Controlling a 555 squarewave oscillator synthesizer with CV sequencer
If the Korg's control voltage is the old analog synth standard of 1 V/octave then it's not a suitable circuit as it is not voltage controlled. 

To make a voltage controlled oscillator with enough linearity to be reasonably musical is an electronic design challenge. It can be done (but you'll need to progress past the 555) and there are published designs including some discussions on this site.



There is a design discussed in Help Needed with Voltage Controlled Synth Circuit. The component count is reasonably low and it looks as though it would actually work!

Note that the gate signal is not used in the oscillator - it is used in the envelope generator to control the ADSR - attack, decay, sustain and release. A separate circuit is required for that.