Page 97 - Master Handbook of Acoustics

Such sum and difference sidebands are generated whenever two pure tones are mixed in a nonlinear
element. The nonlinear element in this case is the middle and inner ear. In addition to intermodulation
products, the nonlinearity of the ear generates new harmonics that are not present in the sound falling
on the eardrum.

Another demonstration of auditory nonlinearity can be performed with the same equipment used
above, with the addition of headphones. First, a 150-Hz tone is applied to the left earphone channel.
If the hearing mechanism were perfectly linear, no aural harmonics would be heard as the exploratory
tone in the right earphone channel is swept upward near the frequencies of the second, third, and other
harmonics. However, since it is nonlinear, the presence of aural harmonics is indicated by the
generation of beats. When 150 Hz is applied to the left ear and the exploratory tone of the right ear is

slowly varied about 300 Hz, the second harmonic is indicated by the presence of beats between the
two. If we change the exploratory oscillator to a frequency around 450 Hz, the presence of a third
harmonic will also be revealed by beats. Researchers have estimated the magnitude of the harmonics
by the strength of such beats. Conducting this experiment with tones of a higher level will make the
presence of aural harmonics even more obvious.

Subjective versus Objective Evaluation

There remains a great divide between subjective assessments of sound quality and objective
measurements. Consider the following descriptive words which are often applied to concert-hall
acoustics: warmth, bassiness, definition, reverberance, fullness of tone, liveness, sonority, clarity,

brilliance, resonance, blend, and intimacy. There is no instrument to directly measure qualities such
as warmth or brilliance. However, in some cases, subjective terms can be related to objective
measurements. For example, consider the term “definition.” German researchers have adopted the
term “deutlichkeit” which literally means clearness or distinctness. It is measured by taking the
energy in an echogram during the first 50 to 80 msec and comparing it to the energy of the entire
echogram. This compares the direct sound and early reflections, which are integrated by the ear, to

the entire extent of reverberant sound. This is a straightforward measurement of an impulsive sound
from a pistol or other source.
Measurements are vitally important, but the ear is the final arbiter. Observations by human
subjects provide valuable input to any acoustical evaluation. For example, in a loudness
investigation, panels of listeners are presented with various sounds, and each observer is asked to
compare the loudness of sound A with that of B. The data submitted by the jury of listeners is then

subjected to statistical analysis; the dependence of human sensory factors, such as loudness, upon
physical measurements of sound level is assessed. If the test is conducted properly and sufficient
observers are involved, the results are trustworthy. In this way, for example, we discover that there is
no linear relationship between sound level and loudness, pitch and frequency, or timbre and sound
quality.

It is desirable to correlate subjective impressions of listeners with objective design parameters.
This allows designers to know where audio fidelity limitations exist and thus know where
improvements can be made. For example, this knowledge would allow optimization of the acoustics
of a concert hall. The correlation between the listener’s impressions and the objective means to
measure the phenomenon is a difficult problem. Correlations are not always known. One way to
correlate subjective impressions with objective data is with research, in particular through critical