An experimental data point for your consideration:
Hanging on the wall of our island cabin in the Puget Sound is a
"tide clock." It has a face labeled with "High Tide" at the
"12:00" position and "Low Tide" at the "6:00" position. The hand
completes two cycles each "mean lunar day"--i.e., in the average
time that it takes the moon to make one apparent revolution around
the sky. It keeps excellent *long term* track of the tides even
if it may be significantly less accurate on a daily basis. In
particular, if I set the clock to "low tide" at the specific time
of the lowest low tide during a spring tide interval, it will
quite accurately read "low tide" again about two weeks later at
the lowest low tide of the next spring tide interval. In between
it will lead or lag the specific times of high and low tides by as
much as a couple of hours.