Perfect middle 3rd plural periphrastic construction

Dear Board,

The perfect middle 3rd plural often has a periphrastic construction with the perfect middle participle plus appropriate forms of εἰμί. While I was at school I never thought to dig deeper into this topic, but now it’s come back to me that it is quite remarkable this is the only periphrastic form taught as a rule in an introductory course.

It seemed especially strange to me since I started reading about the evolution from the proto-language, where a synthetic form should not be impossible. Consider for example the athematic present 3rd plural ending -ασι(ν) < *-ντι. If the original forms were primary *-νται secondary *-ντο, should these not very easily result in primary *-αται and secondary *-ατο, following a consonant stem?

Could anyone kindly shed some light on this form?

Mastronarde, pages 342-3 verifies your thoughts. The ν can be treated as vocalic (and becomes short alpha), and is seen in poetry and a few times in Attic prose.

Examples given are τετάχαται and ἐτετάχατο for the verb τάττω.