Music and Mathematics

Question

Start at the G# below middle A, with a frequency of 43 cps. Using the whole-number ratios in the accompanying table, find the frequency if G# is raised by a fifth to D#. What is the frequency if this D# is then raised by a fifth to A#? What is the frequency if this is A# is then lowered by a sixth to C#? What is the frequency if this C# is then lowered by a fourth to G#? Has returning to the same note also returned to the same frequency?

The frequency when G# is raised by a fifth to D# is 619.5 cps.

The frequency when this D# is then raised by a fifth to A# is 929.25 cps.

The frequency when this A# is then lowered by a sixth to C# is 557.55 cps.

 

Does anyone know how to solve this?

Answer 1

The ratio of the frequencies of the perfect fifth is 3/2.
1) The G# to which the problem refers vibrates at 415.305 Hz (where did you get 43cps??
2) D#, the fifth above, is at (1.5)(415.305)
3) A#, the fifth above, is at (1.5)(1.5)(415.305)
4) C#, the sixth below, is at (0.6) A# (this is "just temperament")