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A Grammar for Chords
Jazz chords could be formulated into the following grammar.
Chord := Quality Suspension? Extension+ Alternation+
Suspension := sus2 | sus4
Quality := triad | 7th | 6th | 9th | 11th | 13th | 69
Extension := add9 | add11 | add13
Alternation := b9 | #9 | #11 | b13
In what follows, we elaborate the four components. Note that extension and alternation requires more constraints beyond the grammar enforcement.
1. Quality
Note:
- All bolded chords are formed by strictly stacking thirds (they typically are more common).
1.1. triad
{1} x {b3, 3} x {b5, 5, #5}
| Chord | contents | special |
|---|---|---|
| dim | {1 b3 b5} | |
| m | {1 b3 5} | |
| m(#5) | {1 b3 #5} | 1st inversion of M |
| M(b5) | {1 3 b5} | |
| M | {1 3 5} | |
| aug | {1 3 #5} |
1.2. 7th & 6th
{1} x {b3, 3} x {b5, 5, #5} x {b7, 7}
| Chord | contents | special |
|---|---|---|
| m7 | {1 b3 5 b7} | |
| m7b5 | {1 b3 b5 b7} | |
| m7#5 | {1 b3 #5 b7} | |
| mM7 | {1 b3 5 7} | |
| mM7b5 | {1 b3 b5 7} | |
| mM7#5 | {1 b3 #5 7} | |
| 7 | {1 3 5 b7} | |
| 7b5 | {1 3 b5 b7} | |
| 7#5 | {1 3 #5 b7} | |
| M7 | {1 3 5 7} | |
| M7b5 | {1 3 b5 7} | |
| M7#5 | {1 3 #5 7} |
{1} x {b3, 3} x {b5, 5, #5} x {bb7(6)}
| Chord | contents | special |
|---|---|---|
| m6 | {1 b3 5 6} | |
| dim7 | {1 b3 b5 bb7} | |
| m6#5 | {1 b3 #5 6} | |
| 6 | {1 3 5 6} | |
| 6b5 | {1 3 b5 6} | 2nd inversion of m7b5 |
| 6#5 | {1 3 #5 6} |
1.3. 9th & 11th & 13th & 69
For all the legal 7th chord with string X:
- its 9th =
X.replace("7", "9")
For all the legal 9th chord with string X:
- its 11th =
X.replace("9", "11")
For all the legal 11th chord with string X:
- its 13th =
X.replace("11", "13")
For all the legal 6th chord with string X:
- the correponding 69 chord =
X.replace("6", "69")
2. Suspension
The sus2 and sus4 suffix can be appended to a chord iff
- the chord doesn’t include such degree
3. Extensions
The add9, add11, add13 suffix can be appended to a chord iff
- the chord doesn’t include such degree.
- after insertion, the chord’s quality doesn’t change
- e.g. it changes to a 6th/9th/11th/13th
4. Alternations
The b9, #9 #11, b13 suffix can be appended to a chord iff
- the chord doesn’t include such degree
Note:
- Typically, alternations happen to dominant chord.
- But it’s possible that other chord include an alternation, via available tension, or to make special sound effect.