Spiral Galaxy Pattern

When the notes between the half-step clusters are connected they can be organized into a pattern that resembles a spiral galaxy. The benefit of this pattern is that it greatly simplifies visualizing the positions of the notes on the fretboard as you play.

Notice that the pattern is based on the top four strings. Also notice that the lower three strings contain their own symmetry. The half-step clusters on the lower three strings are shown as white ovals in the diagram above.

Study the pattern and try playing the notes along the curved arms extending from the center cluster, naming the notes as you play them. Notice that there are only three notes which are not part of any of the half-step clusters; A, D, and G. D the central note in both arms, while A and G reverse their positions relative to the central cluster from one arm to the other, though A is always the lower pitched tone and G the higher. In the arm on the left G is the highest tone, in the arm on the right, A is the lowest tone.

In Fretography, these spiral arms are named for the diatonic super-zones in which they are found, which also coincides with the lowest pitched tone in each arm. The left arm is the Phrygian arm, the right arm is the Aeolian arm.

An interesting characteristic of the spiral arms is that each of them contains six of the seven notes of the key. Arranged alphabetically. the left arm (Phrygian) comprises the notes D, E, F, G, A, B. The right arm (Aeolian) comprises F, G, A, B, C, D. Notice that one begins where the other leaves off. The note D is the beginning of one arm and the end of the other when the tones in each are arranged alphabetically. C is missing from one arm, E is missing from the other. Of course, each of these notes is found inside the half-step cluster from which each arm stems.

Again, by studying the diagram you can discover other characteristics of the symmetry.


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Pentatonic Axis Positions

Pentatonic scales on the guitar are often thought of primarily as the basis of blues solo styles, usually in the minor mode, usually A minor;

-----------------------------------------------------5----8---------

--------------------------------------------5----8------------------

-----------------------------------5----7---------------------------

--------------------------5----7------------------------------------

-----------------5----7---------------------------------------------

--------5----8------------------------------------------------------

In fact, this pattern is both A minor and C major. This is only one of many pentatonic patterns. This particular pattern is by far the most widely used because of its technical simplicity. There is a note on each string at the 5th fret, each played with the 1st finger. There are no notes played with the second finger and there are three notes played with the 3rd finger (3rd, 4th and 5th strings), and three with the 4th finger (1st, second and 6th strings).

Before examining all the other pentatonic patterns, let's examine the actual tonal structure of the pentatonic scale.

The scale in the tablature above has the following tones;

A - C - D - E - G

The scale degrees of these five tones are;

VI - I - II - III - V

The interval pattern is;

A [minor 3rd] C [whole-step] D [whole-step] E [minor 3rd] G

Of course, we can add the octave of the first tone of the scale at the end;

A [minor 3rd] C [whole-step] D [whole-step] E [minor 3rd] G [whole-step] A

All five of these tones are found at the 5th fret. String by string;

1) A

2) E

3) C

4) G

5) D

6) A

Because the interval relationships are the same at all fret positions on the guitar, if the axis of tones on the 5th fret belong to a pentatonic scale, then so do those at the the other axis positions; the open strings, 10th fret, 12th fret, 17th fret.

Remember, the intervals between the strings are;

1)

[perfect 4th]

2)

[major 3rd]

3)

[perfect 4th]

4)

[perfect 4th]

5)

[perfect 4th]

6)

The three axes are shown in the diagram at the top of this entry at the open strings, 5th fret and 10th fret along with a look at the scale intervals for each, and notation. Also, the rest of the tones are shown as white circles, with gray ovals emphasizing the half-step clusters to bring out the overall diatonic symmetry.

So there are actually three pentatonic scales within each key. The major tonic of each scale is on the 3rd string of that axis, and the minor tonic is on the 6th string.

____________________________________________________________________


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Symmetrical Root Position Triads

Triads are simple chords consisting of three tones. In the most fundamental form, the Root Position, the lowest pitched tone in a triad is the root. Chords are named for the root tone. The next tone in the chord is the 3rd, which is two steps above the root. The highest pitched tone in a root position triad is the 5th, which is two steps above the 3rd.

