Were you the student sitting in math
class, wondering what you’ll ever
use this for? Do you like music and
wonder how it all works? Let this
book take you from the basics of
music and the math behind it all up
to complex compositions and
mathematical theory. Whether you
are a 4th grader playing a recorder
or the next Mozart, you’ll find
something to spark your interest in
Behind the Music: A Mathematical
Perspective.
Sources:
http://www.phy.mtu.edu/~suits/notef
reqs.html
http://plus.maths.org/content/os/iss
ue35/features/rosenthal/index
http://plus.maths.org/content/os/iss
ue35/features/rosenthal/index
Behind the Music:
A Mathematical
Perspective
”This book is like music to my ears!”
-Steve Paul, Kansas City
Star
By Julie McKahan
“McKahan makes the connection
between math and music crystal
clear.”
-Oprah Winfrey
“After reading this book, I want to
go back to school and learn all the
math behind my own music…”
-Steven Tyler, lead singer of
Aerosmith
Release date: November 1, 2011
1st Excerpt
2nd Excerpt
3rd Excerpt
The general formula for a sinusoidal
graph is where A represents the amplitude,
B helps determine the period using
Octaves on a piano consist of
altering the frequency (period) of
the sound, or note. For example,
middle C is exactly one octave
below high C. High C’s frequency
is exactly double the frequency of
Middle C.
What makes music sound so
pleasing to the ear is the
combination of notes whose
frequencies have reasonable ratios.
, C is the phase shift (in
the opposite direction), and D is the
vertical shift.
We can use the amplitude to
describe how loud the sound is and
the period, or frequency, to
describe the pitch of a sound.
For example, the function 32 represents a sound that is
louder and higher pitch than a
sound with the function 2sin.7.
For example, Middle C’s frequency
is 261.63 Hz while High C’s
frequency is 523.25. Going the
other way, low C’s frequency is
130.82 Hz, precisely half of Middle
C.
If we were to compare the graphs,
they would like this:
Take Middle C and Middle G. Their
frequencies have a ratio of 2 to 3,
causing the pleasant sound. The
x’s in the diagram represent the
sine function completing a period.
The most pleasing sound is a chord
that combines three notes: Middle
C, Middle E, and Middle G. This
chord has enough complexity to be
interesting to our ears but enough
consistency to sound pleasant.
Their frequency ratios are 4:5:6.
Musicians’ jobs are to find more
combinations with pleasing ratios.