In a manner relating to hearing or through the sense of sound; in a way that involves listening.
From auditorial (relating to hearing) + -ly (manner/how adverb suffix). This creates an adverb meaning 'in an auditorial way' or 'with respect to hearing.'
This is the adverb form of 'auditorial,' so when you say something happened 'auditorially' you're saying it happened through your ears—it's the fancy scientific way to say 'by listening'!
Complete word intelligence in one call. Free tier — 50 lookups/day.