I thought it might be nice to work with a variation on Lesson 1 (Spread Triads) – In this exercise we play spread major triads a tri-tone apart, a sound which will work nicely over a dominant 7th chord with with a b9 and a #11 (or as a substitution).
This is one simple way to begin hearing larger intervals and shapes while still maintaining melodic and harmonic integrity. I like to work on the material slowly with a metronome while trying to sing and memorize each interval right from the start. This helps to internalise the new material quickly and exercise your analytical mind. By singing melody slowly over a drone in a key that fits the range of your voice the larger intervals will become easier to hear and to incorporate into your improvisation.
There is a PDF and video of me playing the lesson below. The melody is played through the 12 keys starting on Concert C7.