The frequencies of notes in standard musical notation are de

The frequencies of notes in standard musical notation are defined in terms of ratios. For example, an octave is defined as a factor of two in frequency. The standard concert A is 440 Hz, so that one octave below concert A is 220 Hz. Each octave is divided into twelve half steps, with the same frequency ratio between any two notes separated by a half step, as shown in figure below on a piano keyboard. Each of the black keys on the piano has two names. For example, the black key just above concert A can be called A] (pronounced A-sharp), meaning that it is a half-step above A, or it can be called B[ (pronounced B flat), meaning that it is a half step below B. [See the figure below.]

(a) Show that the frequency ratio between half-steps is 1.05946.

(b) The lowest note on a standard piano is the A that is four octaves below concert A. If this note is played simultaneously with the A] just above it, and both notes are played at the same volume, what beat frequency is heard?

Solution

a>

and 2^(1/12) = 1.05946

hecne the fequency ratio between half steps is = 1.05946