Traditionally, finishes were rubbed and polished to satin or semi gloss sheens.  I use the same approach to achieve the look the maker intended the piece to have.   After cutting the surface with 600- 800 grit finishing paper, I rub with multiple grits of steel wool, rubbing compounds and lubricant to achieve the finest look in cabinet finishing. 

The piano is first sanded with an inline sanded loaded with 500 grit paper.  Then sanded with 600 and 800 grit paper.  These steps completely remove all finish shrinkage and imperfections.

With the finish completely flat, the sheen is increased with steel wool and lubricant to a beautiful semi gloss sheen.

Just like the case photo above, the fallboard is sanded with 500 to 800 grit paper, before being rubbed with steel wool to a semi gloss sheen.