I came across this calculator for an acoustic diffusor and whipped up a basic static model of it:

http://www.mh-audio.nl/DiffusorCalculator3.asp

My model has a column width of 1cm and max column length of 1cm, which results in low and high frequencies of 17200 Hz, and you can scale the model to tailor it to your needs:

Z scale factor = 17200 / desired low frequency (Hz)
X,Y scale factor = 17200 / desired high frequency (Hz)

Put another way:

Low frequency (Hz) = 17200 / Z scale factor
High frequency (Hz) = 17200 / X,Y scale factor

For example, suppose your 3D printer can print an object 10cm high: this gives a min frequency of 1720 Hz. If the smallest reliable size you can print a 10cm-tall square post is, say, 0.5cm on a side, then this gives a high frequency of 34400 Hz. Just use scale factors of 10 (Z) and 0.5 (X,Y). Easy peasy.

Disclaimer: I'm not really an audio guy and haven't had a chance to test this yet! Thought it looked cool though.