M-Audio Wayoutware TimewARP 2600 User Manual page 28

3.7.1 Linear and Exponential Sensitivity to Control Signals
In designing and constructing a voltage-controlled device, or a digitally-controlled algorithm, we have to consider
how we intend the controlling parameter to relate to the controlled parameter.
Suppose, for example, we build an oscillator that changes its output frequency by exactly 1000Hz for each rise
of 1 volt in electrical pressure at a designated point (a "control input") in the oscillator circuitry. This is a linear
relationship between the control value and the frequency. In order to march such an oscillator through a musical
scale, one would have to provide exponentially increasing voltage steps at each rising musical interval. That's
pretty awkward, and it gets worse very rapidly. The pitch interval produced by a 1-volt control interval will depend—
completely—on what the original frequency of the oscillator was set to before applying the control voltage:
For an initial frequency of ... 1-volt control becomes a pitch increase of ...
1KHz
2KHz
3KHz
500Hz
And so, instead of linear sensitivity, VCO's for audio synthesis are designed, almost universally, with exponential
sensitivity to control signals. Such a design sets up an exponential relationship between control signal and
frequency in order to maintain a simple linear relation between control signal values and audible pitch changes.
Similar arguments apply in the design of voltage-controlled filters: it's more practical to work with a linear
relationship between control-signal and "cutoff timbre," and therefore the relationship between control-signal and
cutoff frequency really has to be exponential.
1 Octave
a perfect fifth
a perfect fourth
2 Octaves
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