Nested Triad Inversions

The previous post showed Root triads in individual Zone positions forming stacks of 4ths. Here we'll look at the 1st and 2nd Inversion forms.

The 1st Inversion triads are formed by moving the root to the top (highest pitch), the 3rd is the low note and the 5th is in the middle of the triad. 

In the diagram below, If we read the "I" as the note G on the 3rd fret on the 6th string:

... then the first chord in the VII Zone (reading from the bottom of the Zone) is an F# diminished. Though the II of the key is the low note, the VII of the key is the root of this triad, as the high notes in all these triads are their root notes. 

The green triad in II Zone is the Tonic chord since it has the high note of "I" even though its low note is III, etc ...

Here's TAB and notation for the 1st inversion triads in the key of G:

2nd Inversion triads are formed by moving the root to the top (highest pitch), then placing the 3rd above it. The 5th is now the low note and the Root is in the middle of the triad. 

In the diagram below, If we read the "I" as the note G on the 3rd fret, then the first chord in the VII Zone (reading from the bottom of the Zone) is a C major. Though the I of the key is the low note of this triad, the IV of the key is its root, as the middle notes in all these triads are their root notes:

Here's TAB and notation for the 2nd inversion triads in the key of G:

Inversions can be found within a Zone by starting with a root triad and either raising the 5th or lowering the root to the next degree of the key. Raising the 5th of any triad to the next key degree will turn the triad into a 1st inversion ... rather than refer to the raised 5th as a "6th", it becomes the root of the chord. 

For example: An A minor triad contains the notes A C and E. Replacing the E with F# we now have the notes A C F#, An F# diminished triad with the root as the high note — a 1st inversion F#º. Likewise, that same A minor triad can have its Root replaced with the note G — one key degree down from the original root note.  Now the G becomes the 5th, the C is the Root and E is the 3rd of a C major chord, which functions as the IV chord in the key of G.

Apply this principle to all the root triads ... and then reverse the process. Any 1st inversion triad can have its hight note (root) lowered to the next key degree down and become a Root Triad, and any 2nd inversion triad can have its low note raised to the next key degree up and that note will be the new triad root.

Nested Triads in 4ths

 A practical approach to mapping triads comprises four 'nested' chords, each spanning three consecutive strings: ⑥⑤④ / ⑤④③ / ④③② / ③②①. Each successively higher triad root is a 4th above the previous one. With the sole exception of the tritone (augmented 4th) between the IV and the VII chord roots, every chord root is a perfect 4th apart. 

In the image above you can see the structure of the four triads in the VII Zone. Below you can see all the triads belonging to a given key. Because the notes are shown as Roman Numerals, you may position the patterns on any fret position. Roman Numeral I indicates the Tonic of the key, no matter which fret or string it's on. Once you've located a specific position to assign the pattern, play them all in the same key, then in another key, until you've become familiar with the patterns in every key.

Here's notation and tablature to play all the patterns in the key of G:

Melodic Minor Zones

A map of E melodic minor on the guitar, based on melodic minor interval symmetry:

Like all symmetrical patterns in the Fretography® system, these patterns are structured so the lower three strings (E A D) form one symmetry, and the top four strings (D G B E) form another, with the D string part of both groupings. 

When studying the patterns, be aware that you are not looking for 'mirror symmetry' but instead you will look for 'rotational symmetry'. This means that the shapes are the same when rotated 180º from each other.

The diagram below shows how mode patterns align with rotational symmetry. The modes are paired in darkened patterns within the zones to emphasize their symmetry:

This symmetry occurs on the fretboard because it is built into the interval structure of the melodic minor modes.

Here's the interval structure of the modes of E melodic minor:

... and as Roman numerals which pertain to any key:

Bebop Scales : "Major 6 Diminished" Scale

 More to come ...