Every major key contains a set of seven triads, one rooted in each tone of the key. Because of the sequence of whole-steps and half-steps which comprise a key, three of the triads are major, three of the triads are minor, and one triad is diminished. The structure of these three triad forms is as follows;

Major Triad

Root [ major 3rd ] 3rd [ minor 3rd ] 5th

C - - - - - - - - - - - - E - - - - - - - - - - - - G

Minor Triad

Root [ minor 3rd ] 3rd [ major 3rd ] 5th

D - - - - - - - - - - - - F - - - - - - - - - - - - A

Diminished Triad

Root [ minor 3rd ] 3rd [ minor 3rd ] 5th

B - - - - - - - - - - - - D - - - - - - - - - - - - F

The sequence of major, minor and diminished chords in each key is as follows;

I - - - - ii - - - - iii - - - - IV - - - - V - - - - vi - - - - vii - - - - I

major -- minor -- minor -- major -- major -- minor -- dimin -- major

The diagram at the top of this entry shows the triads of the keys of C, D and E on the four top strings in their symmetrical positions around the Aeolian Axis and the Void Axis.


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More Symmetrical Triad Inversions

The diagram above shows 1st and 2nd inversion triads. As in the previous entry, they are shown in the keys of C, D, and E. While all the roots of the triads in the previous entry were on the 2nd string. This time, the 1st inversion (blue shapes) roots are on the 1st string, and the 2nd inversion (green shapes) roots are on the 3rd string.

Once again, the chord shapes line up symmetrically around the Aeolian Axis (2nd inversion vi, 1st inversion vi) and the Void Axis (2nd inversion ii & iii, 1st inversion IV & V).


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Symmetrical Triad Inversions

Lets return to the tones of the key of C for a study of chord symmetry on the four top strings. The pattern above (click for larger image) shows the symmetry of some triad inversions.

Triad inversions are simple three note chords where the Root is not the lowest pitched tone in the chord as it is in the Root voicing. In a 1st inversion the 5th of the chord is lower in pitch than the Root, while the 3rd remains above the Root so that the pitch sequence from low to high is; 5th - Root - 3rd. A C major triad in its Root voicing is;

G - (5th)

E - (3rd)

C - (Root)

A 1st inversion C major triad moves the Root to the top;

C - (Root)

G - (5th)

E - (3rd)

A 2nd inversion C major triad moves the 3rd to the top;

E - (3rd)

C - (Root)

G - (5th)

The Diagram above shows 1st and 2nd inversion triads found within the top four strings with their roots on the 2nd string. The green triangles placed on strings 4, 3 and 2 represent 1st inversion triads, the blue triangles on strings 3, 2 and 1 represent 2nd inversions of the same triads. notice that the green and blue triangles are paired so that each 1st inversion and second inversion of the same three tones is connected. The gray triangles are a continuation of the pattern outside the primary symmetry.

Notice that the triads form a symmetrical pattern around the Aeolian Axis (indicated by a red vertical bar) where the E minor (iii chord) and F (IV chord) major chords are aligned in the key of C, and also around the Void Axis (gray vertical bar) which is the position of the B diminished (vii chord) in the key of C.

The pattern is shown in 3 keys; C, D, and E. E is shown with Roman numerals instead of alphabetical note names so that you can see the scale degree relationships. In the key of C, the triads are;

C major, D minor, E minor, F major, G major, A minor, B diminished.

The same pattern can be expressed as scale degrees as follows;

I = major, ii = minor, iii = minor, IV = major, V = major, vi = minor, vii = diminished.

(It's traditional to use lower case Roman numerals to identify minor and diminished chords)

The overall symmetry of the pattern can be expressed as;

vii - I - ii - iii --- IV - V - vi - vii

... with the iii and IV chords at the center, and two instances of the vii chord, an octave apart, as a pair of bookends, or as;

IV - V - vi - vii - I - ii - iii

... with the vii chord at the center and IV & iii at the lower and higher ends of the pattern, respectively.

These relationships apply to every key, so you can extrapolate from the three patterns shown and play the triads in all keys.


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Black Key Chords

Based on the key of C, from the open strings to the 10th fret - within the top four strings, we can group the black-key tones into a symmetrical pattern of chords. These chords are actually not in the key of C, but made up entirely of accidentals in that key. To place them in their own context, we will move to the key of Gb. The notation in the diagram above is in the key of Gb.

