Question

Consider a standard pitch scale of 220 hertz. If a musical performer identifies a 5 range of scale as ideal for both audience engagement and the instruments involved, how many total hertz does the range encompass?

a) 110 hertz
b) 220 hertz
c) 440 hertz
d) 880 hertz

Answer 1

The range of frequencies that humans are capable of hearing is from 20 Hz to 20,000 Hz. In this question, the musical performer identifies a 5 range of scale as ideal, which means a range that spans 5 musical steps. The total hertz encompassed by a 5 range of scale starting from a base frequency of 220 Hz is approximately 440 Hz.

Step-by-step explanation:

The range of frequencies that humans are capable of hearing is from 20 Hz to 20,000 Hz.

In this case, the musical performer identifies a 5 range of scale as ideal, which means a range that spans 5 musical steps. Each step in the standard pitch scale corresponds to a frequency ratio of 2^(1/12).

Therefore, to calculate the total hertz encompassed by a 5 range of scale, we start with the base frequency of 220 Hz and multiply it by the frequency ratio 2^(1/12) five times:

220 Hz x (2^(1/12))^5 = approximately 440 Hz

So, the correct answer is c) 440 hertz.