Improvising with an Intervallic approach is a great way pull from the chromatic scale and achieve an outside or modern sounding phrase. Choose a few intervals and a starting note, then play a phrase. Notice that direction in pitch, up or down, and rhythm are open to whatever you might choose.
If you are new to this way of playing or practicing try starting with two intervals and a simple harmonic background. Alternate between the two intervals and remain aware of the dissonance or consonance each note has with the harmony. Try choosing the interval direction, up or down, to regulate dissonance. For example, if the chord is Cmaj7, the current note in the phrase is E and the interval played is a minor 3rd. Then ascending to G is consonant while descending to D flat is dissonant. Here the interval is the same, but the directions are opposite.
The Intervals min2, maj2, min3, and maj3 are a good place to start and are a staple of many phrases. Notice what happens when pairing certain intervals. In some cases we find that particular interval combinations will have an associated scale other than chromatic. The maj3 and maj2 will tend towards the whole tone scale. So an occasional min2 or min3 interval will help break out of that.
Keep in mind that when playing any single-line phrase we are really playing intervallic. Here we are deliberately thinking about the intervals and choosing which to play based on a set or series of intervals. Enjoy and let me know how it’s going.