^ and ^^ there u have the answers

... the rest is pretty gratuitous or clueless if u ask me..
generate white noise in any softsynth ... and then try to play at different pitches... wont be able... u cant.. its white noise.. its all the frequencies at once

... so no a midi keyboard alone wont do the trick
u could do two things (at least, i guess) :
1) bounce it... as audio and then put it in a sampler... from there ull get a sample that could be played at diff speeds/pitches... playing it ull realize itll sound almost as if it were lowpassed or hipassed... leads us to 2) which has already been explicited
2) there's a second thing u can do tho... and to me it's the best option in order to create a tension similar to pitch rising... : use filters... hipassing the white noise will create some kind of urge... perhaps the one ur after...
experiment! come back and tell us how it went!
no harsh feelings yall...
just felt like op was asking a legit question here