Basic Materials in Music Theory: A Programed Course, Books a la Carte, 13th Edition Solution Manual

Name: Basic Materials in Music Theory: A Programed Course, Books a la Carte, 13th Edition Solution Manual
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Solution Manual
For
Basic Materials in
Music Theory
A Programed Course
Thirteenth Edition
Prepared by
Greg A Steinke, Independent Composer/Musician
Based on materials
originally created by
Paul O. Harder, Late, of Michigan State University

Contents
Introduction vi
1.0 The Basic Materials of Music: Time and Sound 1
Main Points and Objectives 1
Alternative Approaches and Supplementary Activities 1
Classroom Aids 2
Answers to Supplementary Assignments and Quiz Masters 7
2.0 The Notation of Pitch 8
Main Points and Objectives 8
Alternative Approaches and Supplementary Activities 8
Classroom Aids 8
Answers to Supplementary Assignments 14
Answers to Quiz Masters 16
3.0 Time Classification 17
Main Points and Objectives 17
Alternative Approaches and Supplementary Activities 17
Classroom Aids 17
Answers to Supplementary Assignments and Quiz Master 22
4.0 Note and Rest Values 23
Main Points and Objectives 23
Alternative Approaches and Supplementary Activities 23
Classroom Aids 24
Answers to Supplementary Assignments 30
Answers to Quiz Master 31
iii

5.0
Time Signatures 32
Main Points and Objectives 32
Alternative Approaches and Supplementary Activities 32
Classroom Aids 32
Answers to Supplementary Assignments 37
Answers to Quiz Master 38
6.0
Intervals 39
Main Points and Objectives 39
Alternative Approaches and Supplementary Activities 39
Classroom Aids 40
Answers to Supplementary Assignments 46
Answers to Quiz Master 47
7.0
The Basic Scales 48
Main Points and Objectives 48
Alternative Approaches and Supplementary Activities 48
Classroom Aids 48
Answers to Supplementary Assignments 52
Answers to Quiz Master 53
8.0
The Major Scale 54
Main Points and Objectives 54
Alternative Approaches and Supplementary Activities 54
Classroom Aids 54
Answers to Supplementary Assignments 57
9.0
The Minor Scales 59
Main Points and Objectives 60
Alternative Approaches and Supplementary Activities 60
Classroom Aids 60
Answers to Supplementary Assignments 66
Answers to Quiz Masters 67
iv Contents

10.0 Key Signatures 68
Main Points and Objectives 68
Alternative Approaches and Supplementary Activities 69
Classroom Aids 69
Answers to Supplementary Assignments 75
Answers to Quiz Master 76
11.0 Triads 77
Main Points and Objectives 77
Alternative Approaches and Supplementary Activities 77
Classroom Aids 77
Answers to Supplementary Assignments 81
Answers to Quiz Master 81
Appendix: Additional Classroom Aids 83
Blank Masters 85
Blank Quiz Answer Sheet No. 1 87
Blank Quiz Answer Sheet No. 2 88
Musical examples completed in NoteWriter™, NoteAbility Pro™, and Finale 2009™
Pages completed in Ready, Set, Go!™
Contents v

