What matters
Tumblr Post Image dimensions at a glance
Tumblr's dashboard column is 540px wide, so post images scale to fit that width. A 540×810 (2:3) canvas takes up good vertical space in the scrolling feed without being excessively tall.
Tumblr's feed is a single-column scroll, so image height directly controls how much screen real estate your post occupies. Taller images command more attention.
Images wider than 540px get downsized to fit, wasting file size. Very wide landscape images appear tiny in the single-column layout.