The fadings in this quilt make me wonder if the pinks were originally red and the grays were blue. If you can see into the seam allowances somewhere you can research this yourself. Sometimes this fading occurred because the fabrics were vegetable-dyed, and that was common in the 1920-30s.
So, seeing this, I went to Barbara Brackman's Encyclopedia Of Pieced Quilt Patterns and after a search found this block on page 402, image 3365. It looks like a square in a square with the inner squares sides squished in, and it's called Unnamed. It was from Old Chelsea Station Needlecraft Service, at old Chelsea Station post office NY, a mail order company begun in 1933. Originally they offered single full-size patterns through the mail.
I feel the maker of this particular quilt probably added her own design elements in the sashing strips and their circles. Those touches make very interesting secondary designs, signs of a talented and creative quilter.
Jan in VA