British spelling: to bring into agreement or accord; to make compatible or coordinated; in music, to combine tones into chords.
From French harmoniser, from harmonie (harmony), ultimately from Greek harmonia (fitting together, agreement). The -ise ending is the British spelling convention, while American English uses -ize.
The British -ise versus American -ize difference is one of those spelling splits that happened after the US and Britain separated—Noah Webster deliberately pushed -ize in America while Britain kept -ise—so these are literally the same word with a political spelling divide.
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