·         We've seen that we can build chords by combining notes a third apart (I III V VII IX etc).  Let's take a major chord and go further.

·         By adding B to CΔ we get CΔ7.  The next note in the sequence of added thirds is D¹, a third higher than B, which gives us CΔ7 9.  What's the next note?  Since the key is C major, musical convention suggests that it would be a third above D¹, namely F¹.  Play CΔ7 9 with an F¹ on top.  It sounds horrible.  What went wrong?

·         The complete answer to this is complicated and we'll take another look at it later, in Step 11, but one way of thinking about the problem concerns the regular nature of the interval structure of IΔ chords.

·         Take CΔ7.  The interval from C to G is a fifth.  The interval from E to B is also a fifth.  The chord is made from two interlocking fifths.  The fifth is the strongest, most consonant of all intervals (except the octave, of course).  This makes CΔ7 a particularly stable and harmonious chord.

·         In CΔ7 9, the D¹ is a fifth above G.  This gives us three interlocking fifths, and again confers stability on the chord.

·         We can use this pattern of overlapping fifths to predict the next note in the extended chord.  It should be the fifth above B.  Now the reason for the nasty consequence of putting F¹ on the CΔ7 9 chord become clear - it's the wrong note to preserve the pattern.  The note a fifth above B is F¹#.

·         To take the exercise to its conclusion, the next note, a fifth above D¹ is A¹.  This gives us the chord CΔ7 9 11# 13.

·         If we dismantle this chord, we find that it is made from the following notes: C D E F# G A B.  This is a complete scale.  It's the scale that fits the CΔ series of chords.  But it's not the classical C major scale.  The note at position IV is raised a semitone.  This scale is called the lydian scale of C.

·         Work out the Δ7 9 11# 13 extended chords for a number of keynotes, and derive the lydian scale in each case.  Do you see a pattern?

·         The C lydian scale has one more sharp (F#) than the C major scale.  The lydian scales corresponding to all the sharp key major scales (G, D, A etc) have an extra sharp (the fourth degree of the scale is raised by a semitone); for the flat keys (F, Bb, Ab etc) the rule is that a flat is lost.

·         Play some Δ7 shells with the left hand and fill in various combinations of notes from the extended (lydian) part of the chord with the right.  Also experiment by playing some lydian lines with the right hand over left hand shells.