When you play Fusion, Funk, Jazz, Blues, Hip-Hop or R&B, you will often find chords which extend past the 7th, notably various types of 9th, 11th and 13th chords. These higher numbers are formed by repeating the scale from which they are derived over two octaves. Thus, in the higher octave the 2nd becomes the 9th# the 4th becomes the 11th and the 6th becomes the 13th# as shown here in the key of C.
Most chords are made up of various 3rd intervals stacked one on top of the other By going through a scale in thirds (i.e. skipping every second note) it is easy to create chords up to a 13th. A major triad (3 note chord) contains the degrees 1, 3 and 5 of the major scale. A major 7th chord is created by adding the 7th degree on top of the major triad. This 7th degree is a 3rd above the 5th of the chord. By adding another 3rd on top of the major 7th chord, a major 9th chord is created. By adding another 3rd on top of the major 9th chord, a major 11th chord is created. If you add another 3rd on top of the major 11th chord, a major 13th chord is created. The 13th is as high as the chord can go, because if you add a 3rd on top of the major 13th chord, you end up with the root note of the chord again.
Depending on the nature of the 3rd and 7th degrees of the chord, 9ths 11ths and 13ths may be either major, minor or dominant in quality. E.g. if you add a 9th degree on top of a dominant 7th chord, you end up with a dominant 9th chord (usually just called a 9th chord). If you add a 9th degree on top of a minor 7th chord, you end up with a minor 9th chord, etc. Here are the formulas for some typical 9th, 11th and 13th chords.