The system designed to transmit information between electronic musical instruments is called MIDI (Musical Instrument Digital Interface). 
MIDI is a technical standard that describes a communication protocol, digital interface, and electrical connectors.
It allows a wide variety of electronic musical instruments, computers, and other related devices to communicate with each other.
MIDI transmits data about musical notes (pitch, duration, velocity), control signals for parameters like volume and panning, and other musical information.
It does not transmit the actual audio signal itself.