Answer:
a) Q₀ × 1.335 cps
b) 12 fourths
c) 5 octaves
Step-by-step explanation:
The circle of fourth is generated by starting at any note and stepping upward by intervals of a fourth(five half-steps)
(a) By what factor is the frequency of a tone increased if it is raised by a fourth?
consider the following exponential growth formula
:
Q = Q₀ × f
°
Q = Q₀ × 1.05946
ⁿ
Substituting n = 5
Q = Q₀ × 1.05946
ⁿ
Q = Q₀ × 1.05946⁵
Q = Q₀ × 1.335 cps
Therefore, note that five half-step higher will be increased by factor 1.335
(b) How many fourths are required to complete the entire circle of fourths?
<u>SOLUTION</u>
In each step, number of half steps = 5
Total number of half steps in one octave = 12 half- steps
Therefore, total number of fourths required to complete the entire circle of fourths = 12 fourths
(c) Total number of half steps in one octave = 12 half-steps
Total half steps in complete circle of fourths
= 12×5
= 60 half-steps
Calculating number of octaves (dividing it by 12)
= 60/12
= 5 octaves
