Double wing formations based on small high enclosure

Well-developed formations  

Starting with the corner enclosure (marked stones), Black with further plays at a or b, and one of p, q and r, can make an excellent double wing formation.

Classical idea  

For example in Japan of the Edo period this was probably taken to be an ideal result for Black. The positioning of the marked black stone on the fourth line makes it harder to reduce this framework near the corner, than in the case of the small low enclosure. Therefore White commonly intervenes to stop Black constructing the complete double wing formation.

Reduction technique  

The shoulderhit here is the recognised technique for trimming down the framework. See also Reducing an enclosure framework by a shoulder hit. In this case White has a chance left to invade the corner, later. The stones played on the outside would be at a suitable distance to minimise the effect of influence Black would gain from an invasion

Fourth line extension  

Therefore one can understand why Black in modern times prefers the extension on the fourth line. This play reaches for a larger final territory. The logic of go means that currently the framework is looser - successful invasion is more likely; but the shoulderhit reduction isn't available to White.