In this tutorial I answer a question I'm always getting asked: when improvising on the piano, how do I know which notes I can play against a particular left hand chord? As we'll see, the trick is actually to not think too hard about the chords, but rather to focus on the key the chord progression is in, and improvise on appropriate scales. The problem with focussing on the individual left hand chords is that it can make your improvisation sound choppy. A piece of music should be about more than its chord sequence, so it's better to focus on the general arc of the progression.
For each key, there are notes that will work with most chords that might crop up in that key. For example, when playing in C, the notes and natural chords of the C major scale will almost always sound right.
The natural chords are the chords that are built as triads from each note of the scale. However, within that scale there are a couple of notes that to be a little wary of. Firstly, the seventh: B. This is the leading tone of the scale, and causes problems because it pushes you to resolve back to C. The other note to use with caution is F, which makes some minor chords sound major.
These notes are useful as passing notes, but shouldn't be the focus of your improvisation. With these two notes removed, we're left with the C pentatonic scale. This is always safe ground, particularly if you're struggling and need something to fall back on. Expandrive Seriale here. Bear in mind that you shouldn't use only the pentatonic scale, as it has a very distinctive sound and can be limiting. Improvising becomes a little harder when the progression uses chords that are not natural to the key.
These are known as non-diatonic chords and are common in jazz. One option when dealing with non-diatonic chords is to ignore them completely, and use the major and pentatonic scales as usual. This can create quite a nice, jazzy sound. The other option is to use notes from the non-diatonic chord instead. The most important thing to remember is to listen to what you're playing; there are no 'right' or 'wrong' notes when improvising. If it sounds good, then play it!
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If you'd like to know more about blues, jazz or pop piano, you might be interested in my book, How to Really Play the Piano, which teaches improvisation through the medium of 12-bar blues and has loads of information on chords and harmony.