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Contemporary Keyboard
October 1978
Principles Of Voltage Control, Part IV
Bob Moog
In last month's column I reviewed the characteristics and advantages of the exponential-mode VCA. In this column I will show how exponential-mode VCAs can be used not only for gain determination but also for timbre shaping. Then we'll have a look at voltage-controlled oscillators, most of which have exponential control modes.
Two exponential-mode VCAs and two level-adjusting attenuators can be hooked up to give considerable timbre-shaping flexibility from just a few modules. Fig. 1 shows a dual waveform tone generator that produces one waveform of high harmonic content and another of low harmonic content. The first waveform goes through VCA #1, while the second goes through VCA #2. The VCA outputs are mixed to form a composite tone. A slowly varying volume control voltage and an envelope-shaping negative-going ramp are applied directly to the control inputs of VCA #1. These same control signals are applied through attenuators P1 and P2 to the control inputs of VCA #2. P1 allows you to determine how much more slowly the output of VCA #2 increases than the output of VCA #1, which in turn determines how much brighter the overall sound becomes as its volume is increased. P2 allows you to determine how much more slowly the output of VCA #2 dies out as the ramp voltage decreases. These two controls thus enable you to impart to the composite tone two timbral features that are extremely important in determining the quality and playability of percussive sounds: how the brightness changes with loudness, and how fast the higher harmonics die out in comparison with the lower harmonics and fundamental. In many synthesizers, this type of tone shaping is normally done with a voltage-controlled filter, a VCA, and two separate envelope generators.
Voltage-Controlled Oscillators
Now that we've illustrated the linear and exponential control modes by showing how they're used in VCAs, we'll have a look at the control modes of voltage-controlled oscillators. Frequency is the main voltage-controlled parameter of synthesizer VCOs. Pitch relationships are the basis of virtually all music. Since frequency (number of sound vibrations per second) is exponentially related to pitch, a VCO with an exponential control mode has an immediate and obvious advantage to musicians: musical scales can be generated with control voltage sequences that are simple to produce and manipulate.
The relationship between frequency and pitch is shown in Fig. 2. The vertical axis is frequency, calibrated in vibrations per second. The horizontal axis is pitch, calibrated in octaves above and below A-440. Doubling the frequency of a pitched tone increases its pitch by an octave. In fact, any musical interval is a frequency ratio. The ratio corresponding to a semitone is roughly 1.06:1. Multiplying the frequency of a pitched signal by 1.06 will raise its pitch by about a semitone, multiplying twice by this number will raise its pitch by a whole tone, and so on. Conversely, dividing the frequency by 1.06 lowers the pitch by a semitone.
Now let's apply this to synthesizer oscillators to see why the exponential control mode is so musically useful. Voltage-controlled oscillators commonly have a "one-volt-per-octave" control mode. This means that a one-volt increase in control voltage causes the oscillator frequency to double. Fig. 3 shows the exponential relationship between the control voltage and frequency of such an oscillator. Notice that, wherever on the curve you start, you double the frequency when you increase the control voltage by one volt. Furthermore, if you compare Fig. 2 with Fig. 3, you'll see the very simple relationship that exists between pitch (the musical parameter) and control voltage in an exponential-mode VCO: An increase in control voltage of one volt raises the pitch one octave. In fact, a given control voltage increase will raise the tone by the same pitch interval, regardless of the starting pitch.
To illustrate the properties of the exponential-mode VCO, let's assume that we have a VCO with three control inputs and a control signal mixer (adder). All three control inputs are equipped with attenuators. External control signals feed two of the inputs, while a third is supplied by a fixed voltage.
Let's first direct our attention to the control signal source labelled "keyboard." A synthesizer keyboard generally produces a series of voltage changes that define a scale, or succession of intervals, If these voltage steps from key to key are uniform, then the keyboard produces an equally tempered scale (all intervals are the same). Attenuator P1 in Fig. 4 adjusts the size of the voltage steps, and therefore the number of notes per octave. For instance, if the VCO has a one-volt-per-octave control mode and the keyboard produces 1/12-volt steps as succeeding keys are depressed, then a twelve-tones-to-the-octave, equally tempered scale will result. This is our familiar chromatic scale, the basis of virtually all modern Western keyboard tunings. If, however, P1 is turned down so that the voltage steps to the control signal adder are reduced to 1/24 volt, a 24-tones-to-the-octave, or quarter-tone, scale is produced.
Thus, P1 "squeezes" the scale which is produced by the keyboard. In most small synthesizers P1 is an internal tuning adjustment. In modular or experimentally-oriented instruments, P1 is often built into the keyboard rather than the oscillator module itself.
P3 determines the amount of fixed voltage that is added to the keyboard control signal. As such, it transposes (adds a fixed musical interval to) the scale produced by the keyboard. Most synthesizers have two such fixed voltage attenuators, one for coarse adjustment and one for fine tuning. Often the coarse adjustment is a step attenuator that switches the fixed control voltage in one-volt steps, thereby transposing the pitch by octaves.
Feeding a slowly alternating voltage through P2 introduces a frequency modulation to the control signal input. If the modulating oscillator waveform is sine or triangular, vibrato is produced. If the waveform is square or rectangular, a trill results. P2 adjusts the amount of modulation-the width of vibrato or the interval of the trill. With an exponential-mode VCO, the width of modulation depends only on the amplitude of the modulating signal, and not on the "center pitch" that is being produced.
