Entries linking to anthemic
The sense evolved to "a composition (usually from Scripture) set to sacred music" (late 14c.), then "song of praise or gladness" (1590s). It came to be used in reference to the English national song (technically, as OED points out, a hymn) and extended to those of other nations. Modern spelling is from late 16c., perhaps an attempt to make the word look more Greek.
Middle English -ik, -ick, word-forming element making adjectives, "having to do with, having the nature of, being, made of, caused by, similar to," from French -ique and directly from Latin -icus or from cognate Greek -ikos "in the manner of; pertaining to." From PIE adjective suffix *-(i)ko, which also yielded Slavic -isku, adjectival suffix indicating origin, the source of the -sky (Russian -skii) in many surnames. In chemistry, indicating a higher valence than names in -ous (first in benzoic, 1791).
In Middle English and after often spelled -ick, -ike, -ique. Variant forms in -ick (critick, ethick) were common in early Modern English and survived in English dictionaries into early 19c. This spelling was supported by Johnson but opposed by Webster, who prevailed.