Is there a name for the meter used in Clementine:
Drove she ducklings to the water
Every morning just at nine
Struck her foot against a splinter
Fell into the foaming brine
or in Schiller's Ode to Joy:
Freude, schöner Götterfunken,
Tochter aus Elysium,
Wir betreten feuertrunken,
Himmlische, dein Heiligtum!
Most descriptions I've seen of trochaic tetrameter don't mention the possibility of the lost syllable on alternate lines.