Monday, January 29, 2018

Diagonal Chromatic Blocks - Part II

As we described in the previous post, the 4X4 — four strings x four frets per side — block on the top four strings (DGBE) can be teated as of four consecutive major 7th chords shaped like diagonal columns, which makes it essentially an atonal block with no specific key. The chromatic nature of this block does not immediately suggest one key over another.
Each major key has two major 7th chords; the I and the IV. But since these two chords are a fourth or a fifth apart, they are not both found inside the block. How do we determine which of the major 7ths in the block is the I or the IV?

If we place the block so that it aligns with the Center Axis (also referred to as the Aeolian Axis), then none of the major 7ths are diatonically in the key. However, we have the minor tonic chord — the minor 7th on VI —  flanked by two major 7ths rooted on the V and the bVII. Keep in mind that neither of these major 7ths are diatonic ... that is, they are both outside the key, as are the other two greyed out maj7ths partly hidden beneath the diatonic VI chord.

Now look what happens when the tonic chord is the first column:

... Now we have a diatonic major 7th followed by a diatonic minor 7th. Notice the Dorian Axis where the Aeolian Axis was before, followed by The Void, and the Phrygian Axis positions. Perhaps more importantly is the presence of a  major 7th chord related to the minor 7th. Because the minor 7th is preceded by the I, there is clearer diatonic structure in this placement of the block.

There are three minor diatonic minor 7th chords, and two of them are adjacent to a major 7th. The II shown directly above, and the III shown below, which essentially reverses the relationship of the minor and major 7ths: 

We can also find a minor 7th rooted on the 4th column, preceded on the 2nd column by the Tonic or the V:

If the minor 7th is a VI and is rooted in the 4th column, there will be no diatonic major 7ths in the block, but the major 7th rooted on the V can be described as "borrowed" from the possible major 7th of the VII of the melodic minor, the #IV of the major mode shown here being the #VI of the minor mode of the key:

... and finally, the minor 7th can be placed on the 2nd column, thus:

Still, if we want to find another symmetry within this block, and we rule out the criterion of maintaining a diatonic major 7th, we can see that the minor 7th chords rooted on II and III fit nicely in the block's boundaries. The four "shadow" major 7th chords have an interesting symmetry as each of them contains two notes of the key, alternating between the 3rd and 7th in column 1, the root and 3rd of column 2, and repeating the same relationships in the next two columns:

The Major 7th chord (or arpeggio) is our primary element in these blocks, so it makes sense that there always be one diatonic major 7th in the block based on the chosen key. The distribution of the major 7ths in a diatonic key means that there can only be one, and not two, maj7ths in any block, but it can be in any of the four positions.


Lets now add all the surrounding notes as well as another landmark: The faint grey ellipses indicate the half-step clusters ( VII - I - III - IV ) ... and  we'll shift the tonic chord is the 2nd column.  The Void position on the fretboard is now aligned with the 2nd and 4th column of the block, rather than the 1st and 3rd. 
Also, the VII is shown darker so as to bring out the geometry of the Ionian scale which comprises a whole-step on the 4th string, a half-step on the 3rd string, whole-step on the 2nd string and half-step on the 1st. This scale pattern reveals the symmetry of the two tetrachords nicely. It can be fingered; 2nd finger, 4th, 1st finger, 2nd, 2nd finger 4th, 1st finger 2nd.

As you can see, there is now a half-step cluster (B C E F) in the lower left corner of the block. 
If you replace the Roman numerals with note names in the key of C, the geometry of the surrounding notes will of course remain the same. This pattern can be applied to any key until it reaches the end of the fretboard, i.e.; the #VI (which is the 7th of the first column) is eqivalent to E, or the root of the 4th column chord (II) is not above a practical fret position, which will vary depending on the type of guitar you're playing.

These blocks are useful as a way of studying the tonal relationships within keys on the fretboard. Another one of many possibilities is shown next. Here the two major 3rds which share the unison note are called out by short olive-green diagonals. In this case, one is the tonic 3rd and the other comprises the III of the key and its major 3rd which is an accidental, all combining to create an augmented triad on the I, but stretched out across a total span of seven frets. The fingering for this should be simply one finger per string, i.e.: I (4th string) = 4th finger, III (3rd string) = 3rd finger, III (2nd string) = 2nd finger, and #V (1st string) = 1st finger.

