of Microprocessors

614 MUSICAL ApPLICATIONS OF MICROPROCESSORS
phases can be stored in two 64-bit by lO-bit memories. The throughput rate
is 64 X 62.5 kHz=4 MHz or 250 nsec minor clock cycle, which means that
bipolar or fast MOS memories will be needed. U nfoftunately, 64 words is a
somewhat nonstandard size for memory ICs and using the 16- X 4-bit type
7489 memory means that 20 packages would be required. Other possibilities
are the 2101A-1, which has a 200 nsec cycle time, and the 93422, which is a
50 nsec bipolar device. The latter is fast enough to be used directly, whereas
the MOS 210lA-1 would have to be pipelined. Both of these have identical
pin connections and are organized as 256 words of4 bits; thus, three-quarters
of their capacity will not be utilized.
When considering 64 channels, each with harmonically related frequencies,2
the leftmost four blocks in Fig. 17-16 seem to be redundant. In
particular, it would be nice to eliminate the harmonic multiplier as well as
individual frequency generation accumulators. In order to see how this might
be done, consider the case in which the frequency control word has a value of
1 and the entire module had just been reset, that is, all 64 frequency
generation accumulators set to O. After one sample period (16 f.Lsec), the
fundamental accumulatot has a value of 1, second harmonic 2, third 3, etc.
After a second sample period cycle, they are 2, 4, 6, etc., and after a third
cycle they are 3, 6, 9, etc. After a number of sample periods, overflow of the
highest harmonic is inevitable. This is merely an indication that it has
completed a full cycle and can be ignored. In fact, all of the harmonics will
overflow as they complete full cycles.
These same relationships hold regardless of the value of the frequency
control word. Thus, the content of the fundamental's accumulator can be
multiplied by the harmonic number to obtain what would be in the harmonics'
accumulators if they had their own accumulators and adders! This
then eliminates 63 frequency generation subsystems. Only the low 20 bits of
the 26-bit product should be retained to properly implement the overflow
phenomenon mentioned earlier.
Now that the redundant frequency generators are eliminated, let's see
about getting rid of the multiplier as well. If the multiplexing is done in
order of increasing harmonic numbers, then multiplication by 2, 3, 4, etc.,
can be accomplished by successive addition of the fundamental's frequency
generation accumulator into a second indexing accumulator. Thus, the harmonic
multiplier is replaced by an adder and accumulator. The substructure
that accomplishes this is shown in Fig. 17-17. Note that this substructure is
not multiplexed, but it does provide multiplexed data to the 64 sine
generators, which, of course, are multiplexed. The frequency-control register
2If one wishes to generate decidedly nonharmonic tones, the 64 frequency generation
subsystems may be retained. The ftequency control words would then come from a
64-word X 20-bit memory rather than a harmonic multiplier. Thus, one has essentially
64 independent sine wave generarors and a 64-channel mixer with independent
gain control for each channel. The phase control adders are useless in such an application
and therefore can be omitted.