The pitch of a musical note is determined by its frequency in Hertz. The trigono

Question

The pitch of a musical note is determined by its frequency in Hertz. The trigonometric function p(t) = a sin(2.pift) approximates the sound of a note with volume a, frequency f, and a duration of i seconds. For the purposes of the following problems, we will assume all pitches are played at a volume where a = 1. Within a major scale, the frequencies of the notes maintain certain ratios to the first note of the scale. The first note to the third note have a frequency ratio of 4:5, the first to fifth a ratio of 2:3, the first to seventh a ratio of 8:15. and the first to the octave (eighth) a ratio of 1:2. Below, you will see the graph of the standard pitch, A at 440Hz in black, alongside another pitch in grey as well as the eight notes of an octave of the A major scale with their pitch names. Give the equation, p(t), for the function in grey and identify which pitch it is. The note is , and can be modeled by p(t) = Find the equation,p(t), for C# and add its graph to the graph of A440 below. C# can be modeled by p(t) =

Explanation / Answer

32) two spectral pitches at 1000 and 1200 Hz, derived from the physical frequencies of the pure tones,

p(t) = A sin(2pi ft)

33) p(t) = sin2pi*x) +4

:

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