... more to come.

Wednesday, January 24, 2018

Diagonal Chromatic Blocks - Part I

When you play a Major 7th Chord in the root voicing on the top four strings it forms a diagonal line with a note in each of the four strings and spanning four frets. In the diagram below, you see four consecutive major 7th chords of the type just described:

... This block comprises sixteen notes and can be played in any fret position. Notice that the 7th of the fourth chord in the block is on the same fret as the Root of the first chord. Also, due to the diagonal shape of each chord, the four-chord sequence spans seven frets in total.

Now lets look at it with note names:
The same block is now assigned to a specific fret position. In this case it's positioned so that the first chord is Fmaj7. As long as the block is treated as a series of chords, the note names will follow that scheme ... for example; a G major 7th cord has the notes G B D F#, so if we use the grid as a major 7th map, then F# is not Gb. But if we only want to show the chromaticism of each row of notes, then it might be clearer to use only sharps or only flats for every note which isn't a natural tone:

Now if we apply this principle to the entire fretboard — keeping the idea of a four-chord block as our template — we will get three blocks running from the open position all the way to the 14th fret where E is the Root note of the last diagonal chord:

The blocks are each numbered 1 2 3 4 for the diagonals. The bold vertical bars are on the 3rd7th and 11th frets.
Now lets look at a single block from a different perspective.

Looking at all the notes of a block, we'll see that it contains all 12 notes of the system, some of them more than once, some only once. If we use F as the starting note, we can see that F, Gb, G and C appear twice in the block and that the remaining eight notes only happen once:
Notes which occur twice in the pattern are shown in the L shapes.

... Furthermore, of the four repeating notes, three of them: F, Gb and G, form octaves while one: C, is a unison. The eight unique notes form two chromatic runs: Ab, A, Bb, B and Db, D, Eb, E, with a whole-step: B — Db (or B— C#), between the two. 

Below you can see the entire fretboard with the duplicate notes highlighted:

The groups of unique notes look this:

... and like this in all three blocks:

 These blocks are not "in" any particular key. There are may ways to organize the notes within a chromatic block to visualize particular keys. Well look at that in the next post.

This diagram shows the notes grouped into the Unique-Notes and the Clone-Notes across the fretboard.

Wednesday, October 11, 2017

More about the Minor 11th Arpeggio (Part 2)

This form of the Minor 11th arpeggios has the Roots on the 6th string with each Minor 11th topping out on the 3rd string followed by two additional intervals. Notice that the two shapes differ by only the positions of the IV and the VII on the 2nd string.

The Major 7 sharp 11 

In addition to the Minor 11ths, there is one other 11th arpeggio which is built on a symmetrical interval pattern. In the case of the Major7th sharp 11, the pattern is inverted so that it begins and ends with a Major 3rd and has a minor 7th (VI)  at its center.
The interval structure of the Major 7 sharp 11th is: 

Root <major 3rd> 3rd <minor 3rd> 5th <major 3rd> 7th <minor 3rd> 9th <major 3rd> 11th
.. which is the only other symmetrical 11th arpeggio aside from the twin minor 11ths. There is only one Major 7 sharp 11 and it 'straddles' the tritone, being rooted in the IV of a key and ending on the VII.

Below you see the arpeggio rooted in F in the key of C major ...
Next let's see the Major 7 sharp 11 as it fits into the symmetry of the Minor 11ths ...

Sunday, October 8, 2017

More about the Minor 11th Arpeggio

The Upper and Middle forms of the Minor 11th / Symmetrically Extended Major 7th arpeggio tell an interesting story of the symmetry of the diatonic system on the guitar fretboard in standard tuning.

As the Fretography® method is all about symmetry, the diagrams below lay out that symmetry on two levels. Look for the tonic (Roman numeral I) and where it appears in each form. Also notice the fret axis positions indicated by grey bars. 

The Axis frets are rooted in II (Dorian Axis), III (Phrygian Axis), and VI (Aeolian Axis). 

The yellow curve connects the II positions within the four upper strings.

The boldly outlined reversed "Z" shapes comprise the primary arpeggio forms. The extensions are shown behind with shaded edges. Notice that the upper forms differ only in the position of a single note position in each (VII and IV).

The Middle Form of the arpeggio is centered on a different fulcrum with the Dorian Axis at its outer edges. As with the upper form, the overall skewed symmetry of this form differs by only the positions of the IV and the VII in the extensions.

