investigate Music
Examining music involves evaluation. At any level of experience, this begins with
personal taste and preference. As we learn more, our method of evaluation evolves,
becoming both more fluent and more critical. Clearly, over time and study, this
shapes our perceptions and our tastes, regardless of what general direction these
may take.
Any study begins with an examination of fundamental precepts or principles. Music
is no different. The nature of perception, the basic constructs, craftsmanship in
musical construction: all must be mastered in the study of music.
Two broad approaches are employed in the study of music:
• Analysis: we learn to employ commonly accepted techniques and
specialized language to describe musical organization. These
Preface
7
techniques are a shared analytical language throughout the
community of musicians. This is conceptual knowledge and evaluation.
• Composition: either by actively creating our own works, or (more
likely for the beginner), imitating or emulating the works of earlier
composers. This is active knowledge and procedure.
Both of these approaches will evolve as the student acquires more knowledge, skill,
and greater understanding.
How We Perceive Music
At the most primary level, we experience music by five principal distinctive
characteristics.
• Pitch: we perceive the sensation of sound (or tone) as relatively high or
low.
• Duration: we perceive how much time sound (or silence) occupies.
• Timbre: we perceive various qualities or “colors” of sound.
• Intensity: we perceive differences in volume or sound pressure levels.
• Events in time: we perceive pitch collections (events) in the context of
musical space (time).
These broad generalized definitions and concepts serve us well as a departure
point. We can now progress from the general to the specific in our study.
Epigraph
“The man that hath no music in himself,
Nor is not mov'd with concord of sweet sounds,
Is fit for treasons, stratagems, and spoils.”
- The Merchant of Venice (V, i)
Preface
8
Chapter 1
The Elements of Rhythm: Sound, Symbol, and Time
Introduction
The first musical stimulus anyone reacts to is rhythm. Initially, we perceive how
music is organized in time, and how musical elements are organized rhythmically
in relation to each other. Early Western music, centering upon the chant traditions
for liturgical use, was
arhythmic
to a great extent: the flow of the Latin text was the
principal determinant as to how the melody progressed through time.
As Western music moved from
monody
to
polyphony
(“single voice” to “multiple
voices”), sets of symbols developed gradually that allowed musical time to be
established against a recurring background pulse. This also allowed multiple
elements in music to be established in tandem with one another. These symbols
evolved into the
durational values
(“note values”) that form the foundation for music
notation.
9
1.1 Durational Values: Symbols Representing Time in Music
L E A R N I N G O B J E C T I V E S
1. Describing durational values orthographically: how they are drawn.
2. Defining durational values in proportional relationship to one another.
3. Defining durational values in musical time and space.
Durational values
1
are symbols that represent time and action in musical space:
they delineate and mark off varying values of sound (and silence) in a composition.
Additionally, they are proportional to one another as to how they may be divided
from larger into smaller values.
There have been many differing notational systems throughout the history of
music. In the context of other study, you may encounter these various and sundry
systems from early Western notational traditions. Our current system of notation
evolved from these early systems, incorporating aspects of many.
Components of Notes
Let us first examine how durational values are drawn:
Figure 1.1
Components
Note values may be “open notes” (not filled in or blackened), or “filled-in notes.” In
the context of how musical time is organized (discussed below), these will have
greater or lesser lengths or time spans.
Chapter 2 "The Elements of Pitch:Sound,
will discuss general rules and practices as to how note values are
drawn in the context of pitch placement. In the following example they are not yet
assigned any particular value: only proportional values in relation to each other.
1. Durational Values are those
symbols (“note values”) that
are used to represent the
relative length of a particular
sound in music.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
10
Durational Values and Proportional Chain
Below are examples of basic durational values and their common names. Proper
names for these values are in parentheses. These names are commonly used in the
United Kingdom and Commonwealth countries, as well as by some academics.
Figure 1.2
Durational Values and Nomenclature
There are rare examples of “One-hundred and twenty-eighth-notes.” A notable
example is found in the First Movement Introduction to Beethoven’s “Pathetique”
Sonata No. 8, Opus 13.
“Pathetique” Sonata
These occur at the end of the Introduction. See this link:
http://imslp.org/wiki/Piano_Sonata_No.8,_Op.13_(Beethoven,_Ludwig_van)
Durational values are held in proportion to one another. Observe that each value is
proportionally related to adjacent values. If we assign the arbitrary value “1
n
” to a
whole-note, then the half-note equals 1/2
n
. Therefore two half-notes are required
to equal a whole note, two quarter-notes equal a half-note and so on.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.1 Durational Values: Symbols Representing Time in Music
11
Figure 1.3
Durational Value Chain
Tremolo
At times notes may have a diagonal slash (or slashes) through the stem, or below a
note value that has no stem. These slashes are interpreted one of two ways:
1. These indicate a
tremolo
, the performer rapidly repeating the note, or;
2. As a notational convenience, slashes represent flags, denoting
embedded smaller durational values:
Figure 1.4
Smaller Value “Slashes” (Tremolo)
These can be interpreted as “eighth-notes in the space of a half-note” (4), or
sixteenth-notes in the space of a quarter,” (4) and so on. This is merely a notational
convenience employed as needed.
Dotted Values
Durational values may have small periods (“dots”) appended to them. Originally,
this evolved as a notational “convenience,” a proportional division indication, or as
a segment boundary.
Dotted values
2
have three different interpretations:
2. Durational Values may be non-
dotted or dotted. Dotted Values
have three interpretations: (1)
The dot represents the
addition of half the original
value; (2) The dotted value may
divide into two lower dotted
values; (3) Or the dotted value
may divide into three non-
dotted values. This potential
division into three is critical
for comprehending Compound
Meter.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.1 Durational Values: Symbols Representing Time in Music
12
1. A dotted value may represent the addition of half of the original
duration, or “half again as much as the original value” (“1+1/2
n
”).
Figure 1.5
Dotted Values: First Interpretation
2. A dotted value may be divisible into three non-dotted values:
Figure 1.6
Dotted Values: Second Interpretation
3. A dotted value may be divisible into two smaller dotted values:
Figure 1.7
Dotted Values: Third Interpretation
These varying uses of dotted values shall come into focus in subsequent discussions
concerning meter and notational practice in
Section 1.2 "Pulse, Tempo, and Meter"
and
Section 1.3 "Music Notation Practices"
below. As with non-dotted values, dotted
values are in proportion to one another as well.
shows
the proportional chain of dotted values.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.1 Durational Values: Symbols Representing Time in Music
13
Figure 1.8
Dotted Values
Rests
Just as durational values represent the length of sound in music, symbols of
equivalent value represent the length of silence. These are called
rests
3
.
shows rests and their labels. As with durational values, rests are
proportional to one another also.
Figure 1.9
Rests
3. Rests are the symbols used to
represent the relative length of
silence in music. They are
equivalent in value to
durations.
Chapter 1 The Elements of Rhythm: Sound, Symbol, and Time
1.1 Durational Values: Symbols Representing Time in Music
14