Gb has an interesting complementary relationship with C. On the fretboard these to keys are linked through the positions of the black keys and the tones F and B (B is called Cb in the key of Gb). F is the 4th of C and the 7th of Gb, B/Cb is the 7th of C and the 4th of Gb. These two keys are at opposite ends of the Circle of Fifths, so their relationship on the fretboard is perfectly symmetrical.

The chords in this exercise are inversions with the roots at the top and a 6th or 7th as the low note. Notice the first chord and the 4th chord are the same form, while the 2nd and 3rd chords are geometrical opposites.

The chords are: Gb 6/9, Ab-9/Gb, Bb-7#5/Ab and Bb 6/9. These chords are based on the 1st, 2nd, 3rd and 5th tones in Gb.

Play the chords in the sequence shown then group them in pairs; 1 and 2, 2 and 3, 3 and 4, 4 and 1, 4 and 2, 3 and 1. Play slowly, observe the indicated fingering. Be aware of the names of the notes you are playing and focus on their symmetrical relationships.


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The Circle of Fifths

Sooner or later, the legendary Circle of 5ths must make an appearance. For our purposes, we are highlighting the keys of C and Gb/F#. As we've established in the previous post, Gb is preferable to F# in Fretography theory because it's a flat-5th above C, as opposed to F# which is a sharp-4th. The theoretical difference may seem arbitrary, but there are ramifications of each key which lead in different directions.

Consider that all the keys in the circle containing sharps are based on natural tones, F# would be the only practical exception. The key of C#, which follows F# in the circle has 7 sharps, while its enharmonic Db has 6 flats. As a rule it's preferable to opt for the key with more natural tones, so Db wins out over C#. Also, were we to accept F# over Gb, we would have, by default, seven keys with natural tonics, one key with a sharp tonic and four keys with flat tonics. If we choose Gb we have seven natural tonics and five flat tonics; much more logical since there are seven white keys and five black keys.

That said, treating the black-key tones as sharps in no way undercuts the Fretographic symmetry as we have outlined it. This point is largely a theoretical one. If we chose F# as the key, the Axis would still be Aeolian, but it would be based on D# and not Eb as it is in the key of Gb. In fact Fretography theory would be flawed if it was at odds with the enharmonic relationship between F# and Gb.

This blog is more concerned with mapping the notes on the fretboard than explaining every nuance of music theory, so we'll leave it at that for now. Suffice to say that here we will refer to the axis of black-key tones at the 11th fret as the Secondary Aeolian Axis which is based on its theoretical tonic of Gb on the 3rd string.

Next .... Black-key chords.


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11th fret Symmetry

The 11th fret is the location of the only natural alignment of black-key tones on the fretboard. In Fretography we refer to this position as The Void. However these same tones can be part of three flat keys; Db, Gb and Cb which have five, six and seven flats respectively.

Notice that these tone positions follows the same logic of 'paired symmetry' we've previously examined. With five tones to consider, they are paired in rotational symmetry as follows:

Gb - Bb

Ab - Ab

Db - Eb

In other words, wherever you find Gb on one side of the Axis - within the top four strings (white background) or within the bottom three strings (blue background), you'll find Bb in the diametrically opposite position. The same is true of Db and Eb. Ab (the second tone of Gb) is opposite itself, just as D is opposite itself in the key of C. The piano keyboard in the diagram makes the symmetry even more obvious. Can any note other than Ab be seen as the 'middle' of the five black keys?

When seen from this perspective, we are thinking of these tones as belonging to the key of Gb, which is found on the 3rd string of the Axis, shown on the 11th fret in the diagram above. Gb is structured as follows;

Gb W Ab W Bb H Cb W Db W Eb W F H Gb

Notice that our set of black-key tones excludes the 4th and 7th tones of Gb.

Gb W Ab W Bb H Cb W Db W Eb W F H Gb

[ An interesting coincidence is that the Cmajor/Aminor pentatonic scale (C D E G A) is produced by removing the 4th (F) and the 7th (B) from the key of C, and that the elimination of these same tones; The 4th of Gb; Cb (enharmonic of B) and the 7th of Gb; F, result in a pentatonic scale based on 5 different tones (Gb Ab Bb Db Eb). ]

C W D W E H F W G W A W B H C

This is the template for Pentatonic Scales typical in rock and blues. If you are already familiar with Pentatonic scales on the guitar, you'll recognize the pattern. But rather than approach these tones from that angle, we'll look at them in their diatonic context as the black-key chromatic tones of the key of C major/A minor.

