of Microprocessors

MUSIC SYNTHESIS PRINCIPLES 13
The waveforms in Figs. I-2D and E do not repeat either, but each is
composed of a very large (essentially infinite) number of repeating components.
Waveform E, however, is composed of an equal mix of these components,
whereas D contains a greater proportion of some components than
others. The sound of waveform E is that of rushing air, whereas D is similar
to whistling wind. Accordingly, E is purely unpitched and D is semipitched.
All of these waveforms can be described by means ofparameters. .Given
these parameters and a synthesizer or computer, one could reproduce the
essential characteristics of each of these waveforms and an infinity of others
between the extremes. This does not mean that the same exact shape would
be reproduced in all cases (although that too is possible if enough parameters
are defined), but it does mean that those characteristics that are audible
would be reproduced. Not all parameters are of equal importance in accurately
describing the sound, as will be shown later.
The sine wave can be completely described with only two parameters.
One of these is related to the time required for a single repetition of the
waveshape and the other is related to the height of the waveform.
The Frequency Parameter
In Fig. I-2A, the sine waveform repeats every 4 msec (thousandths of a
second); thus, its period is 4 msec. Usually the reciprocal of the period is
used and is called the frequency, which is measured in cycles per second
according to the number of times the waveshape repeats in 1 sec. Recently,
the composite unit cycles per second has been replaced by hertz as the unit of
frequency. Thus, hertz or its abbreviation, Hz, will be used hereafter. Large
values offrequency, usually called high frequencies, are measured in kilohertz
(kHz) and megahertz (MHz), which are thousands and millions of hertz,
respectively.
For the pure sine wave shown, the human ear is generally regarded as
being capable of hearing frequencies between 20 Hz and 20 kHz. The
20-kHz upper frequency limit is usually a bit optimistic, however, with 15
kHz to 18 kHz being more common for young people. Advancing age pushes
the upper limit lower yet. The lower limit of 20 Hz is somewhat arbitrary,
since such low frequencies, if they are loud enough, make their presence
known by rustling clothing, shaking floors, and rattling windows.
The frequency parameter of the sine wave is strongly related to the
perceived pitch of the tone when heard. Whereas frequency is a physical
parameter of the sound waveform, pitch is a subjective parameter that exists
only in the mind of the listener. Without question, when frequency is
increased, the perceived pitch also increases provided that the frequencies
involved are in the audible range. The relationship between pitch and frequency
is not linear, however. For example, an increase of 100 Hz from 100
Hz to 200 Hz results in a large pitch change upward, but a similar 100 Hz
increase from 5 kHz to 5. 1 kHz is a nearly imperceptible increase.