The chromatic scale contains all possible notes between a given note and its next repeat an octave higher or lower. All of the notes in a chromatic scale are one semitone apart. To get to know all possible ways of describing any note in a given key, it is a good idea to call notes all notes which are not natural to the key sharps when ascending and flats when descending.
The following example demonstrates two octaves of the C chromatic scale. Take it slowly at first and memorize all the fingerings so you can play it smoothly and easily without hesitation. It is a good idea to make the chromatic scale part of your daily practice, as a good knowledge of the chromatic scale makes it easy to quickly transpose any melody, as well as making it easier to learn any new scale because it contains all the notes commonly used in music.
Once you can play the C chromatic scale, you already know all other chromatic scales, e.g., to play the E chromatic scale, you simply start on the note E and play all possible notes until you arrive at the next E note one octave higher or lower, as demonstrated in the following example which contains two octaves of the E chromatic scale.
When you can play the chromatic scale, it is easy to work out the major scale for any key. For example, to play the E major scale, start on the note E and follow the major scale pattern (tone, tone, semitone, tone, tone, tone, semitone) until you arrive at the next E note an octave higher. If you are still unsure of the notes, think do, re, mi, fa, so, la, ti, do. The following example shows the E major scale written without a key signature. This is to encourage you to memorize which notes are naturals and which notes are sharps.
As well as the major scale, it is important to be able to play the Blues scale in any key. The following examples show two octaves of the E Blues scale and then