This poem sounds like what it's about: a waltz. Waltzes are songs that are written in ¾ time, and the dance that accompanies them has three steps. The waltz is a graceful, intimate dance, normally performed with a male and female partner. Our speaker is taking the role of the female in this poem.
Just like a waltz, each line of the poem has three distinct beats. Any beat that's a little less defined – if you search, there are a few – is like one of the father's missed steps.
But this poem has musical qualities beyond being like a waltz and having three beats. The rhymes and easy grace of the writing orchestrates the sound of the poem so that it would be fit for any ballroom. Even something as noisy as pans falling of the shelf is graceful in this poem – they don't clatter or crash, they slide, just as dance partners slide across the floor.