The same as when we sing, the precision of our pianistic tuning also depends on how well acknowledged the piece is at a purely intellectual level. This fact is strongly related to how we process the information encrypted at the score at a sight reading level.
In spite of the fact that when we read we need to objectively asses each note in terms of its specific pitch and duration; it is also fundamental to develop the skill of predicting how certain note groups sound in relative terms in order to follow the score properly. In general, it is our projective aural skills the ones in charge of keeping all the sound emissions in line with what the score sets.
This phenomenon also defines the safe speed at which we can manage a performance. We will always be playing on the safe zone if we can manage to keep our fingers a fraction of a second behind our abstract processing. The pitch picturing mechanism, the construction of an imaginary entelechy which summarizes: pitch, duration, volume, texture and relative behavior, is the responsible of orientating our focus to produce rich sounding compounds instead of singular attacks.
The key to success in achieving a perfect performance is to realize that we need to cope with much more that the pitch when we play the piano. This is the main concern when delivering our specialized piano lessons.