In my lab we have a saying: When all else fails, look at the data.
Here's some data for Veracruz, Mexico -- in the heart of a region often
cited as a good example of once-a-day tides. If we look at the data for
today, 4-September-2001 (end of summer, full moon) we see a plain old
twice-a-day tide: http://www.mobilegeographics.com:81/locations/6755.html?y=2001&m=9&d=4
0) New moon has the same effect as full moon; don't be confused by that.
1) In the June 22nd data, there is obviously a twice-a-day component riding
on the signal; it is not a plain once-a-day sine wave. Similarly in the
Sept. 4th data, there remains a small once-a-day component riding on the
signal; one of the low tides is lower than the other each day.
Remember, the overall effect depends on the driving force TIMES the
response function. If we reduce the once-a-day driving force, the
corresponding component of the response is reduced in proportion, leaving
only the twice-a-day component.
(Of course if you want to get fancy you can include additional components,
using the same methods.)