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"one of four children at a single birth," 1787; from quadruple (adj.) with ending from triplet. Related: Quadruplets. Musical sense is from 1873.
quadruplet quad·ru·plet (kwŏ-drŭp'lĭt, -drōō'plĭt, kwŏd'rə-plĭt)n.
One of four offspring born in a single birth.
A group or combination of four associated by common properties or behavior.