5.19 Human Hearing
161
the twelve notes within one octave and the beginning note of the next octave have
frequencies in equal interval ratios, so that the notes within an octave, named C,
C = D , D, D = E , E, F , F = G , G, G = A , A, A = B , and B, are
in ratio
12
√
2. In this way, the corresponding notes in each successive octave are a
factor of two above the previous one, making up harmonics of each other. The fifth
audible octave is taken with the note A having frequency 440 Hz. The next C note
up in frequency is called ‘middle C’. The name octave, with a Latin root meaning
eight, comes from the fact that tonal music is composed with the notes C, D, E, F ,
G, A, B, with the next C included in the count.
The lowest frequency of audible sound produced by a musical instrument is
called its ‘fundamental frequency’. Higher frequency sounds from this instrument
are called ‘overtones’. If the overtones are integer multiples of the fundamental,
they are the harmonics, or ‘partials’ of the sound. Those harmonics which are 2 n
times the fundamental are said to be from the n-th ‘octave’ above the fundamental.
Simultaneous tones which are in ratio of 2 n are in the same ‘musical key’, but n
octaves away.
Humans can become enthralled with rhythmic sounds if they have sufficient
symmetry, but also if they have sufficient complexity to be evocative or challenging
to the mind. Curiously, simultaneous notes which do not have simple ratios
of frequencies are disturbing, perhaps because their ‘beat frequency’ (frequency
difference) does not match another musical tone. Instruments which play sounds
which are dominated by a mixture of integer-multiples of one frequency, together
with a mixture of lower-level anharmonic frequencies, have attractive sounds. The
‘richness’ of a sound refers to the number of distinct component frequencies. The
term ‘quality of sound’ is sometimes used to portray the presence of a set of tones
having frequencies which are in approximate whole number ratio. Such sounds seem
to be pleasing to us, much more than listening to a series of pure tones. In contrast, if
the frequency ratios are irrational, the sounds are dissonant. The vibrational modes
of drum heads and bells produce component sounds whose frequencies tend not to
be in simple ratio.
A ‘musical note’ is a sound of short duration (seconds or less) with a definite
‘sound envelope, determining how the amplitude of the note rises, is sustained, and
then falls.
The spectral distribution of frequencies in a musical note determines its musical
‘timbre’. which is also called its ‘tonal quality’ and tonal color. Physically, if two
sounds have the same loudness, but they have a different frequency spectrum, they
will differ in timbre. Musical notes with different sound envelopes but the same
loudness and spectrum also are said to differ in timbre.
The inner ear and brain performs a kind of Fourier analysis on the incoming
sound. The pitch of two sounds can be distinguished if the stimulation of the
basilar membrane is separated by more than 50 μm (which is about six hair
cells apart). Fourier decomposition can be performed by instruments, generating a
‘spectrogram’, i.e. a visual representation of the frequencies present in the sound as
they vary in time. Spectrograms of speech and song are referred to as ‘voice prints’.
161
the twelve notes within one octave and the beginning note of the next octave have
frequencies in equal interval ratios, so that the notes within an octave, named C,
C = D , D, D = E , E, F , F = G , G, G = A , A, A = B , and B, are
in ratio
12
√
2. In this way, the corresponding notes in each successive octave are a
factor of two above the previous one, making up harmonics of each other. The fifth
audible octave is taken with the note A having frequency 440 Hz. The next C note
up in frequency is called ‘middle C’. The name octave, with a Latin root meaning
eight, comes from the fact that tonal music is composed with the notes C, D, E, F ,
G, A, B, with the next C included in the count.
The lowest frequency of audible sound produced by a musical instrument is
called its ‘fundamental frequency’. Higher frequency sounds from this instrument
are called ‘overtones’. If the overtones are integer multiples of the fundamental,
they are the harmonics, or ‘partials’ of the sound. Those harmonics which are 2 n
times the fundamental are said to be from the n-th ‘octave’ above the fundamental.
Simultaneous tones which are in ratio of 2 n are in the same ‘musical key’, but n
octaves away.
Humans can become enthralled with rhythmic sounds if they have sufficient
symmetry, but also if they have sufficient complexity to be evocative or challenging
to the mind. Curiously, simultaneous notes which do not have simple ratios
of frequencies are disturbing, perhaps because their ‘beat frequency’ (frequency
difference) does not match another musical tone. Instruments which play sounds
which are dominated by a mixture of integer-multiples of one frequency, together
with a mixture of lower-level anharmonic frequencies, have attractive sounds. The
‘richness’ of a sound refers to the number of distinct component frequencies. The
term ‘quality of sound’ is sometimes used to portray the presence of a set of tones
having frequencies which are in approximate whole number ratio. Such sounds seem
to be pleasing to us, much more than listening to a series of pure tones. In contrast, if
the frequency ratios are irrational, the sounds are dissonant. The vibrational modes
of drum heads and bells produce component sounds whose frequencies tend not to
be in simple ratio.
A ‘musical note’ is a sound of short duration (seconds or less) with a definite
‘sound envelope, determining how the amplitude of the note rises, is sustained, and
then falls.
The spectral distribution of frequencies in a musical note determines its musical
‘timbre’. which is also called its ‘tonal quality’ and tonal color. Physically, if two
sounds have the same loudness, but they have a different frequency spectrum, they
will differ in timbre. Musical notes with different sound envelopes but the same
loudness and spectrum also are said to differ in timbre.
The inner ear and brain performs a kind of Fourier analysis on the incoming
sound. The pitch of two sounds can be distinguished if the stimulation of the
basilar membrane is separated by more than 50 μm (which is about six hair
cells apart). Fourier decomposition can be performed by instruments, generating a
‘spectrogram’, i.e. a visual representation of the frequencies present in the sound as
they vary in time. Spectrograms of speech and song are referred to as ‘voice prints’.