C Db D Eb E F Gb G Ab A Bb B C

Keep in mind that, though the diagram shows the pattern from the 5th fret up, the pattern from the 12th fret to the 17th is exactly the same as from the open strings to the 5th fret, so nothing is really missing. By placing the Secondary Aeolian Axis at the center of the diagram, the symmetry becomes clearer (refer to the previous post for the view beginning at the open strings).

In an upcoming post we'll look at chords based on the five black-key tones. But first, more about the difference between the keys of Gb and F#.


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Black Keys /Accidentals in C

There are seven tones in the key of C (as there are in all 12 keys), these are the natural tones. And since there are twelve tones in the entire system, five tones remain. The black keys of the piano are those five tones not belonging to the key of C. These tones are the sharps or flats; C#/Db - D#/Eb - F#/Gb - G#/Ab - A#/Bb. On the guitar these same five tones are aligned at the 11th fret and also distributed across the fretboard in the symmetrical system we've been mapping out in this blog. These 'black-key tones' are also known as the accidentals in the key of C.

The natural tones align in three axis positions on the fretboard between the open strings and the 12th fret; the Phrygian Axis at the open strings (and 12th fret), the Aeolian Axis at the 5th fret, and the Dorian Axis at the 10th fret (see 'What is Fretography'). But there is one more axis; the axis formed at the 11th fret by the alignment of the 'black-key tones.'

Naming this axis is not so simple. We could call it the Black Key Axis, or the Sharp and Flat Axis, or the Accidental Axis But it would be better to use a term that is more in keeping with the names we've assigned the other three axes, which are each based on a Diatonic Mode.

Taken as a group, the five black-key tones can be described as the 5 flats of the key of Db, which is the first of three keys which incudes these tones; Bb, Eb, Ab, Db, Gb (with C and F remaining to complete the key). The two other keys which include these tones are: Gb - has all five plus the addition of Cb (which is enharmonic with B), and the key of Cb - all 7 tones are flats.

The black keys can also be thought of as C#, D#, F#, G# and A#. which can in turn be found in three keys which are enharmonic with the three flat keys we've just described; B (enharmonic of Cb), C# (enharmonic of Db), and F#(enharmonic of Eb).

We'll use the key Gb as the context for this Axis because it comports with the symmetry principle better than F#. In doing so we are choosing a key signature which is a b5 above C, as opposed to F# which is an augmented 4th above C. Theoretically, a flat 5 trumps a sharp 4. Thinking of it as the Secondary Aeolian Axis places it at the center of another layer of symmetry, as we shall see in the next blog post.

In Fretography we the Axis of tones not belonging to the key in which we are working as the Void Axis. The Secondary Aeolian Axis of the key of C is simply the Aeolian Axis in the context of the key of Gb. In C, it is the only fret position made up entirely of tones outside the key. In Gb it is at the center of the diatonic symmetry. Each key, then, contains a Secondary Aeolian (or Void) Axis on the fretboard based on the position between its Dorian and Phrygian Axes.

In music theory there is always more than one way to describe a given concept. For example, The 'Major Scale' is also known as the 'Ionian Mode.' The tones of an A minor 7th chord can also be described as an inversion of a C 6th chord. It all depends on context. For that reason, some structures in Fretography can have more than one name.

__________

The five black-key tones also comprise a pentatonic scale based on the same interval structure as that typically used in rock and blues. If you're familiar with pentatonic scales on the guitar, play the black-key tones shown on the diagram above and you'll recognize the patterns.

But pentatonic scales are not just for playing rock and blues, and the black-keys needn't only be seen in the context of pentatonic scales. As important as it is to know where the natural tones are, it's equally useful to know where they are not. The pattern of black-key tones, studied in their natural context as sharps and flats, will enhance your fretboard comprehension.

We'll look at more theoretical possibilities for the black-key tones in the next post.

