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Definition of Octave
Assume one note has a frequency of 200Hz, the note an octave above it is at 400Hz, and the note an octave below is at 100Hz. The ratio of frequencies of two octaves is 2:1. Another example: 50Hz is one octave below 100Hz, and 400Hz is two octaves above 100Hz.
An Octave band is characterized by the following formulas:
If the F1 is the lower cutoff frequency and F2 is the upper cutoff frequency, the ratio of the band limits is given by:
F2/F1 ≈ 2^N
where N = 1 for full Octave and N= 1/3 for 1/3 Octave bands.
An Octave has a center frequency that is 2^(1/2) (square root of 2) times the lower frequency cutoff frequency and has an upper cutoff frequency that is twice the lower cutoff frequency. Therefore,
F1 = F0 / 2^(1/2)
F2 = 2^(1/2) . F0, where F0 is the center frequency
F2 = 2 . F1
BW = F2 - F1, where BW = Band Width
A 1/3 Octave has a center frequency that is 2^(1/3) (cubic root of 2) times the lower frequency cutoff frequency and has an upper cutoff frequency that is twice the lower cutoff frequency.
Therefore,
F1 = F0 / 2^(1/3)
F2 = 2^(1/3) . F0
Example 1. Calculate the 1/3 Octave band limits for center frequency of 16Hz.
2^(1/3) = 1.26
Lower band limit: F1 = 16Hz / 1.26 ≈ 12.5Hz
Upper band limit: F2 = 16Hz * 1.26 ≈ 20Hz
Example 2. Calculate the 1/3 Octave band limits for center frequency of 125Hz.
2^(1/3) = 1.26
Lower band limit: F1 = 125Hz / 1.26 ≈ 100Hz
Upper band limit: F2 = 125Hz * 1.26 ≈ 160Hz
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