Is this an unusual shape for Satsuma vase?

It is, but there again, it isn't Satsuma, it's porcelain

 

is it even antique?

 

Nope

 

I think it is an old thing, Japanese porcelain

 

I think it’s Chinese, modern. Imitation of debased Satsuma.

 

LOL.

 

I think it could be old. Looks like legitimate wear to the gilding.

 

Satsuma is a place where a lot of porcelain is made so an object can be porcelain in the satsuma style.

 

Woodcarvings and even resin things can also be in the satsuma style, even oranges can be described so. Porcelain vases, OTOH, even if made there, are not described as Satsuma because that term is reserved for crackle ware earthenware pieces made by one particular clan.
In the antique trade, other Japanese crackle ware earthenware pieces are sometimes referred to as "Satsuma type" but porcelain never is.

 

It is an old Japanese porcelain vase of medium quality, as you say. Chinese pieces do not look like this.

 

thanks for the many responses.