It has been noted that straight-string pianos drop [in pitch] very easily. Crossing favors the uniform reaction of the frame and the bridges. Even in cross-string pianos, when tuning by raising it by about a semitone, the reaction of the structure causes the tuning level to drop again, especially on the high notes. So much so that one must aim above 440 to then stabilize. Evidently, in straight strings, the reaction and movement of the structure occurs in only one direction, that of the strings (parallel). Crossing favors a sort of compensation of forces acting in different directions. Good stability, obviously, also depends on the proper sizing of the strings. In the calculation, the Company takes into account finding a compromise between disharmony and tension. Greater uniformity and gradual progression of tension favor stability. However, larger sizing increases disharmony. The load on the soundboard is also important and, obviously, so is the stability of the pins. I hope I have been clear enough. In the grand piano, the phenomenon is a bit less evident.