Does anyone know this piece?

There was a song my mother made me practice growing up. Because of the tempo I think it was a waltz. I’ve been trying to identify it and haven’t been able to despite scouring literally hundreds of pages of sheet music and listening to hours and hours of waltzes via You Tube. If anyone on DU can help to identify it I would be very appreciative. Here is what I remember of what the beginning sounded like:

Play middle C and E together, then play D and F together, then play E and G together, then play D sharp and F sharp together, then back to E and G. Repeat D sharp and F sharp and E and G two more times.

I can hear more of it in my head but can’t find the key combination to it on the piano.

Thanks.