Connections between Math and Music Laura Harlow – HSPVA Rhodora Maligad – Austin HS. A village without music is a dead place. African proverb. Our Goal To understand some of the mathematics found in music
Laura Harlow – HSPVA
Rhodora Maligad – Austin HS
What makes music different than noise? since ancient times.
The answer is in the mathematics.
Functional Connections since ancient times.
y = f(x)
y = f(x) + 2
y = 2 f(x)
y = -f(x)
y = 2 f(x) + 4
Composers use math in subtle ways to create musical compositions that are pleasing to hear.
Geometric Connections compositions that are pleasing to hear.
Many geometric transformations have musical counterpart
repeat horizontal translation
transposition horizontal and vertical translation
Many geometric transformations have musical counterpart compositions that are pleasing to hear.
inversion vertical reflection
retrogression horizontal reflection
retrograde inversion 180° rotation
“That person is a musician, who, through careful rational contemplation, has gained the knowledge of making music, not through the slavery of labor, but through the sovereignty of reason.”
Boethius (A.D. 480)