Depending on how you think about them chords can be many things. Some basic notions and assumptions that one might come up with at first hand:
- They consist of multiple notes sounding together
- They can consist of notes from different octaves
- The notes should be somewhat consonant (sound well together)
- They can be both vertical and horizontal as they can be arpeggiated and thus stretched out in time.
We can thus maybe say that:
In essence a chord is multiple notes sounding together.
The normal definition of a chord then imposes further restrictions on this rather free definition. Among things it usually puts the lower limit of different notes at three. Many times it is also defined as having to contain the intervals of a third and a fifth. These are however rather limiting.
Chords with only three notes (triads) none of which extending beyond the fifth, we shall call simple chords.
Chords with additions consisting of specific intervals will be called added tone chords.
Lastly, extended chords denote chords with added notes that include exotic intervals below the one being added as well.
To construct triadic chords using intervals below or at that of the fifth limits the possible combinations greatly, and only allows for certain possibilities:
- 3rd + 5th
- 2nd + 5th
- 4th + 5th
The first type make chords with minor or major tonality. Type two and three are called suspended chords.
Since the diminished and augumented chords modify the fifth degree only, they still have minor and major tonality in them. The suspended type chords however, do not since the third degree is all but replaced with a perfect interval.
Major and Minor
Using thirds as the second note in the chords and a perfect fifth as the third note, makes for chords made by stacking a minor/major third after each other:
|m3, P5||m3, M3||Minor||Xm, Xmin|
|M3, P5||M3, m3||Major||X|
Diminished and augumented
Stacking a minor third on a minor third or a major third on a major third makes the fifth diminished or augumented respectively.
|m3, d5||m3, m3||Diminished||Xdim, X-, X°|
|M3, A5||M3, M3||Augumented||Xaug, X+|
Having exhausted the possibilities using thirds, we look to other intervals: seconds and fourths. These add up to a fifth
|P2, P5||P2, P4||Suspended 2nd||Xsus2|
|P4, P5||P4, M2||Suspended 4th||Xsus4, Xsus|
|P2, d5||P2, d4||Diminished suspended 2nd||Xsus2aug?|
|P2, A5||P2, A4||Augumented suspended 2nd||Xsus2aug?|
|P4, d5||P4, m2||Diminished suspended 4th||Xsus4aug?|
|P4, A5||P4, A2||Augumented suspended 4th||Xsus4aug?|
Among these the only normal ons is the sus4 chord, which is often just named sus.
Some of the aug/dim sus chords emerge naturally as sus chords in the normal modal scales, but they seem exceedingly rare to me.
Added tone chords
These are like a piece of English toast: the base triad is the bread and then you just add some things on top.
|M3, P5, M6||M3, m3, M2||Sixth||X6, XM6|
|m3, P5, M6||m3, M3, M2||Minor sixth, minor major sixth||Xm6, XmM6|
I suppose chords with an added minor sixth are rare because of the highly dissonant minor second that occurs between the fifth and the sixth for such chords.
Added ninth chords
These correspond to sus2 chords but with the second one octave up.
The bossa nova chord.
A major triad with a major sixth and a (major)ninth (but no seventh). It is in a way a combinantion of the above mentioned sixth and ninth chords.
These are like “Sandwich chords” in the sense that they contain the root and the named interval; the bread around the sandwich, and the relevant intervals in between these intervals; everything in between the bread - the filling.
Modifying the simple chords by adding the interval of a seventh we get the following variations:
|m3, P5, m7||m3, M3, m3||Minor seventh||Xmin7, Xm7|
|m3, P5, M7||m3, M3, M3||Minor-major seventh||Xmmaj7, XmM7, XmΔ7|
|M3, P5, m7||m3, M3, m3||Dominant (Major-minor) seventh||X7|
|M3, P5, M7||M3, m3, M3||Major seventh||Xmaj7,CM7, CΔ7, CΔ|
In addition we can add in diminished and augumented variations into the mix:
|m3, d5, d7||m3, m3, m3||Diminished (minor) 7th||Xdim7, X°7, Xm(♭7)♭5|
|m3, d5, m7||m3, m3, M3||Half-diminished (minor) 7th||Cø, Xm(7)♭5|
|M3, A5, M7||M3, M3, m3||Augumented major 7th||X+M7, X+Δ7, Xmaj(7)♯5|
|M3, A5, A7||M3, M3, M3||Augumented augumented (major) 7th||not used because A7 ~ P8…|
We can equivalently modify the simple suspended variations, these seem rare (?)
|P2, P5, m7||P2, P4, P4||Suspended 2nd minor 7th|
|P2, P5, M7||P2, P4, A4||Suspended 2nd major 7th|
|P4, P5, m7||P4, M2, P4||Suspended 4th minor 7th|
|P4, P5, M7||P4, M2, A4||Suspended 4th major 7th|
|m3, d5, m7||m3, m3, d4||Diminished (minor) 7th|
|m3, d5, M7||m3, m3, P4||Diminished major 7th|
|M3, A5, m7||M3, M3, A4||Augumented minor 7th|
|M3, A5, M7||M3, M3, AA4||Augumented major 7th|
Adding sevenths to the normal diatonic chords taken from the modal scales one gets:
- Major seventh: 1, 4
- Minor seventh: 2,3,6
- Dominant seventh: 5
- Half-diminished seventh: 7
Ninth chords (High seconds)
Eleventh chords (High fourths)
Thirteen chords (High sixths)
A note on Eight, Tenth, Twelwth and Fourteenth chords
These are uncommon not because the numbers bring bad luck but rather because the equivalent intervals one octave down are already present in a normal extended chord:
- The 8th is just the root
- The 10th is a 3rd
- The 12th is a 5th
- The 14th is a 7th
Due to these equivalences these chords would contain several repetitions and thus not add tension to the chord.