LilyPond and Finale are two music notation applications that can be used with TwinNote.

LilyPond

LilyPond is a free, open-source music notation application that runs on Windows, Mac OS X, and Linux. It can be used to create sheet music in TwinNote music notation.

Finale

Finale is a commercial (and expensive) music notation application that runs on Windows and Mac OS X. It can be used to create sheet music in TwinNote music notation.

MuseScore

MuseScore does not currently have the features to support TwinNote music notation, but maybe one day it will. (More info) It is a free, open-source music notation application that runs on Windows, Mac OS X, and Linux.

More information about software for alternative notation systems is available on the Music Notation Project’s Software page.