The meta answer is CLASSIC (Hint: Find a seven-letter adjective.) Four of the Across answers start with an element on the periodic table:
17A. CHLORINETABLETS
19/34/39A. ARSENICANDOLDLACE
51A. SILICONVALLEY
55A. CARBONTAX
The name of the puzzle "Period Pieces," hints that the answer is made of "pieces" from the periodic table. Change each of those elements--chlorine, arsenic, silicon, and carbon--to their periodic table symbols--Cl, As, Si, and C, and you get the letters in the word CLASSIC, a seven-letter adjective that describes many period pieces (the other meaning of the puzzle's title) that satisfies the puzzle's hint.