a. The frequency of a tone is increased by a factor of 2 7 12 = 1.498 if it is raised by a fifth. b. By what factor does the frequency of a tone increase if it is raised by two fifths? c. The frequencies of the other notes in the circle of fifths starting with middle C, at a frequency of 260 cycles per second. d. How many fifths are required for the circle of fifths to return to a C? How many octaves are covered by a complete circle of fifths? e. The ratio of the frequencies of the C at the beginning of the circle and the C at the end of the circle?

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Chapter 11.A, Problem 20E

To determine

a. The frequency of a tone is increased by a factor of $2^{\frac{7}{12}} = 1.498$ if it is raised by a fifth.

b. By what factor does the frequency of a tone increase if it is raised by two fifths?

c. The frequencies of the other notes in the circle of fifths starting with middle C, at a frequency of 260 cycles per second.

d. How many fifths are required for the circle of fifths to return to a C? How many octaves are covered by a complete circle of fifths?

e. The ratio of the frequencies of the C at the beginning of the circle and the C at the end of the circle?

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