Here's the "whatsit" that has generated so much conversation here, on the Civil War Needleworkers forum and on the Antique Pattern Library regarding what this object actually is.
My first thought, echoed by others, was some type of lampshade cover, but the gas and kerosene lamps of the era required a central vent which this object does not accommodate.
Another suggestion was a skullcap:
Um, probably not!
A cover for a domed glass paperweight, again, probably not:
One plausible theory was a cover for wire food safe. I don't have an antique wire food safe, but I do have a rattan version:
My problem with this theory is the handle - like the lampshade cover there is no accommodation for the handle.
Other suggestions include workbasket cover, pillowcover, footstool cover and finally a piano stool cover:
And I do believe we have a winner!!!
Despite having a piano stool, it had not occurred to me to try it on there - but when I did, it was a perfect fit!
It's my opinion, based on materials, construction techniques, color and style, that this cover dates to the late 1870's - 1880's and reflects the Victorian craze for all things "Oriental".
I feel it was constructed, at home, by a middle class lady, to ornament her parlor - which was probably not as ornate as the parlor seen above. She most likely used a published pattern for the crochet and then added the purchased chenille fringe.
A note on the fringe: It was suggested on one of the forums that the chenille "tails" had been knotted in place, not woven as I suggested. However, a closeup photo of one of the tassels clearly shows that it was woven in when the trim was constructed:
Wouldn't it be a wonder to have such trims available for purchase now!
Once I found the proper term - music stool, not piano stool - I found a number of patterns in the period magazines, using a variety of techniques:
This one in crochet even has a central diamond pattern similar to my example!
Thank you so much to everyone who offered suggestions - it's been so much fun exploring the possibilities