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 frequency ration 5:2. It is also very pleasant to hear. a) Calculate the overtone (ringing frequency) from 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 ration is 3:2. b) Calculate the undertone (beat frequency) from 300 Hz pure tone when interfered with a 200 Hz pure tone in-phase (sounded at same time and place). c) This started out with just two notes playing. After the dissimilar frequencies interfere by producing an overtone and an undertone, how many notes might you actually think you are hearing?
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 frequency ration 5:2. It is also very pleasant to hear.
a) Calculate the overtone (ringing frequency) from 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 ration is 3:2.
b) Calculate the undertone (beat frequency) from 300 Hz pure tone when interfered with a 200 Hz pure tone in-phase (sounded at same time and place).
c) This started out with just two notes playing. After the dissimilar frequencies interfere by producing an overtone and an undertone, how many notes might you actually think you are hearing?
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