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Problem: You know that certain musical notes sound good together -harmonious - whereas others do not. This harmony is related to the various harmonics of the notes played. The musical notes C (262 Hz) and G (392 Hz) make a pleasant sound when played together; we call this consonance. As the Figure shows, the harmonics of the two notes are either far from each other or very close to each other (within a few Hz). This is the key to consonance: harmonics that are spaced either far apart or very close. The close harmonics have a beat frequency of a few Hz that is perceived as pleasant. If the harmonics of two notes are close, but not too close, the rather high beat frequency between the two is quite unpleasant. This is what we hear as dissonance. Exactly how much a difference is maximally dissonant is a matter of opinion, but harmonic separations of 30 - 40 Hz seem to be quite unpleasant for most people. A. What is the beat frequency between the second harmonic of G and the third harmonic of C? B. Would a G-flat (frequency of 370 Hz) and a C played together be consonant or dissonant? Explain how you know. 

FREE Expert Solution

A.

The second harmonic of G is n1 = 784 Hz

The third harmonic of C is n2 = 786 Hz

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Problem Details

You know that certain musical notes sound good together -harmonious - whereas others do not. This harmony is related to the various harmonics of the notes played. 

The musical notes C (262 Hz) and G (392 Hz) make a pleasant sound when played together; we call this consonance. As the Figure shows, the harmonics of the two notes are either far from each other or very close to each other (within a few Hz). This is the key to consonance: harmonics that are spaced either far apart or very close. The close harmonics have a beat frequency of a few Hz that is perceived as pleasant. 

If the harmonics of two notes are close, but not too close, the rather high beat frequency between the two is quite unpleasant. This is what we hear as dissonance. Exactly how much a difference is maximally dissonant is a matter of opinion, but harmonic separations of 30 - 40 Hz seem to be quite unpleasant for most people. 

A. What is the beat frequency between the second harmonic of G and the third harmonic of C? 

B. Would a G-flat (frequency of 370 Hz) and a C played together be consonant or dissonant? Explain how you know. 

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