Scientific Literacy PhysicsofMusic

							                     Proposal for a Core Course: Physics of Music
I. Knowledge Area and Learning Outcomes:
This course covers the complete musical cycle from a composer’s idea through the
interpretation of the resulting music by the listener. Fundamentals and history of music
will be introduced, followed by a description of musical instruments and styles. The
technical aspects of sound are thoroughly covered to understand how music is made and
reproduced. The physical characteristics of the instruments are discussed in detail to
realize how instrumentation of orchestras and bands are selected. Concert venue acoustics
are covered to relate how these venues determine the sounds heard by the listener.
Finally, various aspects of music interpretation will be discussed to complete the musical
cycle.

The course is designed for any student who is interested in understanding the
fundamental and technical details of creating music. The technical (prerequisite) level
consists of algebra, consistent with other Core courses in physics. This is a
multidisciplinary course, incorporating many different academic areas. The course
proceeds in three parts. The first explores the structure of music, instrumentation and a
history of musical styles (see days 1 – 8 of the syllabus in the appendix). The second
(days 9 – 20) gives an introduction to the physical principles of mechanics and waves as
applied to music. The final portion combines the music and physics topics in
investigating the inner workings of instruments and fundamentals of acoustics. The
musical portion of the course includes fine arts & history by covering the fundamentals
and history of music. The technical aspects of music incorporate basic topics in physics
and sound engineering. During the final part of the course, students are applying their
knowledge to a project that is approved by the instructor. The academic level is
consistent with other basic Core courses and is intended for students of all majors.

This course uses physics as a vehicle to introduce students to the fundamental principles,
concepts, and knowledge of the sciences, and introduces them to the methodology of
scientific inquiry. This is a course for any student that emphasizes the beauty, symmetry,
and simplicity of physics through its application to music. The course also uses music to
help students understand the nature and impact of the arts on society. The combination
truly integrates music and science and how they influence each other. The experience
gives students another perspective in music appreciation: a technical understanding of
how music is created and perceived. This course satisfies both the Scientific Literacy and
Artistic Knowledge and Experience areas and develops critical thinking, quantitative
analytical and technical skills.


General physics topics covered:
Kinematics, forces, energy, waves, simple harmonic motion, fluids, sound & acoustics,
optical topics related to acoustics (e.g., reflection & refraction), experimental techniques,
graphical interpretation, data & error analysis, project experience and technical writing.
Music topics covered:
Notes, scales, melody, harmony, rhythm, chord structure, instrument groups, musical
styles and interpretation, room acoustics, recording and orchestration.

In principle, this course could be used by science majors to satisfy the Artistic
Knowledge and Experience area and other majors to satisfy the Scientific Literacy area.

A. Scientific Literacy:
Students will be able to:
1. Perceive the basic philosophical and historical foundations of contemporary science.
Applying the concepts of physics to music provides a very rich and meaningful setting to
introduce students to the physics developed over last five hundred years. The course also
helps them appreciate the way scientific models are developed. The roles of theory,
scientific modeling and experimentation are discussed during the physics introduction
(days 9 – 20) and applied throughout the rest of the course.
2. Demonstrate an understanding of the fundamental principles, concepts, and knowledge
of the sciences.
The physics topics listed in the introduction cover much of the classical physics in a
normal physics course. The difference is that there is a common theme to these topics as
they apply to music. Since many of the concepts apply to the design of instruments, the
students gain an understanding of how engineering and the sciences are related.
3. Participate in a direct experience of scientific inquiry using the methodologies and
tools of science, whenever possible, in a laboratory or field setting.
Through participation in the four in-class laboratories, students are able to experience
procedures of a scientific inquiry and learn the methodologies and tools of science. They
will be able to carry out experiments and report on results with their inherent error. They
will understand the limitations of measurement accuracy and precision. Students are
expected to understand the consistency of units, and the conversions between them. Since
the models of how instruments work are built upon these laboratory experiences, the
students will recognize the role of creativity and intuition in scientific discovery and
understanding.

