Teaching Mathematics with the Internet Workshop
1998
Mathematics of Music
by Deborah Taylor
Goal:
To enhance and broaden students' understanding, knowledge, and appreciation of the mathematics in music. Instructional Objective:
The student will... - review basic skills such as ratios, fractions, exponents, square roots, and logarithms.
- use algebra to analyze musical relations.
- quantify various variables associated with music and sound.
Set:
"Everyone enjoys various types of music." Music and mathematics are closely intertwined. The pitch of a musical note is determined by the frequency or vibrations per second, of the sound waves emanating from the instrument. The volume is determined by the amplitude of the waves. Understanding the relationship of harmonic and discordant notes requires a study of theirrelative frequencies. Today, I want you all to discover the beauty and uniqueness of various sounds. Everyone will begin by using the computer to search for the mathematics in music. Let's begin.Instructional Strategies:
The teacher will... - use a tuning fork and give the students a mini lesson in musical pitch.
- monitor and assist the students during the computer activity.
Materials:
Calculators, Tuning Forks, Musical Instruments, ComputersStudent Practice:
The Student will... - use site to learn more about the algebra of acoustics.
- use site to search for mathematical functions in the analysis of music (ratios, exponents, square roots, and logarithms).
- discuss findings during closure of lesson.
Supplemental Activity:
Students can calculate the frequency ratios of various instruments brought in by classmates.Closure:
The closure will be given by random volunteers whichwill be eager to summarize their learned knowledge.Evaluation:
The teacher will constantly monitor and adjust toensure learning has occurred.
Web Sites:
Biography:
Mathematics teacher at the 21st Century Preparatory School.
Photo and/or other images
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