I am sure that these two fragments are early embroideries, of the 'counted thread' technique. They are both of silk thread on fine linen, and both of geometric design.
I feel equally sure that the paler colour of the two is the same embroidery one finds on 17th Century band samplers, as you see on the image shown here from one of Mary Gostelow's [Ed.] embroidery books 1982/151. Both examples seem to be a form of Blackwork embroidery, often also used on clothing and accessories as you see in Image 2 [Mary Gostelow 1978/34] [See The Study for full references]
Now, the name of Blackwork clearly implies black embroidery on a white backgound. But it was not always so. Blackwork spread throughout Europe in the 15th Century from Spain and actually has far earlier origins, but although we see many images of coifs and cuffs that still survive in black embroidery on white, the technique also used other monochrome colours such as red, green & blue. The main feature of Blackwork was the contrast between a vivid colour on a white background, and the counted thread method of applying thread onto linen. 
These two examples are very similar to Blackwork of the 17th and early 18th Century and I would love to know the links between them. Even with freeform design, such as you see with the lady's costume, the geometrics featured within the motifs.
Well, if I am right, you get these at an excellent price! Please help if you know more......!
 
Both examples here are in very good aged condition. The red silk on linen is a simpler design and a small piece measuring approx 8" x 3". Most attractive. There is a blotch of subtle discolouration to one side, but generally very good. The pale example is fascinating, being far longer at 29" and most complex. Sadly the thread colour is very faded, but the complex geometric pattern is based on leaf shapes, except for the upper edges that seem to be single leaf shapes in a simple row. I love it!
This larger length has pale discolouration along one edge, and a few small hole again at the tops, but is generally excellent also. It measures 3.5" deep.
The backs of each are almost the same as the fronts - amazing.
Get out your magnifier for these!
Both pieces came from a single collector's embroidery file and these are the last of the early examples.