The ring verse is taken to presuppose the distribution of rings that Sauron believed was required to subjugate each of the major races in Middle Earth.
Now to me it would seem very odd if there were some "formula" for the number of rings of power needed to enthrall one race over another (humans require nine while dwarves take only seven). Obviously, for The Seven and The Nine Sauron had particular individuals in mind - though I don't know who might have been on such a list.
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