it seems I have to have 3 separate speakers.
At low (bass) frequencies
you'll get partial cancellation when the sound waves mix in the air. In theory you could get perfect cancelation (at any frequency) but the acoustic waves won't match perfectly, especially if you are in a "normal room" where sound bounces-around.
...If you have a normal stereo set-up and reverse the connections to one speaker (180 degree phase inversion), you'll get a LOT of bass cancellation but you'll still hear some bass.* And, you'll get enough cancellation at other frequencies to make music "sound weird", especially as you move around.
At higher frequencies it will be more-dependent on your location, the location of the speakers, and reflections in the room. At 10kHz the wavelength is a little less than 1.5 inches, so 1.5 inches is 360 degrees and there's a phase-difference between your 2-ears and simply moving your head will make a difference.
...If you have 3 speakers, it might be easier to calculate the wavelength and set the distance (between you and the speakers) for 1/3rd of the wavelength.
* I've never tried it outdoors. With no room reflections you can probably get 100% cancellation at low frequencies. At higher frequencies the phase-difference (time delay) between your ears would mean you'd only get cancellation in one ear at a time.