Joe, they weren't called a satin foot...& doesn't look like one! It was called an special purpose foot. It's for satin stitching, using decorative cordings, buttonholes, etc. It may have come with your 401...it was with the accessories when it was sold. I have one that was with my 403. And looks like this
http://www.ebay.com/itm/SINGER-SEWIN...item53ebe7f193. It's got a raised channel underneath & slots to feed cording thru in front if you want to use cording in a buttonhole or a design.
And yeah...you might want more than one. Some have 2 cording holes in front...& some have 1.