The 6/9 chord is a pentad in which a major triad is extended with a sixth and 9th above the root, but no seventh, thus: C6/9 is C,E,G,A,D. It is not a tense chord requiring resolution and is considered a substitute for the tonic in jazz. Its constituent notes are those of the pentatonic scale.
A dominant ninth is a dominant chord with a ninth, but that’s not what a major ninth chord is. The major ninth chord (or just ninth chord), as an extended chord, typically includes the seventh and ninth along with the basic triad structure. Thus, a Cmaj9 consists of C E G B and D . When the symbol “9” is not preceded by the word “major” or “maj”, the implied seventh is a dominant seventh—e.g. a C9 consists of C E G B♭ and D.
A sixth chord is any triad with an added sixth above the root. For example, a major sixth chord built on C (denoted by C6, or CM6) consists of the notes C, E, G, and the added major sixth. Here are the 5 shapes for the sixth chord found in the open position. Other sixth chords (such as F6 and B6) can only be played by using a barred form of one of these 5 shapes.Read More »Sixth Chord Shapes
An added ninth chord (add9) is a major triad with an added ninth. Added ninth chords are different from other ninth chords (9, maj9) because the seventh is not included. Read More »Added 9th (add9) Chords (Closed Position Shapes)
In most sheet music books, Cdim or C° denotes a diminished seventh chord with root C. Some modern jazz books and some music theory literature use Cdim or C° to denotes diminished chord, while Cdim7 or C°7 denotes a diminished seventh chord.
A diminished 7th chord is comprised of a diminished triad ( is a triad consisting of two minor thirds above the root) plus a double flattend 7th (same note as the 6th). It’s primary use is to lead to the tonic, or root note of the song.