Control Voltages are a great way to control sound, thanks in great part to their simplicity. unlike MIDI, which uses a 5 pin DIN cable to send and receive packets of information with values of either "On, Off" or 0-127, control voltages are just that - direct current voltage. most gear that uses CV tends to respect any value in between 0 and 5 volts, and there are no arbitrary stepped values as with MIDI. this allows much more fluid modulation and control.
in the context of the new Akai controller, each key is assigned a fixed control voltage - calibrated to increase by 1v per octave. this will allow most analog oscillators (both in modular synths and non-modular) to play your standard chromatic notes straight from the keyboard. this saves having to convert MIDI messages to control voltages.
CV is also great because all manner of functions can be performed to the voltage before it reaches it's destination, in a much more comprehensive way than MIDI. you can scale the voltage higher or lower with certain devices, invert it, quantize it to different notes etc.
in the typical analog monosynth or similar, CV control is usually provided for Pitch (that's the 1/v per octave oscillator input mentioned above) and Filter Cutoff (we all know what that is), and Gate (usually triggers the envelopes of the synth, allowing the amplifier or filter to open and close when a key is pressed) . this is the most basic of implementations, and in many ways MIDI surpasses this protocol when implemented in this way.
when you start to move into more complex modular synthesizers, the modules need a way to talk to each other. unlike a regular synthesizer with internal connections between the various components, a modular has NO connections - you need to make these connections yourself. that's what all the patch cords are for. in many systems the same cables can carry either audio (the same kind of audio that comes out of the 'output' of your typical synthesizers, though usually a little louder) or our old pal Control Voltage. they can even be mixed and matched! this allows you to change every possible characteristic of the sound over time, sometimes without even touching the instrument.
as an example - typically we hear something like an LFO (low frequency oscillator) routed to filter cutoff. if the LFO is outputting a triangle wave, it opens and closes the filter in the shape of a triangle - so we hear "Wah wah wah wah" and dubstep is born. in a modular system (and most analog synths, though this is not always visible), that LFO is outputting control voltage in the shape of a triangle - so we can take that ramping up-and-down control voltage and plug it into anything that has an input! on a modular, that's a WHOLE LOT OF STUFF. one might apply that to the Resonance of a filter instead of the cutoff, so when the triangle wave gets to its highest point it makes the filter self-oscillate briefly. or, you could apply it to the Pitch CV input of an oscillator, and get a pitch that ramps up and down at the speed that the LFO is set to. this just begins to barely scratch the surface of what is possible with control voltage that is not possible with a standard MIDI synthesizer.
as was mentioned earlier, Control Voltage came before MIDI. it all but died out in the 80s and 90s. now, it's back, and even larger manufacturers like Akai are starting to embrace the resurgence of this more 'open ended' method of controlling synthesizers.
