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In general terms, this is a mathematical curve that starts out relatively flat and then bends to climb steeply. In synthesizer terms, it most often refers to the control voltage scheme where a change of 1 volt corresponds to an increased pitch of one octave, which is doubling in cycles (vibrations) per second. This is in contrast to a linear system where 1 volt increase would always result in the same increase of cycles per second.

Here’s an example of an exponentially controlled oscillator: Start with an oscillator playing a tone at 100 Hz. Increase its input control voltage by 1 volt, and it goes up to 200 Hz. Increase the input another volt to 2v, and it goes up to 400 Hz. Another volt to 3v; 800 Hz. The pitch rises exponentially (in cycles per second) in response to the input voltage.

Exponential can also refer to the response of voltage controlled amplifiers and other level circuits. Our ears also respond to loudness using an exponential instead of a linear scale. That’s why the fade controls on mixers for audio, and some VCAs (voltage controlled amplifiers), also have exponential response. Some envelope generators also follow an exponential (or it’s partner, logarithmic) scale. It gets confusing when you start mixing linear or exponential envelope generators with linear or exponential VCAs – what exactly is correct? Or what if you’re processing a control voltage instead of sound? That’s why it’s nice when VCAs have switches (or even continuous controls) to change them between linear and exponential response.

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