The pentatonic scales are a great way to learn how to improvise on the piano. As you might expect from the name, a pentatonic scale has five notes. For example, a C major pentatonic scale consists of C, D, E, G, and A or the first, second, third, fifth, and sixth notes of the major scale. Or for F major, the notes in the pentatonic scale are F, G, A, C, and D. As long as you know your regular major and minor scales, you can always figure out your major and minor pentatonic scales. Learning the formula for the pentatonic scale allows you to put together a wide array of note combinations for your piano improvisation.
When you're first attempting improvisation with a pentatonic scale, many people find it easiest to focus on the right hand only. Let's go back to C major, which has the notes C, D, E, G, and A. Try using just these five notes to make up right hand melodies. Don't be afraid to experiment with different combinations of notes and different rhythms. Try playing higher notes and then lower notes to determine which sound you like better. With only five notes, you should be able to think about the notion of improvising and have the freedom to improvise lots of different types of music without getting overwhelmed.
Focus on putting together interesting melodies instead of just playing single notes so that you form whole phrases. Some people find it helpful to make their phrases legato or smooth so that the notes are connected and not choppy. Don't lift up one note until you're ready to play the next note to help make the phrases more connected.
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