Music (help please!!)

Question

 Musical tones.  The note middle C on a piano is tuned so that the string vibrates at 262 cycles per second or 262 HZ (Hertz). The C note one octave higher is tuned to 524 HZ. The tuning for the 11 notes in between using the method called equal temperament is determined by the sequence a_n=262*2^n/12. Find the tuning for the 11 notes in between. Round to the nearest Hz. Show and explain your work. 

 

PLEASE WALK ME THRU SOLVING THIS ENTIRE PROBLEM. 

Answer 1

In mathematics, the harmonic series is the divergent infinite series: 

Answer 2

a₁ represents middle C

a₂ represents c#

a₂ = 262(2)^2/12

a₂ ≈ 262(2)^0.1666.

a₂ ≈ 262(1.1224)

a₂ ≈ 294.07

 

Follow this pattern for the remaining 10 pitches.

 

This is generally done by mechanical means.