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 4(cont.)

Example

Here are more examples of finding the fundamental frequency to the nearest 0.001 Hz.

Eb3

Start at A4, go down 6 fifths to Eb1, then go up 2 octaves to Eb3:

G#6

Start at A4, go up 5 fifths to G#7, then go down 1 octave to G#6:

B#4

First, we extend the Circle of Fifths until we get a B#:

Now we start at A4, go up 9 fifths to B#9, then go down 5 octaves to B#4:

Sharps and flats of the "same" note have different frequencies in Pythagorean Tuning. Thus, if the question tells you to find the frequency of an E, finding that of a D would produce an incorrect answer. Similarly, to find a B we must go for that B and would get an incorrect answer if we found a C instead.