Hi,
For what it's worth the moonphase (percentage) differs from time to time during the day. It wil change for more than 10% in 24 hours.
Maybe this can clarify things for you:
http://astro.unl.edu/naap/lps/animations/lps.html
Look at the percentages when you take steps at 1 hour at the time.
I don't know where YoWindow takes the lunar information from, but I'm pretty sure it's a fair average at some point during the day.
Even when you google for it you will find all kinds of values varying from 45 to 55% for today (first quarter).
I've looked up the value at wunderground about 4 hours later than you did and it gave me 55%:

- Moonphase Wunderground.jpg (18.69 KiB) Viewed 10014 times
(This is in Amsterdam Holland, local time)
Hope this may be of help.
Fred
Edit: The actual first quarter phase today was at 05:29 Universal Time, 06:29 Local Time for both you and me (I think).