This is a lovely waltz, and I’m surprised it hasn’t posted yet as it seems to be fairly well known as well, though waltzes rarely get their fare share outside of ceilis.
As far as I can find, it is in fact originally Norwegian, adapted from Gotthard Ericksson’s "Kristiana-Valsen". It was first recorded by Scottish two-row button box player William Hannah in 1931.
Incidentally, the C part is oddly similar to the song "One Kind Word", recorded by the Gallowglass Ceili Band (below).
Re: The Oslo
Haven’t played this for many years.it was a very common tune in Shetland in the 60s but in a more flowing form than the above. Also the third part was in C.