The Math and Music Connection

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The Math and Music Connection

• Or
• Pythagoras
• Forefather of Rock n Roll?

2
When people think of great pioneers in music no
doubt some of these people come to mind

• Beethoven
• Mozart
• Jimmy Hendrix

Surprisingly some of the most important musical
discoveries were made long before any of these
men were born.
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In 6th century B.C. lived a man named Pythagoras

• PHILOSOPHER
• MATHMATICIAN
• SPIRITUALIST
• VEGITARIAN
• ASTRONOMER
• FOUNDER OF THE NOW FAMOUS PYTHAGOREAN THEOREM

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Pythagoras was determined to discover the hidden
connection in all things.

• He believed beneath all that we perceive to be
  real was a mathematical abstraction.
• It was these sets of secret abstractions that
  in turn made up the perfect numerical harmonies
  of the universe.
• He related this concept to the realm of music by
  finding a way to express musical tones in
  mathematical form.

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One day while passing a blacksmiths shop
Pythagoras noted differences in the sound of
various hammers striking the anvil.

• Tonal difference was related to the size and
  weight of the hammers
• A hammer weighing exactly twice as much an other
  hammer produced a sound one octave in difference
• A difference in pitch of a fourth as well as a
  fifth were produced by two other hammers with a
  weight ratio of 43 and 32 respectively

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Pythagoras theorized that number,in the form of
weight, seemed to control musical tone.

• He decided to further investigate this theory.
• He used many different methods to test it.
• Some involved different length pipes and various
  weights attached to strings.
• Perhaps the easiest to explain involved string
  tension.

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Pythagoras set up two sets of strings each with
the same degree of tension.

• He then dived one exactly in half.
• When he plucked at the shorter string the sound
  it made was a pitch exactly one octave higher
  than longer one.
• He concluded once again that number, this time
  being amount of space, again seemed to control
  tone.

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He than continued to test different lengths of
string.

• Holding the string at 2/3 its length produced a
  sound pitch difference of a fifth.

• A string held at ¾ its length produced a pitch
  difference of a forth.
• His theory was proven sound (no pun intended)

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Not surprisingly the method Pythagoras used
closely resembles the structure of the modern
guitar.(only ½ the fret board is pictured)

• ½ way down the neck of the guitar counting by
  fret spacing is what is known as the 12th fret or
  octave.
• The A and B notes on the E string are known as
  the fourth and fifth of the scale and are located
  at approximately the same ¾ and 2/3 distances as
  Pythagoras models.

A
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Okay so maybe the not exactly the forefather of
rock and roll.

• His tone ratio was later discovered to be off by
  1.36 in exact pitch difference when ran through
  an entire scale.
• He did however establish a firm connection
  between music and mathematics that would be
  carried on by the school of Plato and
  neo-Platonists for generations.

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The End
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Bibliography

• http//www.aboutscotland.com/harmony/prop.html
• http//www.newgenevacenter.org/biography/pythagora
  s2.htm
• http//guitar-primer.com/Folk/Fingers.html
• http//www.math.niu.edu/rusin/uses-math/music/
• http//www.homepages.kcbbs.gen.nz/rtomes/alex-ha.h
  tm
• http//www.library.scar.utoronto.ca/ClassicsC42/Ho
  lder/MUSIC.HTM