The Mathematics of Music

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# The Mathematics of Music - PowerPoint PPT Presentation

The Mathematics of Music. By: Phil Boyer, Mark Forman, Brian Glenn, and Arvind Kanna. What is a harmonic?. Any of a series of musical tones whose frequencies are integral multiples of the frequency of a fundamental tone A wave whose frequency is a whole number multiple of that of another.

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## The Mathematics of Music

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Presentation Transcript

### The Mathematics of Music

By: Phil Boyer, Mark Forman, Brian Glenn, and Arvind Kanna

What is a harmonic?
• Any of a series of musical tones whose frequencies are integral multiples of the frequency of a fundamental tone
• A wave whose frequency is a whole number multiple of that of another
Harmonic Series
• This series Diverges.
• For each whole number a harmonic exists.
• In music, only the odd harmonics sound pleasing to the ear.
Structure of Human Ear
• Sounds travel through the ear by way of the cochlea and basilar membrane
Why Sine Waves?
• Sine waves most accurately model how a sound particle travels through the ear.
• The equation that best represents how musical sound waves travel through the ear is the equation for simple harmonic motion
Vibrating Strings Equation
• n is the value of the harmonic being played.
Musical Scale
• The Western Musical Scale consists of twelve notes forming an octave.
• There are 7 natural notes and 5 sharp/flat notes.
• # means “sharp”, b means “flat”
• A A# B C C# D D# E F F# G G#
• A Bb B C Cb D Eb E F Gb G Ab
Musical Harmonies
• There are many musical harmonies that can be played on guitar or any instrument for that matter.
• Harmonies can be played between different types of instruments.
• Most popular artists use harmonies in their songs. Even samples and electronic beats use them.
Why Do Mathematical PeopleExcel in Music?
• 1. generally this is so because of the mind set and thought, which is similar between both subjects.
• 2. math as a subject is generally about thinking, problem solving, seeing patters.
• 3. math is also about working with what you know to find a method of exploring and understanding new concepts.
• 4. Music is very similar to math in this sense.
5.       Arranging a melody on an instrument and finding fingerings that correspond to certain sequences of notes(like piano for example) is definitely a type of math problem.
• 6. Playing the same melody on different instruments is math, as is playing a stringed instrument and changing the tuning.
7. Playing harmonies, playing the same song in different keys--these things all involve recognizing the structure of a piece of music.
• 8. Good musicians can often listen to a song, observe the musical structure, and play along with it, without really knowing it or rehearsing it, because they recognize familiar patterns.
• 9. this type of pattern recognition and mind set of math oriented individuals helps them excel in music.
Bibliography
• Dave, Benson. "Music : A Mathematical Offering." Mathematics and Music. 14 May 2006. Cambridge University. 25 May 2006 <http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html>.
• Harrison, David M. "Standing Waves." 24 Mar. 2003. University of Toronto. 25 May 2006 <http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Vibrations/Vibrations.html>.
• Reid, Harvey. "On Mathematics and Music." Woodpecker Records. Nov. 1995. Woodpecker Records. 25 May 2006 <http://www.woodpecker.com/writing/essays/math+music.html>.