If I’m in a store or listening to the radio, I instantly know if a Christmas song is being played. And it’s not because of the words; it’s the bells. Bells in songs are quintessentially Christmas. Of course, there are exceptions–AC/DC’s Hells Bells is pretty clearly not a Christmas song–but it’s a useful rule of thumb.
The downside with Chanukah is that there is not a single aural indicator that it’s a song for the holiday. Sure, there are numerous Chanukah songs–e.g. Adam Sandler’s well-kn0wn song, the Maccabeats’ great parody of Dynamite called Candlelight that’s been making the rounds–but what Chanukah needs is a distinctive instrument to signal that a song is in the spirit of the holiday. While a shofar is certainly Jewish, it doesn’t quite have the musical versatility necessary for the task. I’m not entirely sure though what a good instrument would be. Perhaps the harpsichord can be the indicator of Chanukah music? Or the flute?