STATEMENT OF PROBLEM

1) The pitch of a musical note is determined by the frequency of the vibration which causes it. Middle C on the piano, for example, corresponds to a vibration of 263 Hz (cycles per second). A note one octave above middle C vibrates at 526 Hz, and a note 2 octaves above middle C vibrates 1052 Hz. You might have noticed that the frequency of vibration increases in powers of 2. Since there are 12 keys on the piano between two octaves, the frequency of each tone between middle C and high C are given by 263 2^(i/12) where i=0, 1, 2, ..., 12. Verify this by animating the scale,
C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C
with Mathematica's Play[] command.

2) Now that you have generated each tone on a standard piano between middle and high C, play the C scale: C, D, E, F, G, A, B, C.

3) Verify by listening to examples that for any tone vibrating at f0 Hz, the tone vibrating at 2 f0 Hz is one octave higher and that in general 2n f0 makes a tone n octaves higher (or lower if n is negative.)

4) Compose "Mary Had a Little Lamb" using Mathematica's Play[] command. Hint: Start with E, D, C, D, E, E, ... and to save time, copy and past the notes that you have already generated except when you need a tone to play longer.