Improvsing over only the tonic

[stillofthenight]

I am trying to improvise over just one chord for 4 bars (looping)...the tonic (I) chord. How would you define a phrase for this one chord if it is at all , according to music theory, possible to make phrases over just one chord. I understand that the basic phrase model incorporates T-D-T harmony for a conclusive phrase, but in my case...there is just one chord. I suspect one would need to just think in terms of scale degrees...but I just want to know what others think.

I am also familiar with the idea of motives which are the smaller components of a phrase, and do not generally cadence. Which scale degrees should I be focusing on and avoiding (in general) to improvise motives on the single tonic chord?

And as mentioned earlier, which scale degrees should I be focusing on and avoiding (in general) to improvise phrases on the single tonic chord?

[nystul]

I don't think the principles behind the melody really change because of using one chord.  The notes that belong to the harmony will typically be consonant and stable, and the other notes have various degrees of dissonance.  The dissonant notes usually resolve by step (one scale degree up or down) to a consonant one.  Thinking in scale degrees is probably good, but it comes down to experimenting at the keys and hearing how the notes interact with the chord.

"Row, Row, Row Your Boat" is probably the most famous one chord song.  It has a very safe melody, in the sense that every note on the beat is a chord tone.  The only dissonant notes are the short passing tones that connect one chord tone to the next.  In comparison, when you do use a dissonant note on a strong beat, it creates a bit of tension which may sometimes be desired.

[quantum]

You could look into two part species counterpoint.  There is the notion of implied harmony, so you don't totally get away from V-I cadences.  However, it does take you further away from chord based thinking and into the creation of melodic lines.  Staying with two parts will also inhibit the creation of triadic harmonies.