This is an iris that's been handed down in my family for several generations -- four at least, maybe more. My sister and I know it as 'Nana's iris,' Nana being the nickname in our family for great-grandmothers. Our Nana was born in 1886, but it's entirely possible that she got this iris from her own Nana.
I have some old irises in my garden -- Alta California, Sindjkha -- but I am pretty sure that this particular iris is Iris x sweertii, and it is the one of the oldest of all.
The irises of the Middle Ages were species irises; the best known are I. pallida and I. germanica. I. x sweertii is a naturally occurring hybrid, probably the offspring of I. pallida and ... something else. We don't really know. It's believed to have entered commerce by 1612, and is named for a Dutch nurseryman, Emanuel Sweerts (1552-1612). Sweerts may or may not have depicted this iris in his Florilegium, or sold it himself, but he was a well-regarded authority on flowering plants in his day.
The iris is not especially popular now. The flowers are small; modern iris enthusiasts often comment that the falls are 'pinched' and 'mar the form.'. To its credit, however, I. x sweertii has pure white petals, a delicate lavender plicata1 edging, and an astonishing grape-y fragrance. Your modern hybrid irises have no such scent.
It is not to be found in commerce. The best way to get it for yourself, if you want it, is to track down someone else who has it and try to arrange a swap of rhizomes. (No, I am not in a position to swap right now; maybe in a few years).
1Plicata is Latin for 'pleated' and when applied to irises refers to a flower with one colour as the 'ground' and another edging the falls, standards, or both. The second colour can be solid or can resemble stitching, feathering, or stippling. I. x sweertii is thought to be the ancestor of all other plicata irises.
Roberta Hill Whiteman