On the equally tempered scale, there are 12 notes or steps, each different by a

Question

On the equally tempered scale, there are 12 notes or steps, each different by a factor of 21/12 . After these notes the next one is 2 times the frequency of the one you start with, and this "octave" repeats the pattern again and again. An interval called a "perfect" Fifth has two notes on the ratio of frequencies of 3 to 2. On the equally tempered scale, how many steps are in a Fifth if the starting note is A and the "Fifth" is E? What is the actual ratio of frequencies?

5 and the ratio is 1.5 exactly

5 and the ratio is (21/12)7 = 1.498

7 and the ratio is 1.5 exactly

7 notes and the ratio is (21/12)7 = 1.498

5 and the ratio is 1.5 exactly

5 and the ratio is (21/12)7 = 1.498

7 and the ratio is 1.5 exactly

7 notes and the ratio is (21/12)7 = 1.498

Explanation / Answer

so there are 7 notes or steps if starting note is A and Fifth is E and the actual ratio of frequency must be 1.5 exactly.

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