This manual has been prepared to assist instructors in the use of Basic Materials in Music Theory: A
Programed Course, Thirteenth Edition. The chapters contained in this volume are correlated with those
of the text, and each contains four sections: (1) Main Points and Objectives; (2) Alternative Approaches
and Supplementary Activities; (3) Classroom Aids; and (4) Answers to Supplementary Assignments and
Quiz Masters.
The method of programed instruction employed in the text has proved to be effective in a wide
variety of educational situations. Because programed instruction provides constant feedback, it is largely
self-tutorial. Thus, the text is especially effective in large classes, where attention to individual needs is
necessarily limited. The text is also effective when used by individuals working largely on their own. In
normal class situations, instructors are relieved from much routine teaching and time-consuming paper
grading. So, instructors are free to design alternate learning experiences, such as creative work, ear
training, or the study of music literature and form. The efficiency of programed instruction provides the
time for such experiences; the suggestions and material contained in this manual help supply the means.
With such help, instructors may enrich their course in various ways. Fuller comprehension and more
rewarding educational experiences should be the result.
The text incorporates two methods for students to reinforce their learning: (1) each chapter contains a
series of mastery frames, by means of which students may assess their comprehension of the key points
that have been presented; and (2) supplementary assignments that provide additional reinforcement. The
assignments also provide a means for the instructor to monitor student progress towards mastering the
subject matter. The material contained in this manual provides the answers to the supplementary
assignments and quiz masters. To simplify the evaluation of student responses, the answers are generally
presented in the same format as the assignments. In some cases, responses need not be exactly as given.
Alternative solutions are often possible, for example, where enharmonic spellings are involved.
Common sense should be applied in such cases.
Although the chapters of Basic Materials in Music Theory have been arranged to provide an orderly
sequence of material, instructors should feel free to alter the order if they wish. Some instructors, for
example, prefer to base the study of intervals on the major scale, so taking Chapter 8.0, The Major
Scale, before Chapter 6.0, Intervals, may be preferred. Each chapter is relatively self-contained, but if
the order of chapters is changed, some explanation in class may be necessary.
The emphasis in Basic Materials in Music Theory is on written theory. Aural experiences are vital,
however, so students should be encouraged to use the “Ear-Training Activities” that appear at the end of
each chapter of the text and to also continue, or certainly start, any ear-training exercises they can in
melodic and rhythmic dictation, sight singing and general music listening. This edition offers recorded
examples of how a student might practice and work with the Ear-Training Activities’ suggestions.
Students should be strongly encouraged to utilize these examples with the text. Students should also be
encouraged to invent exercises on their own and to explore all kinds of music literature through their
particular performance medium. Such activities can be tied to explorations of the creative process. In
any case, the goal is to help students to become more sensitive to all aspects of sound, as well as their
own reactions to various sound stimuli. Such self-awareness can provide an avenue to more mature
musicianship.
Introduction
vi

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The material in this manual is presented in four sections for each chapter. The manner in which the
information contained in these sections may be used is detailed below:
1. Main Points and Objectives
This section summarizes in outline form the principal items of information that are
needed for mastery of the subject matter. These generally are listed in the order in which
they occur in the text. Instructors should find this information helpful in preparing
supplementary lectures, demonstrations, and drills to reinforce in class the individual
work done by the student. This section also identifies the skills that constitute the
objectives toward which the learning experiences are aimed.
2. Alternative Approaches and Supplementary Activities
Suggestions are given to help instructors supplement the text with additional material and
related activities. Advice is also given regarding various ways to use the text, including
the reordering of chapters.
3. Classroom Aids
A set of PDF masters is provided for each chapter. The pages of this manual may also be
used to make masters for use in class. The PDF masters can be placed into a computer
presentation program such as Power Point™, Keynote™, or a PDF reader.
Instructors who have not used computer projector are encouraged to try this technique. Its
advantages include the following:
a. Use of the projector usually does not require that the room be darkened.
b. Masters may be prepared in advance and used with the projector as needed. This
avoids the time-consuming job of writing material on a chalk or white board.
d. A series of overlays may be prepared to trace a sequence of steps to solve a
problem or to demonstrate a particular process.
Instructors are encouraged to prepare other examples to supplement the masters that are
provided. To facilitate this, the Appendix contains blank masters that may be duplicated
for the preparation of additional prepared exercises, or made into a master without
additional writing. Masters can also be prepared on a computer (as indeed this whole
manual was prepared) utilizing one of the many programs now available for this purpose.
Further, masters could be prepared for other short exercises or examples from the many
musical materials available. If this is done, proper copyright notice should be placed on
the master, or the source should be acknowledged. (Please see the Reference
Bibliography in the Basic Materials in Music Theory text for further information.)
4. Answers to Supplementary Assignments and Quiz Masters
The information in this section is provided to facilitate the correction of Supplementary
Assignments and the Quiz Masters.
vi Introductioni