Students are able to relate empirical laws to underlying theories. They are able to
recognize common underlying principles: e.g. how standing waves create the sounds of
all instruments, but how the different structures of the instruments create the unique
sounds they produce. Students are encouraged to think about the limitations of proving
the validity of a model of a physical phenomenon, while it can be falsified by just one
experiment.
4. Use cognitive and mathematical skills employed by scientists.
Most of the physical laws are best expressed in the language of mathematics. Quantitative
analytical skills are indispensable in physics. Quantitative studies of wave phenomenon
and mechanical systems are a major part of this course. Through homework, in-class
discussions, students will acquire quantitative analytical and graphical skills related to
algebra and geometry. They then apply these skills during the project phase of the course.
5. Demonstrate the capacity to make reasoned and ethical judgments about the impact of
science on the individual, community, and society.
The interaction of instruments in different styles of music and the acoustics of the venue
are studied. Specific calculations are made to ensure the best levels of sound for that style
and venue. This helps students understand societal questions related to the arts can be
understood by physical principles and encourages them to apply laws of physics learned
to the world outside.
6. Demonstrate the capacity to utilize scientific knowledge to promote the health and
well-being of the individual, community and society.
The application of physics concepts in the design and use of instruments is extended to
how musical groups are formed to best convey the musical style that can please
individuals. Since many international styles are discussed, this idea extends to society as
a whole.

B. Artistic Knowledge and Experience:
Students will be able to:
1. Study, create or participate in the creation or performance of some forms of artistic
expression as a means of exploring human experience and understanding the creative
process.
All of the major instrument categories are studied in detail. From the design to the
creation and propagation of the sounds, the students recognize the sounds and frequency
content of the specific instruments in each group. Many of the students build instruments
for their term project. All students study the properties of particular instruments and how
they are played during the lecture, guest lecture and lab sessions.
2. Demonstrate visual and aural literacy.
The first two weeks of the course cover the complete structure of music from the
individual notes to scales, chords and specific styles. The history of musical styles is
discussed from the twelfth through twenty-first centuries and how these styles evolved
from the fundamental structure of music and from each other. Throughout the
instrumental part of the course, they gain an appreciation of the capabilities of each
instrument group and how the instruments contribute to specific musical styles. For
example, since electricity was not available during the creation of classical music, the
instrumentation uses acoustic instruments, dominated by the strings and a small sample
of the brass, woodwinds and percussion. Jazz, on the other hand, consisting of faster
rhythms and a more bright sound, emphasizes the brass and single reed woodwinds.
3. Acquire the critical and technical vocabulary enabling them to describe and analyze,
and formulate an argument about artistic productions.
In addition to the section on musical structure, musical styles and their connection to
instrumentation are discussed. During the instrumental part of the course, the three
important parts of each instrument for all groups is discussed. This includes the source of
the sound, the instrument medium and the coupling with the surrounding air. The
physical properties of the source are studied and the wave properties of the instrument
and surrounding air form the basis for modeling how instruments create their unique
sounds. This study is coupled with performing calculations of the acoustic properties of
various venues designed for the various musical styles. Thus, the students understand the
vocabulary and relations between musical styles and corresponding instrumentation in all
aspects of music. Many of the in-class demonstrations are followed by a discussion of
these facets of music. The guest lecturers give detailed information on their instruments
and insight on how to analyze their musical style. See appendix 4 for a description of
“guest lecturers”.
4. Assess how formal qualities of artistic expression are intrinsically tied to an audience.
At the beginning of the formal physics section of the course, there is a discussion of the
structure of the ear and how it processes sounds. This is coupled with the section on
acoustics of rooms, giving both a physical and physiological sense of the audience’s
participation in the musical performance. The students must calculate the acoustic
properties of rooms and musical venues.
5. Examine multiple interpretive possibilities of any artistic production, and know that
such interpretations both reflect the culture that produced them and change over time.
After covering musical structure early in the course, the various styles, their history and
cultural origin are discussed. Examples of each musical style are played from a CD so
students can experience listening to these styles. The guest lecturers are professional
musicians and discuss styles that they play and their interpretation.
6. Acquire collaborative skills through group problem solving and negotiation.
The lab sessions are in-class and data are taken by groups of students. The roles in data
taking are rotated, so that the whole class has an opportunity to participate. Results and
conclusions are discussed in class before the students write up their reports.

