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Sample and Hold Composition Technique


When first exposed to the sample and hold (S/H) module in a college synthesizer course, I was totally thrilled - but also totally confused. Subsequent investigation cleared up my confusion and exposed me to the many sounds of which an S/H is capable. In this article, we'll cover some of the many talents of this versatile module.

Basics of Sample and Hold



Each of the S/H's two inputs and one output introduces a variable worth exploring. The output, which takes the form of a varying control voltage, may be fed to voltage controlled modules "as is" or processed by control voltage processors. Traditionally, one of the inputs samples the voltage of a waveform (Control Voltage In) at a rate specified by the clock rate present at the other input (External Clock In, Sample In, or sometimes Strobe In). For now, let's investigate some of the waveforms suitable for sampling by the S/H.

The easiest way to understand an S/H is to think of it as taking periodic snapshots of the waveform being sampled, with each still shot corresponding to a discrete voltage level. This voltage level becomes the module's output.

On my ARP 2600, as on many synthesizers, the sampling source input is normalled to the white noise generator. Sampling this input results in a series of apparently random output voltages. However, this randomness soon becomes boring; so, I started experimenting with sampling repetitious (periodic) waveforms. The results obtained by sampling a sawtooth wave were most interesting, so we'll discuss this subject in depth. In order to best hear the results of these experiments, I sent the S/H output to a VCO.

Experimenting with the Control Voltage Input



The sampling process is somewhat reminiscent of the story about the blind men and the elephant - we have to get lots of shots of a single wave, or we'll end up with a rather contorted image of what the wave must look like. We can increase the number of shots by coaxing our "photographer" into working faster (increasing the clock rate), or by slowing down the wave in order to keep pace with our reluctant photographer (decreasing the frequency of the waveform being sampled). Since either option will yield the same result, we can perform our experiment by playing with only one of the two variables. I chose to work with the frequency of the wave, rather than changing the clock speed, because this enabled me to concentrate on the different patterns available without being confused by a constantly changing clock rate.


We can begin by sampling a very low frequency sawtooth, which yields a long, ascending scalelike pattern that periodically jumps to the beginning and starts again (see figure 1). Because of the virtual impossibility of getting the clock rate to be an exact divisor of the period of the wave, the odds are very small of generating a pattern that will repeat itself exactly. Because there is a slight amount of overlap at the crest of each wave, the Initial Clock Period (my term for the first sample of each wave and therefore the lowest note in each scale) will constantly shift downward towards the onset of the wave, causing each scale to be lower than the preceding one. Finally, what would have been the ICP of the wave misses the beginning of that wave altogether, lands on the tail end of the preceding wave, and gives that wave an extra note. As a result, every few measures (reverting to musical terminology), there will be a bar with an extra beat, creating such interesting polyrhythms as 7 + 7 + 7 + 8. We can control how often the bar with the extra beat occurs by controlling the rate of descent of the ICPs (a function of the wave frequency); the slower the descent, the less often the longer bar occurs. This makes it possible for us to consciously generate a number of different polyrhythms. Once again, however, because the mathematical relationship between the clock rate and the wave period is not exact, a pattern will not maintain itself indefinitely. We can overcome this problem by taping a segment of the pattern and then getting it to repeat itself with splicing techniques or through the use of a tape loop.


As we increase the frequency of the wave, the descent of the ICPs slows, and they come to a standstill, causing the scale to repeat itself. The ICPs then begin to ascend as we can see on figure 2. During the ascent, the odd bar now contains not one extra, but one fewer, note. As the frequency increases the short bar occurs more and more often, until the two bars alternate with each other (say a 7 and a 6). If we push the frequency a little higher, the 6 will become a more common rhythm, and at the same time the ICPs will start to descend. We are now back where we started, except that instead of alternating 8s and 7s, we alternate 7s and a 6. As we continue to increase the frequency, this whole cycle keeps repeating, going through 6 + 5, 5 + 4, until we get to 2 + 1, as illustrated in figure 3. Push this one step further, and each wave is sampled only once.