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1
Chapter 1.0
The Basic Materials of Music:
Time and Sound
MAIN POINTS AND OBJECTIVES
It is desirable that serious study of music should begin with the establishment of a perspective
that includes the following points:
1. There are two sides to music, the emotional and the rational.
2. Music is a temporal art that involves patterns of sound.
3. The two basic materials of music are time and sound.
To understand music, one must comprehend the manner in which both time and sound are
organized. The purpose of this chapter is to present the four properties of sound: pitch, intensity,
timbre, and duration. This is done in terms of simple acoustical phenomena.
Main points covered:
1. Sound source: vibrating body
2. Sound waves
3. Pitch
4. Frequency
5. Octave phenomenon
6. Amplitude
7. Intensity
8. Timbre
9. Natural harmonic series
10. Partials
11. Fundamentals
12. Overtones
13. Duration
ALTERNATIVE APPROACHES AND SUPPLEMENTARY ACTIVITIES
Each of the properties of sound should be demonstrated in class to provide students with actual
aural experiences. The piano is perhaps the most useful tool and can be employed to demonstrate
the natural harmonic series. Harmonics, through about the 6th harmonic, can be demonstrated
singly by depressing silently the key that plays each successive harmonic (partials 2, 3, 4, etc.),
then playing rather forcefully the fundamental. Sympathetic vibrations will cause the harmonic
to sound, although with decreasing volume as higher harmonics are demonstrated. Brass or
stringed instruments are also effective in demonstrating the natural harmonic series.
Information about the acoustics of music can stimulate student interest, and cultivate keener
awareness of how sound is generated and perceived. Some instructors may wish to expand the
material presented in Chapter 1.0. The books cited below are recommended as being useful for
this purpose.
Backus, John. Acoustical Foundations of Music, 2nd. ed. 1977. New York: W.W. Norton.
Benade, A.H. Fundamentals of Musical Acoustics. 2nd rev. ed. 1990. Mineola, N.Y.: Dover Publications,
Inc.
_ ____. Horns, Strings & Harmony. 1992. Mineola, N.Y.: Dover Publications, Inc.
Bienvenue, Gordon F. & Prout, James H. Acoustics for You. 1990. Malabar, Fla.: R.E. Krieger Pub. Co.
Campbell, D.W. & Greated, Clive A. The Musicians Guide to Acoustics. 1987. New York: Schirmer
Books.
Hall, Donald. Musical Acoustics: An Introduction. 1980. Belmont, Calif.: Wadsworth Publishing Co.
Moravcsik, Michael J. Musical Sound: An Introduction to the Physics of Music. 1987. New York: Paragon
House.
Pierce, John R. The Science of Musical Sound. 1983. New York: W.H. Freeman.
Slawson, Wayne. Sound Color. 1985. Berkeley, Calif.: University of California Press.
Wagner, Michael J. Introductory Musical Acoustics. 3rd ed. 1994. Raleigh, N.C.:
Contemporary Publishing Company.

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2
Additional supplementary activities include the following:
1. Please refer to page 12 in the text for a listing of Supplementary Activities. These
activities, in turn, can be enhanced by the activities suggested in this listing.
2. An electronic studio is ideal for the audible demonstration of various acoustical
phenomena, including not only the basic properties of sound, but also beats,
combination tones, wave forms, etc.
A helpful web site: http://ww.phys.unsw.edu.au/jw/basics.html
3. Films, video tapes, or DVDs shown in class provide an added dimension to the
learning experience; such activities generally stimulate increased interest in the
subject. The films below are recommended; other films, video tapes, or DVDs may
also be available through other sources not currently known to the author.
Sound Waves and Their Sources (second edition), 10 minutes, black and white, on rental.
Explains that all sound originates in vibrating objects and illustrates the three general
types of vibrating sound sources: columns of air, surfaces, and strings and rods.
Describes the major characteristics of sound waves: pitch, loudness, and timbre.
Demonstrates the principle auditory differences between sounds. (Note: This film is
now out of print and may only be sporadically available from a film rental library.)
Sounds and How They Travel, 11 minutes, color, on rental. Illustrates the mechanics
involved in the transmission, reflection, and absorption of sound in air. Uses animation
to visualize the compression and expansion of air molecules in the formation of sound
waves, the special vibrating movement of air molecules in transmitting sound waves,
and the reflection of sound in the formation of echoes.
Sounds Around Us (Discovering Matter and Energy), 10 minutes, color, on rental. Shows
that sound is produced by something vibrating and pictures various ways in which
vibrations are caused. Explains what causes sound to differ in pitch, intensity and
timbre.
The last two films may be rented from the source below:
University of Illinois Film Center
1325 South Oak Street
Champaign, Illinois 61820
4. The “Ear-Training Activities” placed at the end of each chapter of the text are intended
for use by students working alone. They may, however, be used in class as a
supplement to other aural training. In any case, students should be encouraged to
experiment with their own instrument or voice as well as to experience and become
increasingly sensitive to sound phenomena. If time allows, interactively demonstrate
the “Ear-Training Activities” in class.
CLASSROOM AIDS
Masters 1.1A–1.2B are for supplementary classroom presentations, drills, and a quiz related to
the material contained in Chapter 1.0. Masters for this and all following chapters, may be
removed in order to produce masters for use with a projector. For easy identification, each
master is coded to indicate the chapter and sequence. The code (1.1A, 1.1B, etc.), for example, is
interpreted as Chapter 1.0, first master set, consisting of several pages.
NOTE: Starting with this chapter and beyond, it would be possible to also make projection masters of the
Supplementary Assignments to use as reviews, in-class drill, or as quiz material.

