Could you explain a little more about "Bringing in a third melodic melody
Certainly, with the usual proviso that what I do or think might bear little or no resemblance to “common practice” or in fact, anything that musicians do.
I like the effect of more than one thing going on at once. I guess many pianists do, hence the constant preoccupation with counterpoint, cross rhythms and the like. There is something exciting about it and I find it imparts real life to my improvisations in a way that homogeneity and square-toed coincidence cannot. To this end, I found I had to develop some way of consciously getting it into my improvisations. Trying to imitate formal baroque fugues and inventions does no harm but I did not want to waste years growing an ability which is a rough mental parallel of multiplying two big numbers in my head. In any case I needed some sort of ongoing approach general enough to encompass sounds quite outside the range of baroque counterpoint – in particular asynchronous playing incompatible with musical notation.
Therefore I started from the opposite end of the learning curve and worked from the realisation that whatever the density of musical events, they have to be played with the fingers. Once I could improvise reasonably interesting two part inventions, not necessarily synchronous and mostly not notatable, I began inserting other notes via two finger combinations – i.e. double notes. After a while these generate parallel musical events which are independently audible.
Sometimes the oddest comments by the unlikeliest people are profoundly true and stick in the mind. My talented friend Matthew Collett, of Pianoworld, at one of his wonderful Fazioli parties, in connection with some point or other to do with hand displacement (exactly what has faded into irrelevance) made the statement that when we play, when we create sound, we are always perpetrating an illusion, we are never making statements about musical facts, we are making real magic which casts a spell on the listening mind and deludes it into transcending itself, into hearing things which are not objectively present.
This goes straight to the heart of improvisation. And here is where I part company with all orthodoxy, because I assert that intention and effect are most often entirely different. Listen to a recording of your improvisation; any improviser listening to his or her recording knows what I mean - “Did I really play this ! How on earth did I think of that ?” It is another obstacle to the learner of improvisation, this admission of the power of irrationality. It doesn't come easily to the Western mind schooled in cause and effect.
Pardon that digression, but it is relevant. To return to multiple parallel events, begin by inserting double notes in either hand or both hands, into your initially two part inventions. Use them in as many finger combinations as you can imagine until the whole vocabulary becomes part of permanent haptic memory. After a few months, maybe longer, a wonderful thing starts to happen. You will find multiple strand counterpoint forming automatically through your fingers as sure as if they had little minds of their own. It will strike you when you listen to your recordings.
Now once you have established that fluency, it is possible to push your mental arithmetic to imitate baroque fugues and the like – if you really want to. I must admit that I do not. I find the spectacle of a young person, in particular, immersing their own aesthetic in music of the past, whether baroque fugues, stride, ragtime or some other bygone form, rather sad. Personally I have a horror of living someone else's dream in music, but if that is the way which gives you enjoyment then go for it – the above procedure will secure it for you.