These are villanelles by Michael R. Burch, including an adaptation he calls a Trinelle or Triplenelle. There are also related poetic forms with refrains, such as the rondel, roundel and rondeau.

Villanelle: The Divide
by Michael R. Burch

The sea was not salt the first tide...
was man born to sorrow that first day,
with the moon―a pale beacon across the Divide,
the brighter for longing, an object denied―
the tug at his heart's pink, bourgeoning clay?

These are villanelles by Michael R. Burch.

Remembering Not to Call
by Michael R. Burch

a villanelle permitting mourning, for my mother, Christine Ena Burch

The hardest thing of all,
after telling her everything,
is remembering not to call.

Now the phone hanging on the wall
will never announce her ring:
the hardest thing of all
for children, however tall.