At this point, we have a descending scale pattern. As the clock time approaches the period of the wave, the scale becomes almost a smooth glide, as we can see in figure 4. When the clock time equals the period, we get a nearly stable pitch. The glide starts to ascend, individual pitches can be heard and we have an ascending scale (see figure 5). We have now come full circle, and we are back where we started - except that the samples are occurring on successive waves rather than different portions of a single wave (which makes no practical difference). This entire cycle keeps repeating itself as the frequency of the sampled wave increases, even as this goes into the auditory range. The only difference is that the cycle occurs through smaller and smaller increments of the tuning control. This is because the tuning control increases the oscillator's frequency exponentially, but the clock looks at the wave from a linear point of view - it sees an increase of frequency from 100 to 200 Hz as being the same as an increase from 1000 to 1100 Hz.


Exploring the External Clock Input



By using the square wave of a VCO in its low frequency range we can now voltage control the sampling rate. Note that changing the pulse width of the sampling wave will make no difference to the S/H because the S/H responds only to the leading edge of the wave (other S/H designs may not follow this convention, incidentally). We can experiment with a variety of control voltages (CV) to the clock wave. We can, for example, get the sampling rate to be proportional to the pitch of the melody by using the CV from the keyboard or other controller, directly or through an inverter.

Or, we can use an ADSR envelope generator triggered by the gate or trigger voltage. Every time a new note is hit, the sampling rate will speed up and slow down in complex patterns determined by the ADSR control settings. Another alternative is to create a feedback loop by sending the S/H output back to an LFO feeding the clock. This will cause the high CVs to rush by quickly and the slow ones to take their time (again, this is an invertable process by adding an inverter).

There are other interesting clock possibilities. If we use the controller trigger voltage, we can, for instance, get a different timbre with every note we play. We can also use any external source such as an instrument or tape. The clock input of many S/H modules will respond to any sharply rising amplitude change; when there are rapid amplitude changes, the clock gets confused and a strange warbling results. It would be interesting to then feed the tape through a filter which is being controlled by the S/H output, causing timbral changes on the program material to be a function of amplitude changes.

A good tape technique is to record the clock, allowing us to overdub a number of rhythmic layers in sync with each other (editor's note: see Tom Henry's column in this issue for additional information on the tape/sync track interface). The clock can be heard as an audible click on the tape, although it is at twice the clocking frequency because the S/H responds to the leading edge of the wave only.

Output Considerations



I'd like to close this article with a few comments on the final link in the S/H chain, namely, the choice of which module receives the S/H output. Unusual patches can be created by sending this output to the VCA and some of the more esoteric functions available on your system, such as voltage controlled resonance (VCQ) or voltage controlled reverb. However, I will focus on the more common and perhaps more useful choice of the VCO and VCF. One of the most basic usages is to send the S/H CV to the filter, thereby creating a rhythm against which you can play fixed melodies or improvise. High resonance filter settings provide the most dramatic emphasis of the rhythm, if also the most hackneyed. The contrast between beats can be heightened if you have VCQ and send the CV to this input as well as to the cutoff point.

More dramatic rhythms come from using the VCOs, although this eliminates the possibility of creating controllable melodies. I find that the best effects come from tuning the oscillators to an interval and maintaining this interval by putting the CV into the 1V/octave inputs of the oscillators. I like the sound of a few fifths or fourths of the same waveform piled on top of each other, all moving in parallel motion.

One problem that I encountered is that if the CV is going to several different modules, the effects achieved will always work in parallel because a given voltage change will cause a predictable change in each module - for example, a high note will always occur at the same time as an open filter. We can improve the situation by processing the CV before it goes to the one of the modules. In addition to inverting it, we can put it through a lag processor (slew limiter) which will give the pleasant effect of rounding off the sharp edges of each control voltage transition. However, the only true solution would be to use two different S/H units that are both being triggered by the same clock, which would randomize the audio outputs of the two modules yet preserve the same rhythmic relationship.

Many other possibilities remain to be investigated, such as mixing waves before and after sampling them, or mixing the S/H output with other CVs before sending it out. I hope, however, that I have pointed the way towards a few avenues for further experimentation.



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Practical Circuitry


Polyphony - Copyright: Polyphony Publishing Company

 

Polyphony - Jul/Aug 1981

Donated & scanned by: Mike Gorman

Feature by Geoffrey Collier

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