6) Divide the fundamental Frequency of F#5 by the frequency of A4 in the following tuning 5 systems. Round your answers (if necessary) to the nearest 0.000001:a) Equal Temperament Tuningb) Just Intona

Pythagorean Tuning 3(cont)

If you need to get to a sharp or double-sharp note, which you don't see in the Circle of Fifths, extend the Circle of Fifths up (to the right). Similarly, if you need to get to a flat or double-flat note you don't see, extend the Circle of Fifths down (to the left).

For example, to find the fundamental frequency of F7, we start at A4, go down 4 fifths to F2, then up 5 octaves to F7. So the fundamental frequency, rounded to the nearest 0.001 Hz, is

The

and 2 will be present in every Pythagorean Tuning Calculation, as they represent the ratios associated with perfect fifths and octaves respectively.