of Microprocessors

434 MUSICAL ApPLICATIONS OF MICROPROCESSORS
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0.4 r-----~~=--.......;.
180 0
i-TRANSITION INTERVAL-------J
TIME
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180 0 180 0
150 0 150 0
120 0
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120 0 0 0
60 0
60 0
30 0
Fig. 1~8.
00 L------,.e=.=---------"---------'I--=--------
f.---- TRANSITION INTERVAL -------.,
TIME
(S)
Time-variable interpolation between two sine waves. (A) Amplitude
contours; phase difference is parameter. (B) Phase contours;
phase difference is parameter.
30 0
Note on the phase curve that the phase of the resultant shifts during the
transition as well. This dynamically shifting phase means that the harmonic
frequency is actually shifting during the transition region! The magnitude of
apparent frequency shift is proportional to the instantaneous slope of the
phase curve. Thus, at the beginning and end of the transition region, the
frequency is unchanged, but it may momentarily increase or decrease in the
middle.
The preceding applies to each harmonic in the two waves independently.
Thus, a complex harmonic evolution in which some change linearly,
some nonlinearly, and some undershoot is easily set up merely by altering the
harmonic phases in one of the waveforms. It is important to realize that,