It's all about resonant frequencies.
Basically when you strike any percussion instrument a range of overtones (frequencies) a fundamental note (the musical note which one tunes to, the lowest and loudest of all these frequencies) a produced, with your tom there is a resonant frequency that your ride is also producing, when that resonant frequency is played back to a percussion piece the piece will oscillate. This phenomena is observed when an opera singer hits a very high note and breaks a wine glass (the opera singers note is the same as the note you get from striking the wine glass, or atleast one of the frequencies are common). This effect can happen from drum-cymbal, cymbal-drum, cowbell-hats, drum-snares etc.
Theoretically (I haven't tried all these) these methods could work:
- Tuning the effected object.
- Placing down a new head and tuning (certain heads will produce a different combination of overtones, these overtones give them a characteristic sound...fat, wet, warm, deep etc.).
- Moving an object to a different spot.
- Dampening/muffling one or both of the objects to change what overtones will be projected.
- Placing an object inbetween the two objects to block out certain overtones (ie. curtain, other percussion piece).
- Applying dampening in other parts of the room (some overtones/group of overtones bounce off of the walls and change in characteristics, dampening them kills off these boomy overtones, like in a recording studio).