of Microprocessors

582 MUSICAL ApPLICATIONS OF MICROPROCESSORS
waveforms, but blind application of it can lead to errors with rapidly changing
waveforms and unpitched sounds.
In truth, human hearing probably utilizes both kinds of information. It
is unlikely that the pitch of high-pass (I-kHz) filtered 60-Hz buzz is determined
from a frequency analysis because of the resolution necessary to account
for the very precise judgments people are capable of. On the other
hand, waveforms are easily contrived in which the periodicity is not easily
spotted visually yet they are also accurately judged. Then we have the case of
bells and chimes, which are decidedly nonperiodic and therefore nonharmonic
yet produce a strong sensation of pitch. Last, but not least, the
existence of a tone that sounds as if its pitch is continuously risingforever
I-underlines the fact that human pitch perception is a very complex
topic indeed.
Time-Domain Methods
The simpLest pitch detection methods work in the time domain, where
the waveform itself is examined for periodicity. In fact, it is the period that is
measured that requires a division to determine the corresponding frequency.
Most time-domain methods were developed for analog implementation;
however, they can be readily implemented as a program for processing sampled
data. One problem with sampled data is that the period determination
is normally made in terms of an integer number of samples. This can lead to
significant errors unless the sample rate is high or interpoLation is used, both
of which increase processing time.
In order to improve pitch detector performance, it is common practice
topreprocess the signaL. Typically, this consists of low-pass filtering to remove
high-frequency harmonics and noise that may contribute to jitter or confuse
the detection algorithm. An obvious question, then, is what the cutoff
frequency should be. If the sounds being analyzed have a strong (but not
necessarily dominant) fundamental, then it is appropriate to set the cutoff
just above the highest fundamental expected. Often, dynamic filters are
utilized, in which case the cutoff can track just above the current fundamental
frequency. If the fundamental is dominant, as it often is in direct string
pickups and mouthpiece microphones, such preprocessing may be sufficient
to allow a simple zero-crossing detector to do the actual period detection.
Even if the fundamental is not dominant, repeated integration can make it
dominant. U nforrunately, the integrators emphasize low-frequency transients
and may actually blank out the zero-crossing detector for hundreds of
'This is usually demonstrated as a continuous upward sweep or an ascending musical
scale that never stops. [n reality, the effect is much like the stripes on a barber pole,
and, in fact, a spectrogram of the former example is an endless series of upwatd
sloping diagonal bars. For a scale, the continuous rise is simply quantized at musical
scale pitches.