What are the parts of improvisation?

[Bob]

I'm thinking...

Melody

Harmony (along with some kind of voicing)


That over the feeling of the rhythm (assuming their is a steady beat).


I'm wondering what I need to think of for improvising and what other people are thinking of when they improvise.

[quantum]

It is also possible to think of nothing at all.  

What one decides to concentrate on is completely up to them.  Choosing an element would bring such element into focus while placing other elements as secondary.  One can achieve different things by focusing on different elements.  

If you are feeling bogged down by choices, it is probably better to start with less restrictions.  

I think Ted gives some very good info here:
https://www.pianostreet.com/smf/index.php?topic=37873.msg431505#msg431505

[lostinidlewonder]

You can't really think too much or you end up composing and make mistakes. Somtimes I like to think about something that inspires an emotion within me, then the sound is like a story telling device for me, it can bring back past memories, bring the dead alive again, see into the future etc etc. Improvisation the thinking is different from playing composed pieces because you are very much the listeners as much as everyone else observing you improvise. The difference is that you can control which direction improvisation goes, like a rider on a horse, but sometimes the horse has thoughts of its own, which might be connected to you but seems so separate.  

[Bob]

I was also thinking a lot of times the improviser is given something -- like in jazz, usually they have the chord changes and then improvise a melody over that.  The tempo is known.  The style of beat is known.  Form of the piece is known.

[Derek]

I guess in a sense when I play I have a lot of "known" things I could start from, but there are so many "known" things at this point that they can combine in an infinite number of ways, producing the illusion that I started from nothing.  So, you have to start from somewhere and gradually build a vocabulary that can be combined in numerous ways.  For me, I started with a harmonic minor scale and a couple of chords from that scale, say i, iv, V. I messed around with just pulsing chords, strumming chords, broken arpeggios like chopin, etc. and I made up really simple melodies in the right hand. At first these were totally synchronous with the left hand, but as you gain confidence you can start making it more asynchronous. But it is a good way to start. And, if you're already an experienced pianist you might experiment with playing melodies in the left hand at the same time as the right hand. If you start in the same scale it'll actually sound decent even if it is random.  Another thing that I believe helped me start was recording these early attempts. you might play something you would have forgotten, or surprise yourself. This helps build confidence.