Why balanced XLR needs an inverted signal?

[Sokel]

I’d like to make a distinction here.
In practice, balanced differential transmission often results in lower distortion compared to single-ended unbalanced signals.

However, the causation is not that straightforward. The reduction in distortion may be a result of the interaction between the specific transmitter and receiver circuitry, rather than being inherently due to the balanced transmission itself.

Consider these simple cases:
View attachment 435687

• With a transformer-isolated balanced input and output, THD does not change whether the impedance of the hot and cold legs are matched or not.
• It also remains unchanged whether one side is referenced to ground or not.
• The current loop stays the same regardless.

So, to be precise, the improvement in THD may comes from the interaction between the specific input and output stages, rather than from the signal itself being (impedance) balanced and or symmetrical

The above, unless tricked by a chip or software can be even accidental, agreed to that.
It would take enormous precision otherwise only done by the hardware side.

Edit: even at the shown case is difficult if the interface is unstable about its distortion structure, it's only luck that E-MU is stable and I can do it.
ESS on the other hand has handy software tools that can do some work and leave it there, despite the type of connection, that's only a side comment.