Confuse about how to make a tiles to support retina device

I have a map picture(15772*13796) so I break them to tiles using gdal2tiles(512*512px not 256*265px) for support retina device but is this correct?

Because I a had read
this issue
and this. They are talk about scale and pixel ratio of retina device so
I think i break them to 512px not 256px it’s only extend picture size but i expect the output tiles should have quality and clearly(like to use scale(256&scale=2)) when see on retina device. Can someone suggest how can i do this.