Chord Variations

Notes added to a basic triad are called extensions.  Extended chords can be major, minor or dominant depending on the tirad on which they are based.

Major 7 = I-III-V+VII (C, E, G, B)
Minor 7 = I-iii-V+vii (C, Eb, G, Bb)
Dominant 7 = I-III-V+vii (C, E, G, Bb)

Inversion refers to the the order in which the notes of a chord are stacked.  The standard order is called a root invesrion because the tonic is at the bottom (1,3,5).  First inversion is to have the 3rd at the bottom etc.  The notation to indicate inversion uses a slash.  For example, CMaj7/G is to have G as a base for the CMaj7 chord.  The notation can also be used to refer to a bass note not part of the chord.  This is called altered base chord, for example, Am/D.

Compound chords are 2 chords playing at the same time.  The notation use are similar to fraction, e.g.

A
D

Chord substition is to replace a chord with a related chord.  The chords involved should have things in common.  For example, chords with several common notes or chords with similar leading e.g. a dominant chord by another one which also lead back to tonic

Diatonic Substitution is to replace a chord with a diatonic third above or below the original.  For example, C major chord (C-E-G) to be replaced by Am (A-C-E)