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“We can also flatten the 5th of the chord. The structure 1 3 b5 is not very common in music although it does sometimes occur in jazz. However, the structure 1 b3 b5 occurs frequently. It is called a diminished or occasionally a minor b5 chord.”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“To create a major 7th chord we simply extend the ‘1 3 5’ formula by an extra note so it becomes ‘1 3 5 7’.”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“As the major 7th’s chord formula is 1 3 5 7, you might expect that the minor 7th’s formula would be 1 b3 5 7. This, however, is not the case.   To create a minor 7 chord we add a b7 to a minor triad. The formula is 1 b3 5 b7.”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“Any ‘7th’ chord can be played in four different inversions: with either the root, 3rd, 5th or 7th in the bass.”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“As you’re probably wondering, a minor triad with a natural 7 on the top 1 b3 5 7 is called a “minor major 7th” or m(Maj7) chord and we will discuss these structures in chapter twelve as they are an important sound in jazz. They are given this name because they are minor triads with a major 7th added on top.   When we extend a minor b5 chord to become a 7th chord, we once again add a b7, not a natural 7. In fact, it is a general rule that if a triad has a b3, it is more common to add a b7 to form a four-note ‘7th’ chord.   As you can see in the previous paragraph, this is not always the case, so be careful when applying that ‘rule’.”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“Finally, there are two types of triad that do not include a 3rd. These chords are normally named ‘suspended’ (or just ‘sus’ chords), as the lack of the 3rd gives an unresolved feel to their character.   In a ‘sus’ 2 chord the 3rd is replaced with the 2nd of the scale, and in a sus4 chord, the 3rd is replaced with the 4th of the scale.   In C, the notes generated by the formula 1 2 5 are C D and G   Example 1g     The notes generated by the formula 1 4 5 are C F and G.   Example 1h  ”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“To create a minor 7 chord we add a b7 to a minor triad. The formula is 1 b3 5 b7.”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“As the focus of this book is on 7th chords, which are more common in jazz,”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“A (diminished) minor b5 chord with an added b7 has the formula 1 b3 b5 b7 and generates the notes C Eb Gb Bb when built from the root note of C. This chord is named ‘Minor 7 flat 5’ or m7b5 for short. It also is common for m7b5 chords to be referred to as ‘half diminished’ chords.”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“The three triads you have learned so far are   1 3 5 Major 1 b3 5 Minor 1 b3 b5 Diminished or just ‘Dim’ Most chords you come across in music, no matter how complicated can normally be categorised into one of these basic types. Jazz chord progressions however are normally formed from richer sounding ‘7th chords’ which are the focus of this book.   There is, however, one more permutation that crops up occasionally, it is the augmented triad, 1 3 #5.”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application
“Finally, we come to one of the most common chords in jazz; the dominant 7 chord. It is formed by adding a b7 to a major triad. 1 3 5 b7. With a root of C this formula generates the notes C E G Bb.   Because of the fundamental major triad 1 3 5, this chord is a ‘major’ type chord, but the added b7 gives it an extra bit of tension.”
Joseph Alexander, Guitar Chords in Context: The Practical Guide to Chord Theory and Application

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