Dominant ninth 
A dominant ninth is a dominant chord with a ninth. A ninth chord, as an extended chord, typically includes the seventh along with the basic triad structure. Thus, a Cmaj9 consists of C E G B and D play (help·info). When the symbol "9" is not preceded by the word "major" or "maj", the implied seventh chord is a dominant seventh—e.g. a C9 consists of C E G B♭ and D play (help·info), and would usually be expected to resolve to an F major chord (the implied key, C being the dominant of F). The ninth is commonly chromatically altered by half-step either up or down to create more tension and dissonance. Fétis tuned the chord 4:5:6:7:9.
In the common practice period, "the root, 3rd, 7th, and 9th are the most common factors present in the V9 chord," with the 5th, "typically omitted". The 9th and 7th usually resolve downward to the 5th and 3rd of I.
Dominant minor ninth 
A dominant minor ninth chord' consists of a major third, perfect fifth, minor seventh, and minor ninth. In C: G B D F A♭. Fétis tuned the chord 8:10:12:14:17. In notation for jazz and popular music, this chord is often denoted e.g. C7b9.
Minor ninth 
The minor ninth chord is played with the third and seventh both flattened, or lowered a semitone. The formula is 1, ♭3, 5, ♭7, 9. This chord is written as Cm9. This chord has a more "bluesy" sound and fits very well with the dominant 9th.
Major ninth 
The major ninth chord is played with the third and seventh both major. The formula is 1, 3, 5, 7, 9. This chord is written as Cmaj9.
6/9 chord 
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.
Heinrich Schenker, though he allowed the substitution of the dominant seventh, leading-tone, and leading tone half-diminished seventh chords, rejected the concept of a ninth chord on the basis that only that on the fifth scale degree (V9) was admitted and that inversion was not allowed of the ninth chord.
In music, the second factor of a chord is the note or pitch two scale degrees above the root or tonal center. When the second is the bass note, or lowest note, of the expressed chord, the chord is in third inversion Play (help·info). However, this is equivalent to a gapped eleventh chord.
Conventionally, the second is third in importance to the root, fifth, and third, being an added tone. It is generally not allowed as the root since that inversion resembles an eleventh chord on the second rather than an added tone chord on the original note. In jazz chords and theory, the second is required due to its being an added tone.
The quality of the second may be determined by the scale or may be indicated. For example, in both a major and minor scale a diatonic second added to the tonic chord will be major (C-D-E-G or C-D-E♭-G) while one added to the dominant chord will be major or minor (G-A-B-D or G-A♭-B♭-D), respectively.
The second is octave equivalent to the ninth. If one could cut out the note in between the fifth and the ninth and then drop the ninth down an octave to a second, one would have a second chord (CEGB♭D' – B♭ = CDEG). The difference between sus2 and add9 is conventionally the absence or presence, respectively, of the third.
Added ninth 
An added ninth chord is a major triad with an added ninth. Thus, Cadd9 consists of C E G and D. (The D, which might be called an added second, is two fifths up from the root.) Added ninth chords differ from other ninth chords because the seventh is not included.
See also 
- Sadie, Stanley, ed. (1980). "Ninth chord", p.252, The New Grove Dictionary of Music and Musicians, vol. 13. ISBN 1-56159-174-2.
- Benward & Saker (2009). Music in Theory and Practice: Volume II, p.183-84. Eighth Edition. ISBN 978-0-07-310188-0.
- Stephenson, Ken (2002). What to Listen for in Rock: A Stylistic Analysis, p.85. ISBN 978-0-300-09239-4.
- Benward & Saker (2009), p.179.
- Fétis, François-Joseph and Arlin, Mary I. (1994). Esquisse de l'histoire de l'harmonie, p.139n9. ISBN 978-0-945193-51-7.
- Stephenson, Ken (2002). What to Listen for in Rock: A Stylistic Analysis, p.83. ISBN 978-0-300-09239-4.
- Walter Everett (Autumn, 2004). "A Royal Scam: The Abstruse and Ironic Bop-Rock Harmony of Steely Dan", p.208-209, Music Theory Spectrum, Vol. 26, No. 2, pp. 201-235.
- Berg, Shelly (2005). Alfred's Essentials of Jazz Theory, Book 3, p.90. ISBN 978-0-7390-3089-9.
- Jazz Lessons
- Schenker, Heinrich (1980). Harmony, p.190. ISBN 978-0-226-73734-8.
- Hawkins, Stan. "Prince- Harmonic Analysis of 'Anna Stesia'", p.329 and 334n7, Popular Music, Vol. 11, No. 3 (Oct., 1992), pp. 325-335.