In music theory, inversions higher than the third require extended chords; the fourth inversion requires at least a ninth chord, the fifth at least an eleventh chord, etc. Regarding these extensions, the writer Michael Miller notes that:
The fourth inversion of a ninth chord is the voicing in which the ninth of the chord is the bass note and the root a minor seventh (or corresponding compound interval) above it. In the fourth inversion of a G dominant ninth, the bass note is AâÂÂthe ninth of the chordâÂÂwith the root, third, fifth, and seventh above it, forming the intervals of a seventh, second, fourth, and sixth (or corresponding compound intervals) above A, respectively.
The fifth inversion of an eleventh chord is the voicing in which the eleventh of the chord is the bass note and the root a fourth (or corresponding compound interval) above it. In the fifth inversion of a G dominant eleventh with eleventh, the bass note is CâÂÂthe eleventh of the chordâÂÂwith the root, third, fifth, seventh, and ninth above it, forming the intervals of a fifth, seventh, second, fourth, and sixth (or corresponding compound intervals) above C, respectively.
The sixth inversion of a thirteenth chord is the highest possible diatonic inversion, since the diatonic scale has seven notes. (The "seventh" inversion of the dominant thirteenth chord is root position.) Higher inversions would require chromaticism and either nonscale tones or scales with more than seven tones.
Any voicing above the bass is allowed. For example, a fourth inversion must have the ninth chord factor in the bass, but it may have any arrangement of the root, third, fifth, and seventh above that, including doubled notes, compound intervals, and omission of the fifth (A-G-B-D-F, A-B-D-F-G-B, A-G-D-F, etc.)