The Canare quad cable I've used is actually quad twisted and not twisted pair meaning that the 4 conductors are all wrapped together rather than twisted pairs. Twisted pair is used for data and not necessary for audio but works very well.
Twisted pair is essential for the prevention of noise in balanced audio connections. Twisted pair for audio dates back to the creation of the public telephone
network. It is how audio can travel on cables for miles without picking up too much noise.
A balanced audio
circuit has audio of equal amplitude but opposite
polarity on the two signal wires. At the input
amplifier, the two signals are summed together. When summed, the desired audio signal adds together to double the
voltage. Any noise that is equal in amplitude and
polarity (or
phase if you want to be picky) on the two wires adds to zero (gets cancelled). The noise reduction of a balanced
circuit is called common-mode-rejection. By twisting the wires, any noise that gets induced into them should be equal. If the wires were not twisted, a noise source would be induced into each
wire at different amplitudes and phases and the input would not cancel it.
Quad-wire is merely a way of improving common mode rejection. It is comparable to twisting a single pair tighter, in
effect ensuring that the noise is identical on both halves of the input
amplifier. It comes at a small price because quad cable has more
capacitance that can load the source which causes high frequency losses on longer cables. In most cases, the limitation to common mode rejection is the input
circuit design, not the cable. I don't recall ever noticing any kind of improvement from quad mic cable.
Most people assume that the
shield does most of the work of preventing noise pickup. It doesn't. A well balanced audio
circuit can work perfectly without a
shield at all. It just takes well designed output and input stages along with properly twisted pairs in the cable.