Provenance is key. If they were Mikimotos, they would have an authentic Miki clasp with the Mikimoto trademark and you would hopefully have paperwork indicating that you had Mikis. Failing that you may assume they are not Mikimoto.
Also, just FYI, Mikimoto clasps are counterfeited, and it is not unknown for Miki clasps to be strung onto non-Miki pearls as sellers try to make more money, so this is why documents matter.
We get a number of people coming to the forum with graduated strands of this sort which belonged to grandparents, although the size range for the pearls is usually a little larger. Graduated strands were sold in Japan in WWII and Korean War era, and servicemen brought them home. They were more affordable because pearls are sold by weight and graduating the strand means the strand weighs less.
If you feel any attachment to them, have you considered cleaning and restringing them? Use a mild soapy water solution (not detergent) wiping each pearl with a soft microfiber cloth, and you may see they are more lovely than you expected. I have a restringing tutorial stickied on the Lowly Beaders Club forum-- it isn't hard.