Transcript Why is so hard to tune my guitar? A look at the mathematics behind

Why is so hard to tune my guitar?
A look at the mathematics behind
the music
Charlie Burrus
Rice University
School Mathematics Project
November 2007
This entire presentation (and more!) can be found at
http://www.rusmp.rice.edu/
Why is it so hard to tune my guitar?
The Goal: Getting the strings “in tune”.
The Method: Using Harmonics
The Problem: …this is why we’re here.
On this slide, put a picture of a guitar or
something, where they will see the strings
and the names of the strings.
Harmonics
Music = organized sound
Sound travels in longitudinal waves, but we
frequently illustrate it using transverse
waves.
Put a sine wave here.
Terminology
Musical terms:
Mathematical terms:
Volume
=
Amplitude
Pitch
=
Frequency
Pitch
Measured in letters - periodic
Melodies are relative
Twinkle Twinkle Little Star, How I wonder what you are
C C G G A A G
F F E E D D C
or
D D A A B B A
G G F# F# E E D
or
G G D D E E D C C B B A A G
1
1
5
5
6 6 5
4
4 3 3
2
2
1
Notes that sound ‘good’ together
Octave: Different “pitch” but same “note”
Major triad: 1-3-5
C-E-G G-B-D F-A-C D-F#-A
Frequency
Measured in Hertz, or waves/second
NOT periodic
The higher the pitch, the higher the
frequency.
Pitch and Frequency
The Four Pillars of Education
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•
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Mathematics
Geometry
Astronomy
Music! Yes, MUSIC!