E. Cobham Brewer 18101897. Dictionary of Phrase and Fable. 1898.
A consort consisted of six viols, usually kept in one case. When the six were played together it was called a whole consort, when less than the six were played it was called a broken consort. Sometimes applied to open chords or arpeggios.
Here is good broken music.
Shakespeare: Troilus and Cressida, iii. 1.
Lord Bacon in his Sylva Sylvarum gives a different explanation: he says certain instruments agree together and produce concordant music, but others (as the virginal and lute, the Welsh and Irish harps) do not accord.