5.19 Human Hearing
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this doubling sensation, with one sone defined to be 40 phons, and 2 n sones to be
(40 + 10n) phons, with n integer.
5.19.3 Pitch
The musical term for frequency is ‘tone’. The psychological sensation to a dominant
frequency is ‘pitch’. Two sounds may be judged to have the same pitch even though
different mixtures of frequencies may be present. A person’s sensation of frequency
depends on the sound level, and there is a loss of sensitivity to frequency change at
both the high and low frequencies. All tones which are perceived to have a single
pitch are given one value for the pitch in a unit called a ‘mel’, defined to match
the units of frequency when the sound level is perceived to be 40 phons. At middle
sound levels, humans can detect if the frequency has changed by 5% of the interval
between equal-temperament notes, 24 i.e., if > 0.05×(
12
√
2−1) = 3×10 −3 =
0.3%. 25 Because the sensation of frequency change is logarithmic, a “MIDI pitch”
has been defined as the number
m ≡ 69 + 12 log 2 (f/440 Hz) .
(The value 69 is arbitrarily assigned to the frequency 440 Hz, the note A above
middle C, while other notes on the equal-tempered scale are labeled sequentially by
the integers.)
Our sensation of pitch vs. frequency and pitch vs. sound level are shown in the
graphs (Figs. 5.14 and 5.15). Our ability to sense changes of frequency diminishes
as the frequency increases.
As the sound level lowers, we sense a lower pitch than the actual frequency,
and as sound level increases, not only is our sensitivity to the loud sound dulled,
but we hear an increased pitch, when no change in frequency has occurred. These
false sensations are ‘aural illusions’. The pitch illusion is explainable, at least
in part, by the changes in the tension of the muscles of the middle ear. Other
more involved illusions occur, such as the hearing of the fundamental note when
a set of its harmonics is present, known as the ‘residue effect’. and the reduced
sensitivity to harmonics when a strong fundamental is present, known as the
‘masking effect’. Small radios take advantage of the residue effect, in that small
24 The equal tempered scale takes notes with frequencies in each octave as f n = (n + 1) 1/N f 0 ,
where N is the number of notes. An octave is the interval of frequency between one note and
double the frequency of that note.
25 Another way of describing this sensitivity is to give the number of different pitches that a
good ear can distinguish. This number is about 2300, with a logarithmic separation between
adjacent pitches. Taking the range of audible frequency to be from 2 4 = 16 to 2 14 = 16, 384,
each distinguishable frequency in this range can be specified by f n = 2 4+n/230 Hz, where
n = 0, 1, · · · , 2300. In this case, f/f = 2 1/230 − 1 = 0.3%.
157
this doubling sensation, with one sone defined to be 40 phons, and 2 n sones to be
(40 + 10n) phons, with n integer.
5.19.3 Pitch
The musical term for frequency is ‘tone’. The psychological sensation to a dominant
frequency is ‘pitch’. Two sounds may be judged to have the same pitch even though
different mixtures of frequencies may be present. A person’s sensation of frequency
depends on the sound level, and there is a loss of sensitivity to frequency change at
both the high and low frequencies. All tones which are perceived to have a single
pitch are given one value for the pitch in a unit called a ‘mel’, defined to match
the units of frequency when the sound level is perceived to be 40 phons. At middle
sound levels, humans can detect if the frequency has changed by 5% of the interval
between equal-temperament notes, 24 i.e., if > 0.05×(
12
√
2−1) = 3×10 −3 =
0.3%. 25 Because the sensation of frequency change is logarithmic, a “MIDI pitch”
has been defined as the number
m ≡ 69 + 12 log 2 (f/440 Hz) .
(The value 69 is arbitrarily assigned to the frequency 440 Hz, the note A above
middle C, while other notes on the equal-tempered scale are labeled sequentially by
the integers.)
Our sensation of pitch vs. frequency and pitch vs. sound level are shown in the
graphs (Figs. 5.14 and 5.15). Our ability to sense changes of frequency diminishes
as the frequency increases.
As the sound level lowers, we sense a lower pitch than the actual frequency,
and as sound level increases, not only is our sensitivity to the loud sound dulled,
but we hear an increased pitch, when no change in frequency has occurred. These
false sensations are ‘aural illusions’. The pitch illusion is explainable, at least
in part, by the changes in the tension of the muscles of the middle ear. Other
more involved illusions occur, such as the hearing of the fundamental note when
a set of its harmonics is present, known as the ‘residue effect’. and the reduced
sensitivity to harmonics when a strong fundamental is present, known as the
‘masking effect’. Small radios take advantage of the residue effect, in that small
24 The equal tempered scale takes notes with frequencies in each octave as f n = (n + 1) 1/N f 0 ,
where N is the number of notes. An octave is the interval of frequency between one note and
double the frequency of that note.
25 Another way of describing this sensitivity is to give the number of different pitches that a
good ear can distinguish. This number is about 2300, with a logarithmic separation between
adjacent pitches. Taking the range of audible frequency to be from 2 4 = 16 to 2 14 = 16, 384,
each distinguishable frequency in this range can be specified by f n = 2 4+n/230 Hz, where
n = 0, 1, · · · , 2300. In this case, f/f = 2 1/230 − 1 = 0.3%.