Turnabout is fair play, as they say, and we’re going to use the concept to make life and arpeggio study more interesting. This project is really all the previous projects in one with a twist. Ascend with either the triad or octave (or both, first one, then the other) and then descend with the key a half step up. Example: C E G – Ab F Db [i.e. the Db major triad] [continuing] – D F# A – Bb G Eb [=Eb major triad] and so on. Come back down the same way. Repeat, this time descending on C and ascending on Db, etc.
Example 2: Full octave. C E G C – Db Ab F Db – D F# A D – Eb Bb G Eb and so on.
I should need to remind you by now that after you feel comfortable doing this using only one rhythmic value (quarter notes or 8th notes), increase the challenge and the fun by inventing the rhythms as you go along. Or: pick a rhythm and use it throughout, e.g. long short short (bum tiddy bum tiddy, etc). Slur everything first (it’s harder). Later: tongued and also mixed.
Do this for all arpeggio types: major, minor, dom7, diminished.
The truly ambitious can continue the fun by making the turnaround arpeggio a different distance away, i.e. instead of always a half step, jump a whole step or minor third, or major third, or…. You might have to write irregular progressions like these out to keep track of where you are.