Pentatonic/Diatonic Relationships

When you think of pentatonic scales do you connect them to the diatonic key? Do you think of a major pentatonic scales as being rooted in the tonic of the key? 

For instance — most of us might believe the following; C major pentatonic 'belongs' to the key of C major ... G major pentatonic 'belongs' to the key of G major ... etc ... So that each major pentatonic scale is matched to a single major key. And of course, the relative minor pentatonic is matched to the relative minor of each key, so A minor pentatonic 'belongs' to the key of A minor, and so on.

You may also understand that when playing blues based music you can use an A minor pentatonic scale to riff on an A dominant7 chord, and also use an A major pentatonic with that same chord, and that doing so falls outside standard diatonic theory. 

But what about fully exploring diatonic possibilities of the pentatonic scale? Are you aware that each diatonic key contains not one, but three pentatonic scales, each with the same interval structure?

The key of C includes not only the C major/A minor pentatonic scales, but also G major/E minor and F major/D minor. 

Here are the notes of the key of C: C D E F G A B C ... 

... and here are the notes of the C major pentatonic scale: C D E G A C. 

Now, here are the notes of the G major pentatonic scale: G A B D E G, and the F major pentatonic scale: F G A C D G.

Notice that G maj. pent. and F maj. pent. contain no sharps or flats. So not only is each pentatonic scale rooted in the tonic of its own key, but it is also positioned within two additional keys. To be more precise, the I, IV and V degrees of any major key will produce a pentatonic scale with the intervals Wholestep, Wholestep, Minor 3rd, Wholestep,  Minor 3rd. 

Below you see the notes of each scale in the key of C as they appear on the fret board. The first is C major pentatonic, followed by F major pentatonic and then G major pentatonic:

(Zone names are based on the degrees of the diatonic major scale.)

And the interval structure of each scale:

We'll look deeper into the applications of this in the next post.

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 ...

Melodic Minor Mapping Madness! (Part 2)

The Melodic Minor Molecule:

The symmetry of the Melodic Minor is expressed clearly in its 5th mode, also known as "Mixolydian b6". 

In A Melodic Minor we have the scale; "A B C D E F# G# A"... This sequence can be expressed in intervals as "W H W W W W H" ...

If we play a scale in A Melodic Minor with the final note of E, the interval structure is "W W H W H W W" based on the notes "E F# G# A B C D E" ...

When played on the four bottom strings of the guitar, this mode takes the hexagonal shape shown below:

Because this shape is quite easy to remember, it can serve as a kind of scale molecule around which you can develop your melodic minor riffs.

Notice where this mode fits in the Melodic Minor Compass (see previous post in this blog):

The centrality of this mode within Melodic Minor is quite clear, both tonally and geometrically on the fret board. Play the four-note augmented arpeggio starting from C on the 6th string — ascending and descending; "C E G# C G# E C" ...  then play the 4-note tritone arpeggio from the same root; "C F# C F# etc" ...  then play the mode scale from E to E and resolve to an A minor 7.

This will give you a sense of the flavor of this scale and open the door to its modes.

Here is a map of all the positions of the 5th mode of Melodic Minor in the key of Cmaj/Amin:

Notice how the shape changes when it crosses the 3rd-Rail (the 2nd and 3rd string juncture), indicated by the green forms. Also notice that the green form spanning strings 2,3,4 is the same shape as the form spanning strings 1,2,3 but rotated 180º.

(Read Part 1)

Melodic Minor Mapping Madness! (Part 1)

The Melodic Minor scale is one of the more challenging patterns for the guitar. The myriad of fingering possibilities make it a daunting task to develop a full command of this scale and its modes.

Using the Fretography® principle of fretboard symmetry and teasing out the symmetry of the scale itself, a few interesting patterns emerge that can be very useful in navigating the Melodic Minor landscape.

Fundamentally, Melodic Minor starts out as an alteration of the Aeolian Mode. Starting with the key of A minor, we raise the 6th and 7th, resulting in this group of notes: A B C D E F# G#. At first you may find it's easy enough to take a familiar minor scale pattern and just change the two notes, but you'll quickly realize that all your well practiced fingerings will have to be thrown out and you'll have to retrain your hand to 'instinctively' find these new note positions else it will be hit-or-miss when it comes to applying this scale effectively. 

There are many applications of Melodic Minor beyond the Tonic mode, and memorizing all seven modes with their many hand-position shifts takes great effort and time. As with any difficult pattern, it helps when you can find some aspect that can be easily visualized. On the fretboard, scales are inherently non-linear and the variations involving crossing between the 3rd and 2nd strings add even more complexity. But whenever symmetry is present in the theory of a musical structure, it can also be found on the fretboard if you know where to find it.

Playing scales is — ironically — not enough to be able to play scales. In other words; you need more than just scale patterns to visualize the structure of the Melodic Minor as it is arrayed across the whole fretboard.

Enter: "The Melodic Minor Compass" ...

This pattern is drawn from the notes of the Melodic Minor, but presents them as a set of arpeggios. The blue lines represent a Tritone arpeggio, the Orange line is an Augmented arpeggio. In addition, the green trapezoids are two modes: "D Lydian Dominant" and "F# Aeolian Flat5." These modes are emphasized because of their symmetrical relationship with the overall pattern. 

Below is a more elaborate look at the pattern as it is arrayed across the whole fretboard:

Play the indicated notes on the staves and experiment with finding your way around the pattern. Notice the gray notes ... these are the natural tones which are replaced by sharps. They can still be played when appropriate, but if you want to develop command of Melodic Minor you may want to avoid them until you've gotten the lay of the land in this new environment.

(Read Part 2)