I've been looking at / listening to grille effects on the SCS4. It is somewhat eccentric in that it has no fabric and the full-baffle is covered by a perforated steel mesh that is quite transparent. The electrical / magnetic fields meter shows that the intense fore-aft fields through the center of the coax are modulated by the metal grille. The EMF changes shape (becomes wider), but most notably, the electrical field is reduced by an order of magnitude in front of the grille. Back fields are unaffected. With my head a foot in front of the coax, I can hear a slight lifting of a veil by removing the grille. I would call this change so slight as to be barely noticeable. Other products may differ. My high-frequency hearing is far from what it was. So others may hear more difference. With all this pesky learning I would remove the grilles while listening.
Over the years that seems to be common among reviewers and listeners. I always attributed that to the fabric, but it seems there are other elements involved.
