Improvisation - Major Scales
A thorough knowledge of scales and their uses is essential for the aspiring improviser.
Scales form the framework from which you may select notes that should work as an improvisation over any given chord progression. "Should work" being the operative words, because not only the key, but the feel and the chords used will determine which scales can be used where. And ultimately, as in substitution, you need to use your own judgment.
If playing in a major key, the most obvious scale to use is the major scale. For instance, the A major scale would be a natural choice for the key of A major. Naturally, we are assuming that all the chords being played are diatonic. Chromatic chords must normally be treated differently and will be dealt with separately.
So, in the following table, we have the diatonic chords in C major. Underneath are the notes in each chord, and under them, the remaining notes of the scale which are treated as passing notes.
(A passing note is a note that does not belong to the chord, but which forms a bridge from one chord note to the next. Passing notes can be accented or unaccented. That means they can be used on an emphasised part of the bar or an unemphasised part of the bar.)
The chord notes are the most important ones. The other notes will either create new chords or discords (usually lasting only a moment). For instance, if you play A while the C major chord is in use you will create C6, but if you play F, you have a discord.
If we extend our triads into quadrants, we have only three passing notes per chord, which means that four out of the seven notes in our scale will always be right. (In practice, the playing of the seventh note over a triad will produce a quadrant effect anyway.)
For information on improvising with minor scales, buy Contemporary Music Theory. (This link will take you to Createspace.com, a subsidiary of Amazon.)