An element meaning “extension” in the term ómataima “vocalic extension” from both versions of Tengwesta Qenderinwa from the 1930s (TQ1: PE18/34) and around 1950 (TQ2: PE18/86), as well as other linguistic notes from the 1960s (VT42/24-25). Sometimes Tolkien used an alternate form ómataina for “vocalic extension” (PE22/137; WJ/371, 417), but I think the final element in this variation is a nominalized form of the adjective taina “stretched, elongated”. The noun taima seems to be a combination of √TAY “stretch” with the instrumentation suffix ✶-mā, so I would use this noun with the sense “extension = an extended thing”, as opposed to Q. tailë for the process of extension.