Each chord is described as a series of intervallic relationships to the root of the chord. This provides an accurate and easily understandable basis for working out these chords in each key.
The terms used to describe intervals are as follows:
- r = root of the chord
- ♭2 = minor second = 1 semitone above root
- 2 = major second = 2 semitones above root
- ♯2 = augmented second = 3 semitones above the root
- ♭3 = minor third = 3 semitones above the root
- 3 = major third = 4 semitones above the root
- 4 = perfect fourth = 5 semitones above the root
- ♯4 = augmented fourth (tritone) = 6 semitones above the root
- ♭5 = diminished fifth (tritone) = 6 semitones above the root
- 5 = perfect fifth = 7 semitones above the root
- ♯5 = augmented fifth = 8 semitones above the root
- ♭6 = minor sixth = 8 semitones above the root
- 6 = major sixth = 9 semitones above the root
- 7 = minor seventh = 10 semitones above the root
- M7 = major seventh = 11 semitones above the root
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 (major chord). 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.
- ♭9 = compound minor second (minor ninth) = 1 semitone + an octave = 13 semitones above the root
- 9 = compound major second (ninth) = 2 semitones + an octave = 14 semitones above the root
- ♯9/♭10 = compound augmented second/minor third (augmented ninth/minor tenth) = 3 semitones + an octave = 15 semitones above the root.
- 10 = compound major third (tenth) = 4 semitones + an octave = 16 semitones above the root
- 11 = compound perfect fourth (eleventh) = 5 semitones + an octave = 17 semitones above the root
- ♯11 = compound augmented fourth (augmented eleventh) = 6 semitones + an octave = 18 semitones above the root
- ♭13 = compound minor sixth (minor thirteenth) = 8 semitones + an octave = 20 semitones above the root
- 13 = compound major sixth (thirteenth) = 9 semitones + an octave = 21 semitones above the root
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) are more important in defining the function of the chord than the upper intervals or extensions (9th, 11th, 13th), which add color. 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 (C7♯11) comprises 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".
Basic chord types
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)
- Δ7 has the same meaning as maj7. Often the melody note or other pitched phenomena influences which of the above chord types a performer selects. For example, if the melody note is the root of the chord, including a major seventh can frequently cause a harsh dissonance.
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))
- The Lydian chord has a strange quirk, where if you put the root both above and below the augmented eleventh it creates an unpleasant dissonance of a tritone.
- The interval of the sixth is used even though it is described after other compound intervals, and perhaps should also be a compound interval (i.e. 13th). However, convention in Jazz dictates that when describing the major sixth, the simple interval, i.e. 6 is almost invariably used instead of the compound interval, i.e.13. This helps avoid confusion with the dominant thirteenth (see below).
Basic dominant chords
"Basic" is used to describe those dominant chords which are based on the major scale. In many instances, dominant chords that 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 C7♯11) 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, it can be substituted for a C13♭9. Likewise a C9 can often be substituted for a Cmaj9♯5, 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
- This particular symbol is often used if the 13th is found in the melody.
Sus, or suspended chord (C7sus)
r 4 (5) ♭7 (9) (10) (13)
Minor seventh chords
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
Complex chord types
Complex dominant chords
These chords can be voiced in a great variety of ways, including building the chord on the ♭7. They usually, 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. Often for the sake of expediency, the abbreviation "alt" is used, as in C7alt, to describe the family of dominant chords which have "altered" tones (including the ♭5, ♯5, ♭9, ♯9, or ♭13). Coincidentally, all of the altered tones mentioned above are present in the melodic minor scale whose root is a half-step above the root of the alt chord (i.e. E♭ melodic minor for D7alt)
Dominant ♯9/♯5 (C7♯5 ♯9)
r 3 ♯5 ♭7 ♯9
Dominant ♭9/♯5 (C7♯5 ♭9)
r 3 ♯5 ♭7 ♭9
- Nettles, Barrie & Graf, Richard (1997). The Chord Scale Theory and Jazz Harmony. Advance Music, ISBN 3-89221-056-X.