A cord is (1) a string or rope, (2) an electrical cable, (2) a measure of wood equal to 128 cubic feet, (3) a ribbed fabric (short for corduroy), or (4) one of several types of cords found within the bodies of animals (e.g., spinal cord, umbilical cord). Chord is only a musical term (though it is sometimes used metaphorically). It denotes any combination of three or more pitches played at the same time.
The cliché strike a chord is a metaphorical reference to music, so chord is correct.
Examples
These writers use cord well:
A damaged extension cord caused a massive fire Sunday afternoon that destroyed Points West Sales and Leisure Sports. [PA Herald]
It takes one cord of wood or 60 gallons of oil to boil 800 gallons of syrup. [Post-Gazette]
And these writers use chord well:
Rather he deploys it to float a perfectly weighted melody against a broken-chord accompaniment as unruffled and beautiful as a blue lagoon. [This is London]
He calls the final chord of ” A Day in the Life,” from “Sgt. Pepper’s Lonely Hearts Club Band,” in a typical aside, “the greatest E major chord in the history of Western music.” [New York Times]
