Using aspect ratios for responsive design breakpoints

I am trying to figure out what the best way to make my site responsive would be. It seems a lot of people base responsive design off screen pixel dimensions, but I feel breakpoints in aspect ratio would lead to the best design for my website.

I just want to know if this is an unusual approach with any potential disadvantages, in any way. Of course, I will still use screen dimensions in order to adjust things like font sizes, but the majority of the css will be re-jigged based on aspect ratio.

I'm just a bit concerned because I don't see this approach talked about much anywhere.