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6
MASTER 1.2B
6. The frequency of a tone two octaves lower than another is (1) one-half; (2) one-fourth; (3) half
again; (4) double; (5) four times the frequency of the latter.
7. The lowest partial is called the (1) first overtone; (2) harmonic; (3) fundamental.
8. A 2:1 frequency ratio refers to a(n) (1) third; (2) fourth; (3) sixth; (4) octave.
9. The NATURAL HARMONIC SERIES is a(n) (1) group of harmonies; (2) complex of pitches;
(3) harmonic progression.
10. Write a natural harmonic series on "G" on the bottom of your answer sheet on the grand staff.

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7
ANSWERS TO SUPPLEMENTARY ASSIGNMENTS
ASSIGNMENT 1–1
1. acoustics
2. sound waves
3. vibrating
4. a. strings; b. columns of air; c. wooden bars; d. metal plates
5. Pitch
6. Frequency
7. The frequency of a tone is 100 cycles per second.
8. Frequency
1, 760
880
440
220
110
9. Intensity
10. Intensity (volume) diminishes as the distance increases.
11. partials
12. The quality of sound.
13.
14. 1. F 7. D
2. E 8. A
3. K 9. G
4. B 10. H
5. I 11. C
6. J
15. duration
16. a.
17. octave
ANSWERS TO QUIZ MASTERS
MASTERS 1.2AB
1. 2 6. 2
2. 3 7. 3
3. 3 8. 4
4. vibrating bodies 9. 2
5. duration 10. (harmonic series on G; cf. no. 13 in
SupplementaryAssignment1–1)
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8
Chapter 2.0
The Notation of Pitch
MAIN POINTS AND OBJECTIVES
The objective of this chapter is to be able to identify, write, and interpret correctly the various
signs that indicate pitch.
Main points covered:
1. Staff
2. Treble, bass, and C-clefs
3. Names of notes on the various lines and spaces
4. Ledger lines
5. Grand staff
6. Ottava sign
7. Half and whole steps
8. Accidentals
9. Bar lines
10. Enharmonic notes
11. Chromatic scale
12. Octave designations
ALTERNATIVE APPROACHES AND SUPPLEMENTARY ACTIVITIES
For most beginning students, it may be desirable to stress the treble and bass clefs, with the alto
and tenor clefs introduced for information only. Knowledge of the C-clefs, however, is needed as
preparation for orchestral score reading, composition, or the study of music history and literature
involving the original notation of Renaissance or Baroque music.
The terminology of octave designations may be stressed to a greater or lesser extent as the
instructor sees fit. The need for precise identification of pitches is perhaps greatest in the fields
of composition, orchestration and acoustics.
Stress should be placed upon the fact that, in spite of appearances, not all adjacent notes on the
staff produce the same interval. There is a half step between the notes E–F and B–C. All other
adjacent notes produce whole steps.
Aural experience at this point is very helpful. Students should play the basic notes at a
keyboard to visualize and hear the difference between half and whole steps (a black key
separates two white keys that produce a whole step; there is no black key between two white
keys that produce a half step.) The chromatic scale should be played and sung. Also review with
students how to work with the ear-training activies by practicing some or all of them in class.
Please also see Supplementary Activities listed on page 52 in the text.
CLASSROOM AIDS
Masters 2.1A–2.2B are for supplementary classroom presentations, drills, and a quiz related to
the material contained in Chapter 2.0.

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