MATH AND MUSIC

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MATH AND MUSIC

• Ms. Wiltshires Math Class
• Horace Mann Middle School

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PYTHAGORAS

• I was considered to be a Greek philosopher who
  was responsible for developments in mathematics,
  astronomy and the theory of music. 
• Born 582? BC in Samos, Ionia y-ohn'-ee-uh
• Died about 500 BC in Metapontum, Lucania

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PYTHAGOREANS

• The Pythagoreans and I noticed that vibrating
  strings produce harmonious tones when the ratios
  of the lengths of the strings are whole numbers.

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BASIC MUSIC TERMS

• Rhythm is the basis of music just as numbers are
  the basis of math

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BASIC MUSIC TERMS

• "Measure" is the space between two bar lines on
  the staff that represents the division of time by
  which air and movement of music are regulated.

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BASIC MUSIC TERMS

• The pitch of a tone is the listeners evaluation
  of the frequency (number of vibrations per second
  usually shown in Hertz) and is perceived as how
  high or low a note sounds. The higher the
  frequency ,the higher the pitch. The lower the
  frequency, the lower the pitch.

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BASIC MUSIC TERMS

• Time signature is found at the beginning of the
  piece next to the key signature. It looks like a
  fraction without a dividing bar such as 3 4 or 4
  4 .

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PYTHAGORAS MUSIC

• He observed that when the blacksmith struck his
  anvil, different notes were produced according to
  the weight of the hammer.
• Pythagoras discovered that the frequency (pitch)
  of a vibrating string is proportional to its
  length. Doubling the length of a vibrating string
  lowers the pitch by one octave. If one string is
  twice as long as the other, the pitch of the
  shorter string is one octave higher than the
  longer.  If the length of one string is 2/3 the
  length of the other, the change in pitch is a
  fifth.  If the length of one string is 3/4 the
  length of the other, the change in pitch is a
  fourth. 

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Thanks to Pythagoras, we have a scale that
measures pitch and frequency called the dB scale.
The scale is based on a logarithm function. As
the dB level increases the rate at which one can
have hearing loss increases. The softest sound a
human can hear is set at 0 decibels. A rock
concert can be 1013 times stronger. We need to
understand that loud music can have harmful
effects and it is, of course, measured
mathematically. Again thanks, Pythagoras.
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Are math and music related?

• Math and music are related.
• Without math
• We could not have timing or beats in our music.
• We may have high levels of hearing loss because
  we would not be able to measure sound.
• We would not have different types of instruments.
• We would not be able to distinguish between types
  of music.
• And last, we would not make any money at concerts
  ?

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Resources
Astronomy.Rocks Pythagoras of Samos.
Intelligent Child. Intelligent Child. 26 June
2001 http//www.intelligentchild.com/astronomy/
pythagoras.html.   Eisenkraft, Arthur.
Medicine Hearing. Active Physics. 2000. Its
About Time.   Katz, Nikki. Mathematicians
Pythagoras. Math For Kids. 12 March 2001.
About.com. 26 June 2001. http//kidsmath.about.c
om/kids/kidsmath/library/weekly/aa031201a.htm  
Online Math Applications Math and Music. Online
Math Applications. 26 June 2001. Thinkquest.
http//tqjunior.thinkquest.org/4116/Music/music
.htm