This can be traced back to the days of plainchant, in which a device called
"hocket" (French for "hiccup")
But the effect in Tchaikovsky is very different from the hocket of Machaut and his mates (and different even from the hocket device as used by the avant-garde naughty boys). In Tchaikovsky it's more subtle, more mysterious if you will, as I said, I don't think it's there by accident.
In fact, I'm not sure it's the same effect at all - in Tchaikovsky it's a question of there being something there, you can hear it, but you can't find it - it isn't written down, it appears only when the music is performed.
All the best,
Lawrence
http://lawrenceyates.co.uk