of Microprocessors

MUSIC SYNTHESIS PRlNOPlES 17
In actual audio work, the unit decibel, which is a tenth of a bel, is more
commonly used. It is abbreviated dB and represents a power ratio of about
1.259 to 1. Three decibels (which is 1.259 3 ) represents almost exactly a ratio
of 2.0 and 6 dB is a ratio of 4: 1. Note that these are power ratios. Since power
increases as the square of voltage (assuming constant load resistance), a 10: 1
ratio ofvoltage is equivalent to 100: 1 ratio of power or 20 dB. Consequently,
6 dB represents only a doubling ofvoltage amplitude. Expressed as a voltage
ratio, the 120-dB range of human hearing represents a million-tO-one voltage
range.
Since the decibel scale is relative, a basis point is needed if an absolute
decibel scale is to be defined. For sound in air, the O-dB reference is taken as
10- 16 Wlcm 2 , a very small amount of power indeed. For electrical signals,
the reference point is 0.001 W into a 600-ohm impedance or about 0.775 V.
For the maximum amplitude of 120 dB, the figures would be 0.1 mW/cm 2
in air and a million kilowatts ofelectrical power, more than most generating
plants put out. Clearly, the standardized electrical basis point has nothing to
do with sound amplitude.
It should be apparent by now that there is a strong relationship between
the amplitude of a sine wave and the loudness of the sound it represents.
Also, as expected from the trillion-to-one audible amplitude range, the
relationship is highly nonlinear. However, when amplitude is expressed in
decibels, the relation is reasonably linear. The amplitude of a sound must be
increased an average of 8. 3 dB to be perceived as a doubling of loudness. For
moderately loud sounds, 1 dB is about the smallest change in amplitude that
is noticeable. The basis point of 10- 16 W/cm 2 for sound in air is about the
softest sine wave at 2 kHz that can be heard by a person with good hearing.
The basis for the electrical O-dB point is purely arbitrary.
Frequency and Amplitude Interaction
The frequency and amplitude parameters of a sine wave are completely
independent. Thus, one may be varied over a wide range without affecting
the value of the other whatsoever. This may not always be strictly true in a
practical circu.it for generating sine waves, but the amount of interaction in
good-quality equipment is very small.
When this sound is heard by the human ear, however, there is significant
interaction between loudness and pitch. The most dramatic interaction
is the effect on the apparent loudness of a constant amplitude sine wave tone
caused by changing its frequency.
Figure 1-3 shows the extent of this interaction. The curves show the
amplitude change necessary to preserve constant loudness as frequency is
varied. Note that there is relatively little interaction at large amplitudes,
but, as the amplitude decreases, the lower-frequency sounds decrease in
loudness much faster than higher-frequency sounds. For example, at an