a quantizer doesn't necessarily transpose - some can but most won't, you would normally use a precision adder for transposition, what a quantizer does is drag the input voltage to the voltage of the nearest note in the specified scale (which may be up or down depending on how the quantizer has been programmed...
with a quad quantizer all 4 inputs are usually quantized to the same scale
if all 4 of the outputs are voltages in the same scale, then they will be harmonious - this doesn't necessarily mean that they will sound how you want them to... the oscillators or voices need to be tuned - probably to the same root note, but not necessarily in the same octave - and they have to be able to track in the range that you are sending notes to them - ie probably not over 10 octaves - and the sequences have to be programmed etc
how do I use a quad quantizer in my setup? I have a sinfonion, I send it 3 or 4 sequences (made up from marbles, erica black sequencer, tesseract step fader etc), note mask each part as required and send the outputs to different vcos/voices - which are tuned to a reference C from the sinfonion - one really useful thing in the sinfonion is that you can set the starting octave of each channel - both the quantizers (and arpeggiator) and the chord progression sequencer (and the tuning C is in the correct octave) - I also use another sequencer to change song parts on the sinfonion when needed and a clock to advance within the song part
"some of the best base-level info to remember can be found in Jim's sigfile" @Lugia
Utility modules are the dull polish that makes the shiny modules actually shine!!!
sound sources < sound modifiers < modulation sources < utilities