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interval (n.)

early 14c., "time elapsed between two actions or events," from Old French intervalle "interval, interim" (14c.), earlier entreval (13c.) and directly from Late Latin intervallum "a space between, an interval of time, a distance," originally "space between palisades or ramparts" [OED], from inter "between" (see inter-) + vallum "rampart, palisade, wall," which is apparently a collective form of vallus "stake," from PIE *walso- "a post" (see wall (n.)).

Metaphoric sense of "gap in time" also was in Latin. From c. 1400 in English as "a pause, an interruption in a state or activity." Musical sense "difference in pitch between two tones" is from c. 1600. Related: Intervallic.

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Definitions of interval from WordNet

interval (n.)
a definite length of time marked off by two instants;
Synonyms: time interval
interval (n.)
a set containing all points (or all real numbers) between two given endpoints;
interval (n.)
the distance between things;
Synonyms: separation
interval (n.)
the difference in pitch between two notes;
Synonyms: musical interval
From wordnet.princeton.edu