Funnels and Hats

You are looking at a single chord shape as it is arrayed across the fretboard.

The interval structure of these voicings is shown below:

The shape can be rotated 180º to form two voicings of minor 7th and major7th chords

as well as one voicing of dominant 7th and one voicing of a minor(major7th) chord.

The chords on the four top strings are all minor 7ths.

The chords on the bottom four strings are all major 7ths.

The chord in the middle four strings is a dominant 7th.

All these forms of the shape can, of course, be moved to any fret position and retain their interval structure, however, certain keys allow open strings to be added and so the funnel/hat form can be treated as both open and moveable chords. 

Next you can see all of the Funnels. Try playing them in this order using the Roman numeral Root notes a a guide:

VI - V - IV - II - V - I - III ...

Here's notation for the pattern:

Commonalities: The Big Picture

The Commonality Patterns comprise four of the five Diatonic Zones, omitting the V Zone. But even so, all the note positions of the every key are included. In other words, the entire fretboard can be distilled down to two fingering patterns, each one occurring in two positions per key.

The diagram shows all four positions of the patterns. The top grid shows the II and VI Zones — the bottom grid shows the III and VII Zones. They are separated in the diagram for clarity, since   they overlap. Notice the dotted lines indicating the Axis frets.

Play the green arpeggio paths first as ascending lines. The blue and purple paths represent isolated 3rds. See how the junctures between the patterns, on the 6th and 1st string (the highest fret position of one pattern to the lowest fret position of the next), are always either a whole-step or a major 3rd, i.e.; I to II, II to III, IV to VI, and V to VII. This will help navigating between the Zones.

The diagram below shows the background Zones of the Commonalities. The starred note positions correlate with those omitted from the Commonalities. The IV is left out of the VI and VII Zones, while the VII is left out of the II and III Zones.

Commonalities: VI and II Zone

Like the previous examples, these patterns each comprise the same interval relationships and geometry in two separate zones. Again, one zone omits the IV and the other omits the VII and in doing so eliminates the notes which are not common to both zones:

Play the green paths as shown in the notation below for the key of A:

There are may ways to apply these patterns. Experiment with rhythmic variations and breaking the sequence up into ascending and descending melodic ideas, juxtapose different chords, etc.

More Commonalities: Two For the Price of One

You are looking at the common notes of the VII and III zones. The starred note positions are the IV (C) and VII (F#) of the Key of G. Notice that when these stars are excluded, both zones are geometrically identical:

 When the C and the F# are removed the remaining notes follow the same geometry even though they are in different places within the key. Notice the grey ellipses which indicate the 'half-step cluster' positions ...

There are many ways this patten can be brought into your repertoire. Consider that you can use precisely the same fingerings in both positions and never go outside the key. That's two notes for the price of one.

Using scale degrees, you can move the pattern to any position. There will always be two patterns in any key in the same relative positions as dictated by the ket degrees.

"Goes to Eleven" (Commonalities in Diatonic Zones VII and III)

The VII Zone and the III zone are the only two patterns which contain all the notes of a key across all six strings within single hand positions. There are a few interesting similarities in the arrangement of notes within these two patterns. Knowing their common characteristics will give you an edge in finding your way around as you play.

Here we see all of the 3rds which align the same way in both zones. Since the same exact fingerings happen in two places within any key, if you practice these forms in one position you are practicing the other at the same time. Your muscle memory will thank you.

The first diagram shows the patterns using Roman numerals which are the same for every key. Notice the differences in the peripheral notes between the two patterns. As you become familiar with the highlighted patterns, you can start adding the other notes in, being aware of how these notes relate to the commonalities.

The next diagram shows the patterns in the key of F:

Here is notation for the patterns in the key of F:

Next, here's the pattern in the key of G:

Try playing the VII Zone ascending and the III Zone descending at a steady tempo:

Parallel Key Wedges

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.

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 3rd, 7th 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.