In traditional harmony something is considered "dissonant" if it's not part of the root triad in root inversion. All such chords are unstable, the theory goes, and must eventually resolve to some tonic chord. Classical harmony sticks almost exclusively to diatonic intervals, triads, and sevenths, and uses inversions and juxtaposition of chords (in sequence, via 'suspension', and so on) to provide "dissonance".
This isn't the kind of dissonant the OP is talking about. I'd be very surprised if you can come up with a clashing jumble like a Dom7#11 in Bach, even as a suspension or pedal. Cluster chords in classical music are almost unheard of.