Logarithmic Spiral  

The derivative of the radius allows TurtleStitch to draw the logoartimic spiral.

Human detection of sound is logarithmic. This spiral represents the shape of the cochlea in the inner ear.

The length of lines between the center of the circle and where the spiral intersects the segments determine the string lengths of each note within the octave. Starting at top red dot which represents C1, moving along the radius, the next intersection of the spiral where the next red dots is shown, reflects the note C2. This note is twice the frequency of C1,

Each segment is a note within the octave. Starting at the top and going to the right, the first segment is C sharp, D, D sharp, E, F, F sharp, G, G sharp, A, A sharp and B. As the spiral continues inward, the notes repeat at higher octaves.