The term "fillet," as it is used by framers, may not crop up in most people's casual conversations but everyone has probably seen quite a few of these decorative elements without thinking much about them. Their point, after all, is to draw the eye in and sharpen the focus on a work of art. Basically a fillet is a thin strip of molding commonly placed between the art and the matting, as shown above and below. It's like a second "inner frame."
Typically made of wood, a fillet may be gilded,
painted, or stained depending on the style of frame chosen.
Classically fillets are used with watercolors to bring a bit of weight to something delicate, or to literally add depth. But the decision to use one is rather subjective; some eyes prefer to rest on a cleaner, more minimal picture. In the example of Hollyhock's framed Regency-era needlework shown at the top, a decision was made to go all out. The diminutive piece is anchored with a gilt fillet, hand-painted matting, and a gilt frame.
Double matting, in contrast, is the layering of two mats commonly made with paper, linen, or silk. Some drawings, documents, paintings, and prints are triple matted.
Credits: image one via Hollyhock and 1stdibs; photo four was taken by Amanda Talley, and all others are mine. Painting in image two by Vicky Molinelli.