Vocal processor harmonizer for intentional dissonance

[BunchyMutt]

I have next to nil experience with vocal harmonizers. Is it possible to achieve intentional dissonance with either hardware or plug-ins? Every walkthrough I've seen has been harmonizing within the key. Is it possible, using a midi input, to play a half step removed (or, depending on the midi keyboard/mapping, +/- >100 cents) from a vocal line?

I'm thinking of The Great Comet of 1812, specifically parts like 1:28 of "Natasha & Bolkonskys"

 

[seamonkey]

Waves Harmony is your ticket
Waves Harmony – Real-Time Vocal Harmony Playground | Waves

You play or program whatever harmonies on a keyboard in real time.

 

[Basslice]

Most DAWs should be able to detune and time stretch. I know that Ableton Live and ProTools can. This can be done on the timeline or through various plugins and which route you go may depend on how much work you want to put into it.

 

[BunchyMutt]

Waves Harmony is your ticket
Waves Harmony – Real-Time Vocal Harmony Playground | Waves

You play or program whatever harmonies on a keyboard in real time.

That looks like what I'm looking for. Thanks!