GOALS
- To develop breadth of knowledge in music and physics: In studying music through
    physics, students develop a curiosity and open-mindedness essential to good scientific
    inquiry and are able to apply scientific methodology to other areas. Foundational
    knowledge is also provided about understanding the sense of sound. Students are able
    to make connections with the artistic (musical) and societal views experienced or
    studied in other courses.
B. To enhance ability to integrate: The course interrelates physics of vibration and waves,
biophysics of the voice and ear, psycho-physics of auditory processes, musical acoustics,
architectural acoustics, and electronic sound reproduction.
C. To enhance capability for reflection: How rather than what we know is stressed; e.g.,
how we know sound travels through air in waves. Reflection occurs on the use of
quantitative laboratory measurements, development of models (hypotheses), making
predictions and testing them.
D. To increase communication skills: Quizzes, tests, experiment reports, and the use of
graphs and simple mathematical expressions develop some skills. Precise concepts,
concise statements of relationships and simplicity of expression are stressed. Students are
required to write lab reports and a term paper reflecting their project work.
E. To develop value consciousness: Music and hearing play a major role in life. Many
societal issues are related to these topics. For example, more deterioration of hearing in
increasingly larger segments of the population has accompanied technological
advancement. Even medical advances are developed to address the issues of hearing and
acoustics. Interpretation of music is largely a societal issue that is discussed in the course.

II. SKILLS DEVELOPMENT
A. Critical Thinking Skills & Dispositions
Comprehend, paraphrase, summarize and contextualize the meaning of varying forms of
communication, including written work, speech, film, visual art, multimedia and music.
The history of musical styles is discussed from the twelfth through twenty-first centuries
and how these styles evolved from the fundamental structure of music and from each
other. The interpretation of styles is discussed and the end of semester project written
papers reflect students’ interpretations of the styles represented in their themes.
Analyze relationships among statements, questions, concepts, descriptions or other forms
of representation intended to express beliefs, judgements, experience, reasons,
information or opinions.
Underlying various empirical laws there are fundamental theories based upon models of
nature. These models never account for all of the details, but should be good
approximations to the phenomena they represent. For example, vibrations and waves
model musical phenomena. One of the experiments performed in class analyzes models
of transverse waves using a wave machine. The analogy is made to the workings of a
guitar. Similar measurements are made on actual guitar strings to illustrate the
comparison. When the model is applied to an actual guitar, it is close but does not include
the effects of a sounding board. The strengths and weaknesses of this model are
elaborated upon to decide how to assess the validity of a scientific model. Similar class
discussions on other topics require students to answer questions and make their own
scientific arguments, by compiling relevant data, formulating scientific hypotheses, and
applying modes of scientific reasoning. Students would be able to distinguish between
scientific and artistic problems, by recognizing the criteria that define science and the
arts.
Generate new ideas, hypotheses, opinions, theories, questions and proposals; and develop
strategies for seeking, synthesizing information to support an argument, make a decision
or to resolve a problem.
Class discussions of lab and demonstration results require students to answer questions
and make their own scientific arguments, by compiling relevant data, formulating
scientific hypotheses, and applying modes of scientific reasoning. Students would be able
to distinguish between scientific and non-scientific (especially arts and esthetics)
problems, by recognizing the criteria that define each.

B. Quantitative & Qualitative Analysis & Research Methods (Please note that this course
only addresses quantitative skills.)
Represent and interpret quantitative information symbolically, graphically, numerically,
verbally and in written form.
To understand the quantitative nature of physics by solving physics problems using
mathematics: algebra and geometry. For example:
 To set up and solve physical problems using algebra and geometry.
 To construct and analyze graphs, especially those related to waves and acoustics.
 Understand how to mathematically analyze data, perform error analysis and interpret
   results.

Students will be using the above skills in solving problems in music theory, mechanics
and acoustics. Through these examples they will develop quantitative skills learn how to
represent word problems into mathematical equations. Examples of exams and labs are
given in the appendices.
Recognize the limitations of mathematical and statistical models.
The wave experiment and guitar model cited above illustrates the limitations of modeling
physical phenomena. The error analysis performed in each of the experiments illustrates
the limitation of measurement in science and requires students to quantify this limitation.
Develop an understanding of the nature and history of mathematics, its role in scientific
inquiry and technological progress and its importance in dealing with issues in the public
realm.
To understand the interaction between theory and experiment in physics. We model the
working structure of instruments and experimentally test these models. Their aural
qualities are compared to these models.

III. EXAMPLES OF LEARNING ACTIVITIES
   Lectures
-   Demonstrations
-   Class discussions
-   In-class laboratory experiments
-   Final Project
Learning activities for Physics of Music include lectures, class discussions, a variety of
physics demonstrations, in-class laboratories and out-of-class reading. These learning
activities are designed to encourage students to extend their understanding of basic
principles of physics and scientific methodology to explain every days phenomena
described in the textbook and that they see around them.
Lectures: Lectures provide introduction to fundamentals of music, classical physics and
their historical development and the connection between the two. These lectures and
discussions will also integrate their acquiring of knowledge in music and physical science
with development of an understanding of philosophy of each.
Pedagogical approach -- A large part of this core course content is delivered in a lecture
format coupled with discussion. In addition, students are also expected to learn from
interaction between students and the teacher and among students. Pedagogies which best
suit student learning: interactive engagement, Socratic dialogue and group work are
extensively used.
Lectures and demonstrations -- Phenomena pertaining to a particular topic in sound will
be demonstrated in class as an introduction to the discussion of that topic.

