Waltzes in the classical world were usually written for dancing, like the famous Viennese ones. Chopin was maybe the first to compose them just for listening, the way composers like Bach and Handel did for the dances of their day, the allemandes, gavottes and such. Although you don't dance to the Chopin waltzes, you can often feel that rhythmic drive, spinning on an axis, while slowly revolving around the room, like a planet around the sun. Think Burt Lancaster and Claudia Cardinale in The Leopard, or maybe Kris Kristofferson and Isabelle Huppert in Heaven's Gate.
Of course the Chopin waltzes don't sound like Viennese ones transcribed for piano. It's the rhythm in each bar. All these waltzes are in 3/4 time, UM-pa-pa, with an emphasis on the UM, but the Viennese ones have a distinctive lilt, where the second beat is moved closer to the first. Graphically, it's going from 1xx2xx3xx to something more like 1x2xxx3xx. Notice that with this scheme, the time from the second beat to the third is the same as from the third beat to the second of the next bar. The result: if you tap out just the second and third beats, you hear a steady 2/4, superimposed on the 3/4! It's nice and very danceable, but doesn't sound right to me for Chopin, where I expect a slight delay after the third beat, more like 1xx2xx3xxx, say.
I was originally planning to perform eight waltzes by Chopin. I was surprised to learn that his lovely "Valse Mélancolique" in F# minor was found in 2012 to have been composed by one Charles Mayer, a Chopin contemporary from Prussia. Ok then, an opportunity to go for something else. Just so we don't settle on the notion that Chopin was nothing but melancholy or waltzes, I decided to take on his "Heroic Polonaise" in Ab B.147, as a bonus after the seven waltzes. It's again in 3/4 time, but the mood is plainly different: strong, fiery, proud, anthemic even. A change of pace, as my Mon Oncle Jean would say. I'm told that my Dad used to play the piece on the upright at home, his left hand flying over those 16th-note octaves (at 3:00). I was too young to remember, but the tune has always stayed with me.
Just to be clear, none of these pieces were played by me on a real piano; they're well beyond my ability. What I did for each piece was I changed the MIDI file representing the original score (which I found online at the wonderful Classical Archives) to suit my own taste, to make it sound like I would have wanted, had I been able to play it myself on a real piano. This is what I mean by a MIDI performance. You don't need any piano talent to do this. You just need some computer tools and plenty of opinions about what sounds better or worse. I have both of those.
A final word about "melancholy," the noun and adjective. You can look it up in a dictionary, but it's tough to tease apart from other related feelings: wistful, nostalgic, longing, languid. Imagine sitting at a window with a hot cup of coffee, on a rainy day in autumn, staring out at the falling leaves. You might not be jolly or joyful, but the feeling is not something to fight either, like gloom or despair. You can be melancholy and happy at the same time, especially if the coffee is good, the seat is comfortable, and you have all the time you need for an extended Chopin spree.