Headcanons: On the Nine Rings
"And into this ring he poured all his cruelty, his malice and his will to dominate all life."
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The Nine Rings were designed as a discrete set, balanced carefully and meant to be used by a like-minded group working in concert.* All of the Nine function similarly in many ways. They have preservative abilities built into them, and a certain affinity for the natural world and for a certain type of harmony sought by elves. In this way, they are similar to the Three made later.** But each of the Nine Rings also possesses a particular specific quality, referred to as its "Grace," which interfaces with and enhances the abilities of that bearer. (Lelya's Grace is Guile, for example.)
Because of these Graces, the Nine actually communicate with their bearers in a very literal fashion, having each acquired a "voice" which speaks or sings within the bearer's mind. The power of the Rings is woven completely through both the fëar and hröar of the bearers, sustaining and enhancing them. But this is a two-way process, and was meant to be one from the start.
The Nine were, in short, designed to be used by a bearer, and, in a very real way, the Rings are not actually complete without their bearers. The powers of the Rings are necessarily, therefore, bound up very tightly in the minds and personalities of those using them. The Rings influence their bearers, but the bearers also influence the Rings.
If the Nine Rings had been borne by Elves as Celebrimbor expected, the bearers would likely have understood that this was happening and would have been able to exert some kind of control over the process, carefully crafting the personalities and strengths of the Rings to match the needs and desires of the bearers--just as Sauron was able to craft the One Ring to his own purposes and put into it what he needed there.
But the human ringbearers were never informed of the two-way flow of this process and therefore had no conscious control over it or understanding of it at all--which did not stop if from happening, of course. In effect, the "personalities" of the Nine Rings as they exist today are quite nearly accidental, and are drawn more from a sort of psychic leakage from their bearers than from any deliberate intent.
However, humans being humans, the bearers' subconscious needs and desires are very strong, and shaped the Rings regardless of conscious knowledge. Each Ring is now exactly what some hidden part of its bearer needed or wanted, a complement or balance or support to their personalities.
*Of course, the real reason Annatar designed the Nine as a set wasn't such that they could be used together by a group of elves to some noble purpose, but such that he could forge his Nazgul hunt-pack all the more easily, each of the Nine being linked to the others in some ways by the Rings' design.
**The Three, having been made separately from the Nine and the Seven, are similar but with certain key differences in their functioning. The interlocking flow from ring to bearer to ring again is absent, particularly; Celebrimbor was cautious by this point because he had begun to suspect some foul play at work.
((Usual caveat applies: Unless the other Nazgul, and, in this case, any given Sauron muse and/or Elven Ringbearer muse and/or Celebrimbor muse says so, this headcanon applies only to Uvatha.))