1610s, in music, "vary or inflect the sound of," especially to give expressiveness, "vary the pitch of," back-formation from modulation, or else from Latin modulatus, past participle of modulari "regulate, measure off properly, measure rhythmically; play, play upon," from modulus "small measure," diminutive of modus "measure, manner" (from PIE root *med- "take appropriate measures").
General sense of "modify, adjust, adapt, regulate in measure or proportion" is from 1620s. The intransitive musical sense of "pass from one key to another, or between major and minor" is attested by 1721. In telecommunications from 1908. Meaning "exert a controlling influence on, regulate" is by 1964. Related: Modulated; modulating.