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

We will now look at the most primitive known system of tuning instruments: Pythagorean Tuning.

Pythagorean Tuning has two rules.

• A perfect fifth is associated with a frequency ratio of

3/2

• An octave is associated with a frequency ratio of

2/1

Pythagorean Tuning was probably the earliest technique used to tune instruments; it was done in Ancient Times. It also is, not coincidentally, the easiest to tune by ear, as there are only two intervals for which one needs to listen.

Here is the Circle of Fifths. Notice how A4 is in the exact middle.