The headword is aorist passive participle of tetrai/nw, masculine accusative singular or neuter nominative/accusative plural; the former if, as is reasonable to suppose, it is extracted from the epigram quoted.
[1] Greek Anthology 6.296.3-4 (read o)/rtugi), attributed to Leonidas of Tarentum: from a list of items dedicated to Hermes by a retiring hunter. See Gow and Page (vol. I, 123), (vol. II, 358-359), and further extracts from this epigram at alpha 522 and alpha 4229. As Gow and Page remark, the perforated pipe is evidently a quail-call, with holes drilled so that it produces a whistle by which a hunter might attract the birds (vol. II, 358). They also note that, while quail-calls have been employed by hunters in recent times, this seems to be the only mention of this type of hunting instrument in antiquity (ibid.).