2. Violin Fibonacci Segments: Neckboard off the instrument to neckboard on the instrument Open strings to remaining portion of unstringed instrument Unboarded neck to body of the instrument

3. Scales There are eight notes in each scale. A full scale plays a variation of A, B, C, D, E, F, G, and repeats the root tone. (8) Chromatically, there are thirteen notes in each octave. (13) The third (3) and the fifth note in each scale make up the main chord. (5)

4. Scales Fibonacci in C Major 12345678 CDEFGABC First note of Second Major Dominant Octave scale tone chord tone in finishes chord note the scale the scale 261.6 293.66 329.63 349.23 392 440 493.88 523.25 http://www.onlinetuningfork.com/ Interestingly, the hertz intervals of each note change as the notes get farther from 440A. The sharper the pitch, the larger the interval between notes. This partially disproves Fibonacci, because the notes can’t be thought of as natural numbers in a scale. The interval ratio between the notes gets larger as the notes get sharper. E.X. C=1x, D=2.1x, E=3.2x, F=4.3x, etc.

5. Wolfgang Amadeus Mozart Phi is most prominent in Mozart’s many sonatas. The Fibonacci Sequence, by Deux- Elles, contains songs specifically attributed as being based in fibonacci numbers. This CD features Mozart’s Oboe Quartet in F Major, KV 370.

6. Ludwig Van Beethoven Beethoven’s Fifth Symphony is the most famous example of phi in classical music. There is much debate about whether or not Beethoven was aware that he was using fibonacci, or even that fibonacci is actually employed in he Fifth Symphony.