1) Impertinence 2) Perkiness 3) Pertness 4) Playfulness 5) Quality of a main element 6) Roguishness 7) Sauciness 8) Sly humor Found on https://www.crosswordclues.com/clue/archness
Arch'ness noun The quality of being arch; cleverness; sly humor free from malice; waggishness. Goldsmith. Found on http://www.encyclo.co.uk/webster/A/116