To me, one of the most valuable study practices has been the exploration of arpeggios (also known as "broken chords," wherein each note of a chord is played individually and in succession) played across all the strings. Like most guitarists, I began on six-string and soon graduated to seven- and then eight-string guitar. This month, I'd like to demonstrate some cool ways to perform a variety of arpeggios on the seven-string guitar.
An approach that has worked well for me is to devise a specific arpeggio fingering pattern diagonally across the strings, spanning over two octaves, for which I can then alter one or two notes in each octave to morph from one chord quality to another, for example, from minor seven to dominant seven or major seven. This way, the fingerings are visually and physically similar and thus easier to memorize.
Prog-Gnosis w/Tosin Abasi - June 2013 - Roller-Coaster Ride — Seven String Arpeggios