Again, consider that these arpeggio forms are based on the only instance of a six note interval sequence which occurs twice in every key. There is literally no arpeggio on the fretboard which
contains such clear symmetry over such a wide range both tonally and geometrically.

Next time we'll look at the lower form.

Thursday, October 5, 2017

More About the Minor 11th Arpeggio

Apart from and underlying its symmetry on the fretboard, the structure of the twin minor 11th arpeggios is something to think about from a theory perspective.

Understanding this symmetry on its own, away from the fretboard, will strengthen your awareness of the how all arpeggio sequences relate to every key.
(Click image to expand. Downloaded image will be 1600 X 1233 pixels.)

The diagram above shows the symmetrical interval structure of the two minor 11ths. Notice that there is only one instance of two consecutive minor 3rds and no instance of two consecutive major 3rds. Knowing this, you can navigate the fretboard with greater certainty. Think how useful it is simply to know that there are never two consecutive half-steps in a diatonic scale, or how the minor 3rd/whole-step sequence works in a pentatonic scale.

Sunday, September 24, 2017

More Ways to Play Minor 11th (Sym-ex Major 7th) Arpeggios

( Continued from: )

Here's another way to play the Minor 11th arpeggio, which is rooted in either the II or the VI of any major key. I call this set of patterns "Lightning Bolt" arpeggios.

Notice that there are three shapes, the two lower forms are identical in shape and the two upper forms are simply rotated 180ยบ from each other. 

Here again, from a previous post, is an overview of the theory behind these arpeggios ...

The concept of "Symmetrically Extended Arpeggios" is part of the Fretography Symmetry in which you can think of certain chords or arpeggios as starting with a central interval and extending both up and down equally. In the case of the Major 7th chord, the interval structure is:

Root <maj3rd> 3rd  <min3rd> 5th <maj3rd> 7th

Notice that the intervals themselves form a symmetrical sequnce; two major 3rds around a central minor 3rd. When this 7th chord is extended to the next 3rd above and below the structure is:

Root <min3rd> 3rd <maj3rd> 5th <min3rd> 7th <maj3rd> 9th <min3rd> 11th

The above diagram shows the A minor 11th and D minor 11th structure and how they are both contain the same extended major 7th forms based on identical interval structure.

Another way to play these arpeggios is to begin and end with a minor 3rd between two strings, unlike the pattern above, which begins and ends with the minor 3rd played on a single string;

 (Low A minor 11th Arpeggio - ascending and descending) 

 (High A minor 11th Arpeggio - ascending and descending) 

As you can see, these patterns span four strings each resulting in three different forms.

Thursday, July 20, 2017

Combining 'Sym-Ex.' Major 7th Arpeggios

The image above shows the two Symmetrically Extended Major 7th arpeggios, each in two different forms. On the left you see the IV/II in the middle voicing (purple) overlapping the upper I/VI (yellow). On the right the middle voicing I/VI (blue) overlaps the IV/II upper voicing (orange).

If you were playing this in the key of C, with "II" placed on the 5th fret of the 5th string, the form on the left could be written:

In the key of Eb, the form on the right would be positioned with "VI" on the 3rd fret of the 5th string:

Keep in mind that the Roman numerals in the diagrams indicate the key degrees of each arpeggio. These numerals remain the same for every key. Since there are two identical Extended Major 7th arpeggios (or minor 11ths) in each key, the only way to determine their relative positions is to decide which is the I/VI and which is the IV/II.

Also, notice that these arpeggios happen within specific "Zones" as detailed in my book "Fretography."

Another interesting combination is the lower forms with the upper forms of the same scale degree:
Here, you'll see that in the lower forms — rooted in the 6th string — both the I/VI and the IV/II are connected to the upper forms in the same geometry. 

We'll place the first grouping in the key of C as shown in the notation above. The next, we'll put in the key of G, as per the notation below:

Look carefully at the notes in both above examples. You'll notice they are the same. But their context it different within the key and will result in different possibilities in each depending on the additional chords and riffs in a particular piece of music.

Here's what they sound like ...

 (Low A minor 11th Arpeggio - ascending and descending) 

 (High A minor 11th Arpeggio - ascending and descending) 

Because this form can exist in an identical form within two different tonal contexts, it is a dynamic bit of riffage to have in your vocabulary.