Wikia

A double guitar was a form of stringed musical instrument similar to a lute.

While under the euphoric effects of Harry Mudd's love potion crystals, Lieutenant Arex sat at his station on the bridge of the USS Enterprise and did nothing but play a double guitar. (TAS: "Mudd's Passion")

The name for this variety of instrument comes from the final draft script of "Mudd's Passion"

String instruments

Guitar • Double guitar • Vulcan lute

Double guitar