Class discussions are used:
-   to guide students in the critical evaluation of the data, and analyze them using
    scientific methodology and the fundamental principles learned by that time.
-   to compare, discuss or evaluate different reasoning and explanations
-   to develop their own reasoning and explanation
-   to inculcate the basics of effective and civil verbal expression
-   to help students develop the ability to defend their positions with evidence and to
    respond to the arguments of others.

Laboratory & Group work: Physics is a group enterprise at all levels, from novice to
research scientist. In addition to in-class group activities, students should work on
physics homework in groups. Students would first read the chapter and work on
homework questions and problems alone, and then get together with others in the class
and compare; i.e., teach each other. Cooperation of this kind is not only allowed, it is
strongly encouraged. (However, each student must bring in his or her own set of written
work.) Class discussion can take a variety of forms and differ according to teacher.

Laboratory -- The laboratory provides an opportunity for a continuation of the class
demonstrations or for more thorough investigations. The laboratory provides a setting for
class interactions and discussions. Students will perform four in-class laboratories.
Final Project
Students are required to do a final project that incorporates both physical and musical
aspects of the course.
Project ideas: Acoustics of concert halls, instrument analysis, design and build an
instrument – describe why it is unique, related physical concepts in other areas (arts,
sciences & nature)
Project Logistics: Abstract – 1 page (10 points); Midterm progress report – 2 pages (30
points); Final paper and presentation of project (e.g., a working instrument) – (60 points).

IV. EXAMPLES OF ASSESSMENT STRATEGIES
Assessment:
Assessment includes homework (8 assignments=1 exam), exams (4), in-class laboratory
write-ups (4 lab writeups=1 exam), one final exam and a final project incorporating the
ideas of the course.
Written exercises:
Examinations, homework problems, laboratory reports and written project paper.
In-class discussions will provide very relevant information about students understanding
of the material covered.
Homework will help the teacher get a feel for the difficulties experienced students in by
various topics discussed in class.
Laboratory experience helps them understand the nature of experimental work and its
relation to theoretical models. This is applied to understanding the nature and design of
musical instruments and musical venues.
Examinations:
This is the most important instrument for assessment. There are 4 hourly exams and 1
final exam. Each exam will consist of about 2/3 problem solving and 1/3 discussion of
physical and musical concepts and their applications. Exams will assess
- knowledge of fundamental laws of physics
- the understanding of conservation principles in physical sciences
- the ability to discern the effect of different perspectives demonstrating awareness of
    changing values and methods of interpretation
- music topics

Examples that relate to quantitative analytical skills
All exams and laboratory write-ups require mathematical calculations.

Examples that relate to critical thinking skills
Problems based on scientific methodology require students to think critically to
determine which of several possible scenarios is the best possible answer.
1. Categorizing information in word problems into: what is known, what is sought, what
equations relate the known and unknown quantities.
2. Distinguishing between mathematical operations for vectors vs. scalars.
3. Relating empirical laws to underlying theories.
4. Carrying out experiments and reporting on results and their error.
5. Understanding the limitations on measurement accuracy and precision; demonstrating
this on homework and exam calculations.
6. Recognizing common underlying principles.

Multiple instructors Possible: The course is presently taught by a physicist who has
performed music professionally. The possibility exists to have the course team-taught,
one instructor from physics and the other from music.

