Ratios and Music
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Do-Re-Mi
 by Richard Rodgers and Oscar Hammerstein
Do, a deer, a female deer,
Re, a drop of golden sun,
Mi, a name I call myself,
Fa, a long long way to run,
So, a needle pulling thread,
La, a note to follow so,
Ti, a drink with jam and bread,
That'll bring us back to Do -
do-re-mi-fa-so-la-ti-do!


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This popular song by Rodgers and Hammerstein is built around the basic musical scale.  The mathematician Pythagoras discovered that there is a simple mathematical relationship between the frequencies of sounds that produce the musical scale.

do 2/1 of x
ti 15/8 of x
la 5/3 of x
so 3/2 of x
fa 4/3 of x
mi 5/4 of x
re 9/8 of x
do
(middle C)		 x
Note Frequency

Pythagoras discovered the relationships displayed in the chart on the left.

Students that play musical instruments may be asked to give a short presentation on their instruments for the class.  

Possible mathematical questions:

1.  A guitar string vibrates 264 times per second to produce a middle C.   Based upon this
    information, ask students to find the frequencies of the other notes of the musical scale.

2.  Ask students to extend the chart two octaves above middle C based upon x representing
     middle C.

3.  Ask students to extend the chart one octave below middle C based upon x representing
     middle C.

(Information Adapted from Foundations of Algebra and Geometry by Addison-Wesley)