·         An augmented chord (symbol aug or, usually, +) has a sharpened fifth.  Example [5.1] shows D+ and [5.2] D-+ (D minor augmented).  You can augment the basic seventh chords, and use shell voicings as before.  Examples [5.3], [5.4] and [5.5] are DΔ7+, D-7+ and D7+ respectively.  The 7+ chord is sometimes also symbolised as 7 13b (work it out!).

·         If we flatten the third and the fifth of the major triad, we get the diminished triad I IIIb Vb.  The parent scale of such chords is the diminished (see Step 9).  Adding the note of the seventh degree of this scale gives us the diminished 7 chord, I IIIb Vb VI, symbol dim7 or o7, or (as I prefer) just plain o.  Example [5.6] is Do.

·         If we add the b7 to the diminished triad we get I IIIb Vb VIIb.  This handy chord is -7 5b, sometimes also called the half-diminished, symbol ø.  Example [5.7] is Dø in the two-handed shell format.

·         Try this: work out the notes of Fo, Abo and Bo.  You should find that they are all identical to the notes of Do.  In fact there are only three diminished chords - the D,F,Ab,B group, the Eb,Gb,A,C group and the E,G,Bb,Db group.

·         Similarly there are only four augmented chords.  C+,E+,G#+ is one group.  You can work out the other three.

·         Because the augmented and, particularly, the diminished chords have this uncertainty about just which note is the root, they are very useful general-purpose "joining" chords, connecting sevenths and other, less ambiguous, chords.

·         You may be wondering how diminished chords fit into the system of sevenths and shells.  The answer to this is very complex and takes us into advanced jazz harmony.  But we can make two simple points here.

·         First, we can make a shell for a diminished chord just by playing 1:6 and moving 3b:5b to the right hand as before (Example [5.8]).

·         Second, Example [5.9] shows D7 voiced as a shell, but with the addition of the flattened ninth - symbol D7 9b.  If you work it out, you'll see that this chord is made up of Co with D in the bass.  In other words, you can often use the diminished chord on the dominant seventh as a substitution - Co for D7 (9b).  Go back to some of the previous examples and work out diminished substitutions for dominant sevenths.