Appendix 1: Physics of Music detailed outline.
List of topics with class coverage and text references (D. Hall, Musical Acoustics)
Overview:
Day 1: Description of the complete cycle from the composer’s idea through interpretation
of the music by the listener. Sections 1.1 & 1.2. Refs: PoMusicDay1.doc posted online.
Music:
Day 2: Language: notes, intervals & frequency ratios, scales (temperament), dynamics,
timbre, styles Sections 7.1, 7.3 & Ch. 18.
Day 3: Structure: melody, harmony & rhythm Sections 7.2, 7.4 & Ch. 19.
Day 4: Mathematics interlude: Powers & logarithms, frequency ratios and fundamentals,
cents intervals Ch. 19.
Day 5: Tools (instruments): strings, woodwinds, brass, percussion, voice, electronics
Sections 3.1 – 3.5.
Day 6: Sounds and ranges of instruments Ch. 19
Day 7: History of music and musical styles: e.g., classical, jazz & blues, international,
rock, country Section 19.4.
Day 8: Quiz 1
Physics
Day 9: Introduction to physics as a science, the role of the laboratory & lab techniques;
sensory perception (ear) Sections 6.1 – 6.3
Day 10: Construction of notes: force, power (energy and intensity), pure tones Sections
1.3 – 1.5 & 5.1 – 5.3.
Day 11: Energy transfer of sound & sensory perception of music Sections 6.1 – 6.4
Day 12: Introduction to wave properties (speed, medium, frequency, wavelength,
reflection & diffraction) Sections 2.3 – 2.5.
Day 13: Sound as a wave (sources) Sections 2.1 – 2.2, 6.4. Lab #1
Day 14: Superposition of waves & Standing waves: harmonics, beats Sections 10.1, 12.1
& 15.1.
Day 15: Simple harmonic motion in nature Sections 4.5, 7.4 & 9.4.
Day 16: Simple harmonic motion lab Sections 4.5, 7.4 & 9.4. Lab #2
Day 17: Superposition and construction of complex waves: frequency content, scales &
intervals Sections 6.5 & 8.1 – 8.2.
Day 18: Longitudinal, transverse waves & instruments Sections 9.1 – 9.4 & 10.2.
Day 19: Quiz 2
Day 20: Standing waves Sections 4.5, 7.4 & 9.4. Lab #3
Combining physics & music
Day 21: Characterization & physical properties of instrument groups Ch. 3, sect. 8.2.
Day 22: Guest lecture: Nick Drozdoff – Physics and trumpets
Day 23: Longitudinal waves and fluid flow Sections 12.1 – 12.3.
Day 24: Helmholtz resonators & discussion of project Section 2.5 Refs: Helmholtz, On
the Sensations of Tone; Rossing, Science of Sound
Day 25: Instrument lab with longitudinal & transverse waves Section 8.2 Lab #4
Day 26: Sound effects (attack & decay, vibrato & tremolo, reverberation) Sections 3.2,
6.7, 8.3 & 14.4.
Day 27: Reproduction of sound via frequencies: CDs Sections 8.3 & 8.4.
Day 28: Strings: general characteristics & design, plucked Sections 10.3 & 10.4.
Day 29: Strings: hammered and bowed Ch. 10, section 4, Ch. 11.
Day 30: Woodwinds: general characteristics & pipes Sections 12.1 – 12.3, 12.6.
Day 31: Woodwinds: single & double reed: Guest lecture Sections 12.5 – 12.6 & 13.1 –
13.2.
Day 32: Quiz 3
Day 33: Brass: general characteristics, mouthpiece & bell Sections 13.3 – 13.4.
Day 34: Brass: trumpet, trombone & French horn Brian Holmes VHS
Day 35: Percussion: vibrating bars, xylophone & glockenspiel Sections 9.1 – 9.4.
Day 36: Percussion: membranes, drums & cymbals Sections 9.5 – 9.7.
Day 37: Voice, electronics (organs & MIDI) Ch. 14 & 8.4.
Day 38: Orchestration as related to musical style & physical venue Review.
Day 39: Acoustics of concert halls: reflection, sound diffraction, resonance Ch. 15.
Day 40: Acoustical effects: Doppler effect, decibels, polarization & absorption Sections
4.1 – 4.4, 15.6.
Day 41: Quiz 4
Day 42: Factors affecting the interpretation of music Chs. 17 & 20.
Day 43: Course review

NOTE: For appendices 2 & 3, the Core areas assessed will be labeled as follows.
SL (numbers) represents the Science Literacy areas by their number described in the text.
AK (numbers) represents the Artistic Knowledge & Experience areas by their number
described in the text.
SD (letters) represents the Skills Development areas by their letter described in the text.

One lecturer from the Spring 2005 semester was Nick Drozdoff, a professional trumpet
player who teaches high school physics. He has extensive knowledge and experience
playing different types of trumpets in professional settings. For example, he has played
with the Chicago Symphony Orchestra (classical), Maynard Ferguson (jazz), the
Temptations (Rhythm & Blues) and Styx(classic rock). He also has M.S. degrees in both
physics teaching and music. He used his expertise to present a history of the trumpet,
performance techniques, explanations of how trumpets work and how the player can get
unique sounds out of the trumpet by using special techniques. Information was also
provided to the students on his Web site.