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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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the mathematics of music

The Mathematics of Music

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

what is a harmonic
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
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
Structure of Human Ear
  • Sounds travel through the ear by way of the cochlea and basilar membrane
why sine waves
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
Vibrating Strings Equation
  • n is the value of the harmonic being played.
musical scale
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
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 people excel in music
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.
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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.
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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
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>.