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Asked Dec 26, 2019
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How many octaves does normal human hearing span? How many octaves are on a common piano keyboard?

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Given information: Lowest musical note taken from standard tables is 16.35 Hz. The range of human hearing is from 20 Hz to 20 kHz. Musical notes are generally classified into octaves. An octave consists of notes that are included between a frequency and the frequency double its value. The lowest musical note is called CO and it lies slightly below the audible range for humans. The first octave occurs at a frequency which is 2 times the frequency of Co. The number of octaves contained within the audible range is got by finding how many times the frequency doubles within the 20 Hz to 20 kHz range.

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Calculation: If the frequency doubles n times within the range, then 2" (16.35 Hz) = 20000 Hz Divide 20000 Hz by 16.35 Hz to get the value of 2". 20000 Hz 27 16.35 Hz = 1223.2 The power of 2 which is closest to 1223.2 is 10, since, 210 = 1024.

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(b) Lowest musical key in a standard piano is27.5 Hz and the highest key has a frequency 4186.01 Hz. A standard piano has around 88 keys with the lowest note being Cl with frequency 27.5 Hz and the highest is A8 with a frequency 4186.01 Hz. To determine the number of octaves contained within this frequency range, it is necessary to determine how many times the minimum frequency is doubled. If the frequency doubles n times within the range, then 2" (27.5 Hz) = 4186.01 Hz Divide 4186.01 Hz by 27.5 Hz to get the value of 2". 4186.01 Hx 27 27.5 Hx = 152.2 The power of 2 which is closest to 152.2 is 7, since, 27 = 128.

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