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Comparisons of two numbers, measurements, or quantities.

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Keepin' in Tune

Credit: Gabriel Pollard
Source: http://www.flickr.com/photos/61181002@N00/2467308300
License: CC BY-NC 3.0

Do you know how musicians use ratios? With a little knowledge of music theory and Pythagoras, you will be able to understand how ratios are a part of all music.

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Pythagoras, an ancient Greek philosopher and mathematician, accidentally discovered the mathematical connection between intervals in music. It is said that he was traveling past a blacksmith's shop one day when he heard music in the sounds that the hammers were making as they struck anvils. He noted that when struck in unison, some hammers produced sounds that were more pleasing than those produced by other combinations. Pythagoras was fascinated and went on to work out the mathematical relationships between different pitches and intervals.

Credit: Horia Varlan
Source: http://www.flickr.com/photos/10361931@N06/4268315679
License: CC BY-NC 3.0

An interval refers to the spread between notes on a scale. Pythagoras began to determine the ratios between different pitches. He found that a perfect fifth interval has a pitch ratio of 3:2 and an octave has a pitch ratio of 2:1. Today, the musical tuning of all intervals is based on the discoveries of Pythagoras. You can use these ratios to determine intervals and notice the pleasing relationships between different sounds. Pythagoras' work makes all the difference as to whether things are "in tune" or not!

See for yourself: http://www.youtube.com/watch?v=0NSZ7KkCP5Q

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Learn more about the relationships between math and music at the following website.


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  1. [1]^ Credit: Gabriel Pollard; Source: http://www.flickr.com/photos/61181002@N00/2467308300; License: CC BY-NC 3.0
  2. [2]^ Credit: Horia Varlan; Source: http://www.flickr.com/photos/10361931@N06/4268315679; License: CC BY-NC 3.0

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