c. 1300, "a beating, whipping; the beating of a drum," from beat (v.). As "throb of the heart" from 1755. The meaning "regular route travelled by someone" is attested from 1731, also "a track made by animals" (1736), from the sense of the "beat" of the feet on the ground (late Old English), or perhaps that in beat the bushes to flush game (c. 1400), or beat the bounds (1560s). It was extended to journalism by 1875.
The musical sense is by 1842, perhaps from the hand motion of the conductor and the notion of "beating the time":
It is usual, in beating the time of a piece of music, to mark or signalize the commencement of every measure by a downward movement or beat of the hand, or of any other article that may be used for the purpose .... ["Godfrey Weber's General Music Teacher," 1842]
Earlier in music it meant a sort of grace note:
BEAT, in music, a transient grace note, struck immediately before the note it is intended to ornament. The beat always lies half a note beneath its principal, and should be heard so closely upon it, that they may almost seem to be struck together. ["The British Encyclopedia," London, 1809]
"in a state of decline or decay (from a former condition of excellence)," 1837 (Carlyle), from French décadent, back-formation from décadence (see decadence). In reference to literary (later, other artistic) schools that believed, or affected to believe, they lived in an age of artistic decadence, 1885 in French, 1888 in English. Usually in a bad sense:
Bread, supposedly the staff of life, has become one of our most decadent foods — doughy, gummy, and without the aroma, flavor, texture, taste and appearance that is typical of good bread. ["College and University Business" 1960]
Beckoning sense of "desirable and satisfying to self-indulgence" begins c. 1970 in commercial publications in reference to desserts.
As a noun, "one whose artistic or literary work is supposed to show marks of decadence," 1889 (from 1887 as a French word in English), originally in a French context.
On the subject of poetry I am bound to signalize one of those grotesque, unexpected apparitions which would appear to be constitutional to our country [i.e. France] .... I refer to the recent appearance of a literary clique of madmen or idlers, the self-named décadents. I own I am almost ashamed to occupy your time with this unworthy subject, which I should not have thought fit to introduce had not our newspapers and even our reviews taken the décadents to task, and were it not that they have furnished chroniqueurs short of copy with matter for articles, and that the serious Temps itself has taken up their trashy nonsense. [The Athenaeum, Jan. 1, 1887]