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Physics / Physics for Scientists and Engineers: A Strategic Approach, Standard Edition (Chs 1-36) 4 / Chapter 17 / Problem 17.84

Physics for Scientists and Engineers: A Strategic Approach, Standard Edition (Chs 1-36) | 4th Edition | ISBN: 9780134081496 | Authors: Randall D. Knight (Professor Emeritus)

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Western music uses a musical scale with equal temperament

Chapter 17, Problem 17.84

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QUESTION:

Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by fn+1 = rfn for all n. In this system, the frequency doubles every 12 notesan interval called an octave. a. What is the value of r? b. Orchestras tune to the note A, which has a frequency of 440 Hz. What is the frequency of the next note of the scale (called A-sharp)?

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QUESTION:

Western music uses a musical scale with equal temperament tuning, which means that any two adjacent notes have the same frequency ratio r. That is, notes n and n + 1 are related by fn+1 = rfn for all n. In this system, the frequency doubles every 12 notesan interval called an octave. a. What is the value of r? b. Orchestras tune to the note A, which has a frequency of 440 Hz. What is the frequency of the next note of the scale (called A-sharp)?

ANSWER:

a. The value of r is 2^(1/12) (the 12th-root of 2).

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