The terms used to describe intervals are as follows:
All root chords are described starting with the lowest note, and ascending in pitch. For instance, a chord described as
r 3 5
contains the root, a major third above the root and a perfect fifth above the root. If this chord were built on B (with B as the root), it would contain the notes
B (root) D (root + a major third) F (root + a perfect fifth).
Compound intervals are those intervals greater than an octave. They can also be described as an octave plus a simple interval. Note that this is not a complete list of compound intervals but only those that are commonly used in Jazz chords.
Optional extensions to the chords are written in parentheses, e.g. (11). These notes are not necessary to define the function of the chord, but are included to add colour or fill out the sound according to the tastes of the performer. Extensions are written into the chords when a specific colour or texture is warranted.
Chords are described here in terms of intervals relative to the root of the chord, arranged from smaller intervals to larger. This is a standard method used when describing jazz chords as it shows them hierarchically: Lower intervals (third, fifth and seventh) tend to be more important in defining the function of the chord than the upper intervals or extensions (9th, 11th, 13th), which add colour. Although it is possible to play the chords as described here literally, it is possible to use different orderings of the same notes, known as a voicings, or even by omitting certain notes.
For instance, the dominant 7th 11 or Lydian dominant (C711) is comprised of the notes:
r 3 (5) 7 9 11 (13)
Basing this chord on the pitch, C, results in the pitches:
C E G B D F A
The same chord type may also be voiced:
C E B F A D F
This voicing omits the perfect fifth (G) and raises the major ninth (D) by an octave. The augmented eleventh (F) is also played twice in two different registers. This is known as "doubling".
The above chords, despite their differences, share the same harmonic function and can be used interchangeably.
Major Seventh (CΔ7, Cmaj7)
r 3 5 7 (9)
Major Sixth (C^6)
r 3 5 6
Major 6-9 (C69, C6 Add 9)
r 3 5 6 9
r 3 5 7 (9) 11 (6))
"Basic" is used to describe those dominant chords which are based on the major scale. In many instances, dominant chords than are written as a basic chord (e.g. C13) can be substituted for a more complex chord, as long as it remains part of the same group (i.e. dominant chords) and does not clash with the melody note.
Dominant chords tend to sound unstable (the exception being C711) and often resolve down a perfect fifth or up a perfect fourth (e.g. C7 tends to resolve onto chords based on F). For more details, see Chord Progression.
Many of these chordal alterations are derived from minor scale modes, as opposed to the major scale modes. (See Musical mode). If the performer retains the 13th in the chord and/or avoids playing a 13th, in can be substituted for a C139. Likewise a C9 can often be substituted for a Cmaj95, as long as the 9th is retained or the 9th and 9th is avoided.
Dominant seventh (C7)
r 3 5 7 (9) (13)
Dominant ninth (C9)
r 3 (5) 7 9 (13)
Dominant thirteenth (C13)
r 3 (5) 7 (9) 13
Sus, or suspended chord (C7sus)
r 4 (5) 7 (9) (10) (13)
Minor seventh (C-7, Cmin7, Cmi7, or Cm7)
r 3 5 7 (9) (11) (13)
Minor ninth (C-9, Cmin9, Cmi9, or Cm9)
r 3 5 7 9 (11) (13)
Minor eleventh (C-11, Cmin11, Cmi11, or Cm11)
r 3 5 7 (9) 11 (13)
Minor thirteenth (C-13, Cmin13, Cmi13, or Cm13)
r 3 5 7 (9) (11) 13
These chords can be voiced in a great variety of ways, including building the chord on the 7. They very often, but not always, lead to a minor chord built on an interval 4th up from the root. It is also not unusual for either the 9 or 9 or the 5 to be expressed in the melody.
Dominant 9/5 (C75 9)
r 3 5 7 9
Dominant 9/5 (C75 9)
r 3 5 7 9
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