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late 14c., "a musical sound, a succession of musical notes," unexplained variant of tone. Meaning "state of being in proper pitch" is from mid-15c.
"bring into a state of proper pitch," c.1500, from tune (n.). Non-musical meaning "to adjust an organ or receiver" is recorded from 1887. Verbal phrase tune in in reference to radio (later also TV) is recorded from 1913; figurative sense of "become aware" is recorded from 1926. Tune out "to eliminate radio reception" is recorded from 1908; figurative sense of "disregard, stop heeding" is from 1928. Related: Tuned; tuning.
In the amount of; to the extentof: It'll cost him a bundle, to the tune of sixty grand or so (1716+)