Greg brings up an interesting point, which is probably a side issue since murchana seems to be a concept for which I don't see a ready English equivalent. It is amusing that some of the best Indian teachers are more likely to use translated English terminology when teaching English speaking students, as compared perhaps to Western teachers who may (this is a gross overgeneralization) be more inclined to relish in the exoticism of the lingo. My teacher (also of Etawah gharana) generally doesn't load me up on Hindi terminology. He refers to "exercises" instead of paltas, "practice" instead of riyaz, "pulling" instead of meendh (although he's about half and half with that one), etc. However, there are some terms best left untranslated...alap, gat (although he often refers to a "composition"), taans instead of "runs", tihai, etc.
But if he ever starts telling me the ascent of Yaman is Ti Re Mi Fa La Ti Do, I'm out! Sargam into solfege is a bridge too far!
Back on topic, my understanding of murchana comes from this website, where it seems more a theoretical construct showing how a shifting Sa creates, from the same swaras (SORRY! "notes") various new thaats/modes.http://chandrakantha.com/articles/scales.html