1. 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/

2. 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.

3. On this slide, put a picture of a guitar or something, where they will see the strings and the names of the strings.

4. Harmonics

5. Music = organized sound Sound travels in longitudinal waves, but we frequently illustrate it using transverse waves. Put a sine wave here.

6. Terminology Musical terms: Volume Pitch Mathematical terms: Amplitude Frequency ====

7. Pitch Measured in letters - periodic

8. 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

9. 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

10. Frequency Measured in Hertz, or waves/second NOT periodic The higher the pitch, the higher the frequency.

11. Pitch and Frequency

12. The Four Pillars of Education Mathematics Geometry Astronomy Music! Yes, MUSIC!