This question was inspired by playing around on the piano. I held some keys gently in one hand without letting them sound: sometimes one, sometimes two a fifth apart, and sometimes a major triad. I then played a scale with the other hand. Sometimes the held keys were below the played keys and sometimes above. No use of the pedals.
As expected, the held keys resonated after the scale had finished. This occurred both ways round but when the held keys were below, they did not sound at their normal pitch but at the pitch of the note that triggered them.
The effect was most noticeable with octaves but, despite the well tempered 12th not being quite the third harmonic, it also worked.
I doubt that I am the first to think of this but is it ever used and, if so, how would it be notated?