Hi Wim, regarding the SAT not picking up the partial, try standing it on end when this occurs. The common explanation is that it is caused by a standing wave. Here's something to watch out for with the SAT- I find that it is a good idea to be sure I tune a piano aurally every 2-3 days. Otherwise I find it far more difficult to analyze the tuning of the piano.
This PTG archive page provided courtesy of Moy Piano Service, LLC