Seems a lot more confusing than it has to be... and BJC seem to be using it to push twisted pair cables (more on that in a moment) they've combined two explanations into one, dare I say erroneously.

BALANCED LINES
One conductor carries the signal (Pin #2 is standard), one carries the signal 180 degrees out of phase (Pin #3)... noise hits both conductors equally (or equally enough) and when Pin #3 is inverted 180 degrees again at the destination and mixed with Pin #2 - the noise is also inverted, and cancels itself out. Easy and ingenious.

Balanced lines do NOT have to be made from twisted pairs.

TWISTED PAIRS
All you MCSEs (I know Microsoft says it's Microsoft Certified System Engineer - we all know it's Minesweeper Consultant and Solitaire Expert!) stand up now. You have nightmares about CAT5 cable - now how do all those twisted pairs carry a cleaner signal than station wire (non-twisted)?

Easy... by twisting the wires, you keep them close to one another, sharing - as close is as physically possible in the real world - the same space. Interference affects both signals in nearly identical ways, instead of how a balanced connection uses an extra wire to cancel noise, TP uses voltage differential between the conductors as the signal. Say your signal is a 100% duty cycle of 10mV (10mV on the hot, 0mV on the neutral), and the noise is a constant +1mV... your conductors would be carrying 11mV (10mV + the 1mV interference) on the hot, 1mV (0+1) on the neutral... leaving you with a difference of 10mV - exactly the signal you want.

Bren R.