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Using the procedure outlined in section 15.5 where the ideal ratios for a justly tuned scale are described, find the frequencies for all of the white keys between middle C (264 Hz) and the C above middle C (a C-major scale). If you have worked synthesis problem 4, compare the frequencies for just tuning to those for equal temperament.
a. G (sol) is a fifth above C
b. F (fa) is a fourth above C
c. E (mi) is a major third above C
d. B (ti) is a major third above G (sol).
e. D (re) is a fourth below G (sol).
f. A (la) is a major third above F (fa).
(a)
The ideal-ratio frequency of G.
Answer to Problem 5SP
The ideal-ratio frequency of the G is
Explanation of Solution
Given Info: The frequency of the tune C is
Write the formula to calculate the ideal-ratio frequency of G.
Here,
Substitute
Conclusion:
Therefore, the ideal-ratio frequency of the G is
(b)
The ideal-ratio frequency of F.
Answer to Problem 5SP
The ideal-ratio frequency of the F is
Explanation of Solution
Given Info: The frequency of the tune C is
Write the formula to calculate the ideal-ratio frequency of F.
Here,
Substitute
Conclusion:
Therefore, the ideal-ratio frequency of the F is
(c)
The ideal-ratio frequency of E.
Answer to Problem 5SP
The ideal-ratio frequency of the E is
Explanation of Solution
Given Info: The frequency of the tune C is
Write the formula to calculate the ideal-ratio frequency of E.
Here,
Substitute
Conclusion:
Therefore, the ideal-ratio frequency of the E is
(d)
The ideal-ratio frequency of B.
Answer to Problem 5SP
The ideal-ratio frequency of the B is
Explanation of Solution
Given Info: The frequency of the tune G is
Write the formula to calculate the ideal-ratio frequency of B.
Here,
Substitute
Conclusion:
Therefore, the ideal-ratio frequency of the B is
(e)
The ideal-ratio frequency of D.
Answer to Problem 5SP
The ideal-ratio frequency of the D is
Explanation of Solution
Given Info: The frequency of the tune G is
Write the formula to calculate the ideal-ratio frequency of D.
Here,
Substitute
Conclusion:
Therefore, the ideal-ratio frequency of the D is
(f)
The ideal-ratio frequency of A.
Answer to Problem 5SP
The ideal-ratio frequency of the A is
Explanation of Solution
Given Info: The frequency of the tune F is
Write the formula to calculate the ideal-ratio frequency of A.
Here,
Substitute
Conclusion:
Therefore, the ideal-ratio frequency of the A is
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Chapter 15 Solutions
Physics of Everyday Phenomena
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