
Concept explainers
(a)
Show that the ratio of the frequency of any semitone to the frequency of the note just below it is 21/12

Answer to Problem 104QAP
The ratio semitone to the frequency of the note just below is 21/12
Explanation of Solution
Given:
The 12 semitones of octave are as follow.
Introduction:An octave or perfect octave is the interval between one musical pitch and another with double its frequency.
Further octaves of a note occur at times the frequency of that note (where n is an integer), such as 2, 4, 8, 16, 32, 64 etc. and the reciprocal of that series.
The octave is divide into 12 semitone of equal ratio r.
Calculation:
Conclusion:
The ratio semitone to the frequency of the note just below is
(b)
The frequency of F# in the tempered scale, If

Answer to Problem 104QAP
The frequency of F# is 370 Hz
Explanation of Solution
Formula used:
The ratio of the frequency of any semitone to the frequency of the note just below it is
Calculation:
Conclusion:
The frequency of F# is 370 Hz.
The value by which tension should change so that the string tuned from Bb to B.

Answer to Problem 104QAP
The tension should be increased by a factor of 1.12
Explanation of Solution
Given:
Formula used:
Calculation:
Conclusion:
The tension should be increased by a factor of 1.12 so a string on a musical instrument is tuned from Bb to B
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