Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
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band, the louder frequency can overpower
the quieter one. This is the phenomenon of
masking, first observed in Fletcher's
original experiments.
Critical bands within the ear are not
fixed areas but instead are created during
the experience of sound. Any audible sound can create a critical band centered on it. However,
experimental analyses of critical bands have arrived at approximations that are useful guidelines
in designing audio processing tools. Table 4.4 is one model taken after Fletcher, Zwicker, and
Barkhausen's independent experiments, as cited in (Tobias, 1970). Here, the basilar membrane is
divided into 25 overlapping bands, each with a center frequency and with variable bandwidths
across the audible spectrum. The width of each band is given in Hertz, semitones, and octaves.
(The widths in semitones and octaves were derived from the widths in Hertz, as explained in
Section 4.3.1.) The center frequencies are graphed against the critical bands in Hertz in Figure
4.10.
You can see from the table and figure that, measured in Hertz, the critical bands are wider
for higher frequencies than for lower. This implies that there is better frequency resolution at
lower frequencies because a narrower band results in less masking of frequencies in a local area.
The table shows that critical bands are generally in the range of two to four semitones
wide, mostly less than four. This observation is significant as it relates to our experience of
consonance vs. dissonance. Recall from Chapter 3 that a major third consists of four semitones.
For example, the third from C to E is separated by four semitones (stepping from C to C#, C# to
D, D to D #, and D# to E.) Thus, the notes that are played simultaneously in a third generally
occupy separate critical bands. This helps to explain why thirds are generally considered
consonant each of the notes having its own critical band. Seconds, which exist in the same
critical band, are considered dissonant. At very low and very high frequencies, thirds begin to
lose their consonance to most listeners. This is consistent with the fact that the critical bands at
the low frequencies (100200 and 200300 Hz) and high frequencies (over 12000 Hz) span
more than a third, so that at these frequencies, a third lies within a single critical band.
Aside: A bandpass filter allows only the
frequencies in a defined band to pass
through, filtering out all other frequencies.
Bandpass filters are studied in Chapter 7.
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