That would explain why I hear an ascending aftertone when I strum certain chords and let the 'ring' until they disappear. Thank you, JiC.

Superficial comment:

The usual situation is that when a string is pulled away from it's rest position it is stretched slightly, and thus the initial frequency is higher for large amplitude string motions than for the lower amplitudes as the motion decays. The base frequency normally decreases, and pitch goes down as the note dies.

In a chord, the "beats" between strings can be quite complex, and it's possible for a harmonic from one string to feed another string to produce a sense of "rising pitch" during the decay.

If the bridge on a plucked instrument is "normally non-linear" it's also possible for some of the lateral vibration of the string to excite the longitudinal vibration mode of the string. Since for most string materials the "wave velocity" for the longitudinal mode is 4 to 6 times that of the lateral mode, a "ringing upward" sound can result.

(Several other possibilities ignored in the interest of simplicity.)

The bottom line is "don't suggest a simple question if you want a simple answer." The simple ones are usually the toughest to get right.

John