When teaching improvisation to players of melody instruments, I like to differentiate between the skills needed to perform a solo or over a bass line, two contexts which call for radically different reflexes –even opposite at times.
Initially it may seem that performing with a bass line is the most obvious choice and should be the first technique to learn. However, over the years, I have noticed that concentrating on creating solo pieces, has many advantages, including getting closer to the instrument, developing a harmonic consciousness and acquiring a working understanding of thorough-bass.

My proposals can often be demanding and there is a risk of overwhelming the student with too many notions of harmony. However I always strive to find a good balance between cognitive activity, planned thought and harmonic anticipation on one hand and spontaneity and intuition on the other. Otherwise improvisation would just be the story of our frustrations.

Possible fields of investigations:

I With Bass

Grounds, Chacones and Folies
Improvisation with bass.
Improvisation over a Ground Bass is one of the essential skills required of our art.
How to develop a striking narration, using contrast, amplification, breaks or linearity when performing over an unchanging harmonic canvas.
How to devise solutions when improvising in a group with several musicians: alternating, taking the floor, inviting, assigning the voices; roles for a simultaneous improvisation (structured protocol or spontaneous responses).

The Art of the Partimento
Improvisation with bass.
Longer than a Ground Bass, using a Partimento is an excellent solution for improvising chamber music. This developed harmonic support is a mutual reference point, which allows not only the chance to work on affects and variation but also on counterpoint and harmonic compatibility in the context of group improvisation.

Fantasticus
Improvisation with bass.
The point here is to make use of all means available. To research, even invent, a code for free improvisation between treble and bass in the baroque style of the second half of the 17th century.
Here nothing is prepared, no Ground Bass or fixed Partimento on which to lean. We will see how the musicians can nonetheless direct and lead one another, may it be by melodic inflexions or anticipations and incitements of the bass, through a newly created common musical landscape, gradually evolving as they go.
Shared knowledge of this style will enhance the experience!

II Solo

Preludes and Fantasies
Solo improvisation for all melody instruments.
In this class, we will improvise with absolute freedom, while keeping in mind the duty of form.
We will learn how to produce an inizio (opening), setting the tone, metre, texture, etc., how to modulate and find one way in the twists and turns of a tonal plan without loosing sight of the expressive meaning of the modulation, how to develop drama, and how to conclude.

Harmonic Reflexes
This class is intended for string players (violin, viola, cello).
The goal is to demonstrate how to develop accurate polyphonic reflexes that allow for more immediacy and build up self-confidence beneficial to improvisation. It is a system I have developed personally and was created very much by trial and error …
Hand Play: cadential exercises, typical harmonic movements, sequences, etc. How to build a repertory of gestures and sounds and create base material on which to build.

Sei solo: An approach to improvisation through Bachs works for solo violin and solo cello.
Solo improvisation for all melody players.
Deep harmonic knowledge is required.
Between extravaganzas and conventions, the Sonatas and Partitas seem an unreachable ideal. The works are so sublime and usually so assimilated that one forgets to question them.
With improvisation as our goal, we will start from the masterpieces and will lose ourselves along the way: transposing, paraphrasing, rewriting, looking at other possibilities, correcting, normalising etc.
There are no limits to the way the material can be altered. Although deep respect is always accorded to the original music, hopefully leading to a greater knowledge and a renewed admiration of the works!