Definition and background:
Term used in Medieval theory having several meanings: Polyphony having four vioces. The fourth voice (highest) in a polyphonic composition ( organum) having four or more voices. Diminution or augmentation by a factor of four in mensural notation. (1) the fourth voice to be composed; in organum and the early motet, it is found above the triplum, duplum/motetus, and tenor. (2) in organum, a piece which has a fourth "quadruplum" line can be called an "organum quadruplum" or "quadruplum" for short. Perotin wrote two quadrupla: "Viderunt omnes" and "Sederunt."
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Wikipedia - Glossary of Musical Terminology
Virginia Tech Multimedia Music Dictionary
ORB -- Medieval Music Glossary