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A justly-intonated “perfect fifth” in musical harmony is described by a frequency ratio of 3:2. A perfect fifth is a very pleasant pair of notes to hear. An “octave” is a culturally universal musical interval to recognize and can be described by the frequency ratio 2:1. An octave is just about as pleasant as it gets. A justly-intonated “major third” (with an octave in-between) can be described by a frequency ratio of 5:2. It is also very pleasant to hear. This exercise may demystify musical harmony a little. a) Calculate the overtone (ringing frequency) from a 300 Hz pure tone (sine wave) when interfered with a 200 Hz pure tone in-phase (sounded at same time and place). Note that the frequency ratio is 3:2. b) Calculate the undertone (beat frequency) from a 300 Hz pure tone when interfered with a 200 Hz pure tone in-phase (sounded at same time and place).

A justly-intonated “perfect fifth” in musical harmony is described by a frequency ratio of 3:2. A perfect fifth is a very pleasant pair of notes to hear. An “octave” is a culturally universal musical interval to recognize and can be described by the frequency ratio 2:1. An octave is just about as pleasant as it gets. A justly-intonated “major third” (with an octave in-between) can be described by a frequency ratio of 5:2. It is also very pleasant to hear. This exercise may demystify musical harmony a little. a) Calculate the overtone (ringing frequency) from a 300 Hz pure tone (sine wave) when interfered with a 200 Hz pure tone in-phase (sounded at same time and place). Note that the frequency ratio is 3:2. b) Calculate the undertone (beat frequency) from a 300 Hz pure tone when interfered with a 200 Hz pure tone in-phase (sounded at same time and place).

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A justly-intonated “perfect fifth” in musical harmony is described by a frequency ratio of 3:2. A perfect fifth is a very pleasant pair of notes to hear. An “octave” is a culturally universal musical interval to recognize and can be described by the frequency ratio 2:1. An octave is just about as pleasant as it gets. A justly-intonated “major third” (with an octave in-between) can be described by a frequency ratio of 5:2. It is also very pleasant to hear. This exercise may demystify musical harmony a little.

a) Calculate the overtone (ringing frequency) from a 300 Hz pure tone (sine wave) when interfered with a 200 Hz pure tone in-phase (sounded at same time and place). Note that the frequency ratio is 3:2.

b) Calculate the undertone (beat frequency) from a 300 Hz pure tone when interfered with a 200 Hz pure tone in-phase (sounded at same time and place).

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