The diagram above shows all the positions of the black-key tones, and also includes Cb and F (in gray) which complete the key of Gb.


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Tritones and Major 3rds (The Double Helix)

Here's a simple exercise based on the diatonic symmetry we examined in the previous post. The notation includes fingering in small italics and strings indicated with circled numbers. The diagram shows the symmetrical geometry of the pattern, beginning with C and E at the 5th fret and then moving out from there, first higher, then lower. Click on the image to enlarge.

C and E (red) comprise a major 3rd (two whole-steps). F and B (black) are a tritone (three whole-steps).

You can also see how the positions of middle C and E on the piano align with the same pitches at the center of the system on the fretboard, at the 5th fret.


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Diatonic Symmetry 2

The key of Gb is halfway around the circle of 5ths from the key of C natural. The relationship of these two keys is significant because it illustrates the relationship between the symmetry of the Diatonic system and the geometry of the tonal array of the guitar fretboard.

The diagram above shows how Gb is arrayed on the fretboard and the piano keyboard. Notice how the axis positions of Gb are nested symmetrically between those of the key of C. For instance; the Aeolian Axis of C is found on the 5th and 17th frets, while the Aeolian Axis of Gb is on the 11th fret, precisely halfway between them. The Phrygian Axis of Gb is at the 6th fret, one fret above the 5th fret Aeolian Axis of C, while the Dorian Axis of Gb is at the 16th fret, one fret below the 17th fret Aeolian Axis of C. The Dorian and Phrygian Axes of C are at the 10th and 12th frets respectively, flanking the central Aeolian Axis of Gb.

Of course Gb has the same symmetry as C, but its complementary relationship with the Natural key makes it unique. Any two keys at opposite ends of the Circle of 5ths (A major and and Eb major, for example) will have a similar complementary symmetry.

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Diatonic Symmetry

Fretography focuses on the symmetrical distribution of tones on the guitar fretboard. This symmetry is not some graphic trick. It's not an accident that the notes line up the way they do. The symmetry is inherent in the Diatonic system itself. Out of the twelve tones which comprise the diatonic system (which is the basis of western music), a set seven tones make up each key. The interval relationships within each key are the same (see "Tetrachords" in this blog).

The whole-steps and half-steps are sequenced symmetrically in a repeating pattern. Strangely, this symmetry is obscured in the major scale;

W-W-H-W-W-W-H

However, if we look at the Dorian mode, which begins on the second scale degree, we can see a clear mirror symmetry around a central whole-step;

W-H-W-W-W-H-W

This mode is central to the Diatonic system, and the underlying element of the symmetry of the fretboard.

In the key of C, D becomes the fulcrum around which the entire system revolves;

--------------------------------------------------------------------------

D W E H F W G W A W B H C W D W E H F W G W A W B H C W D

---------------------------------------------------------------------------

If you study the line above you'll see that the whole-steps and half-steps are symmetrically arrayed around the D. There is no other tone in the key which can function as the fulcrum. Place any other tone at the center and you will have asymmetry.

Notice that, except for D, all the other tones are paired symmetrically; C&E, G&A, B&F are each paired. They are three sets of symmetrical counterparts on either side of the fulcrum, while D is its own 'partner'. This arrangement is precisely what we see on the guitar fretboard in the Fretography system.

From the open strings to the 10th fret, within the four top strings as a set (D-G-B-E low to high), and within the three bottom strings as a set (E-A-D low to high) the tones are found in symmetrical opposition to each other in the same pairs as we've just laid out. Where C appears on the 1st fret of the 2nd string, E is found on the 9th fret of the 3rd string. At the center of the span, C is on the 3rd string 5th fret, E is on the 2nd string 5th fret, and so on.

Study the diagram at the top of this post, and those in the previous posts and you will see how this method will enable you to achieve a greater awareness of the relative positions of all the notes on the fretboard, not simply as linear progressions, but connected over the entire grid in every direction and across wide distances.


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Middle C

There are three 'half step cluster' positions on the fretboard between the open strings and the 10th fret that correspond to middle B - C - E - F on the piano keyboard. These are shown in gray in the diagram above. The 'semi clusters' E and F below middle C are shown in blue, and B - C above middle C are shown in pink.

The diagram only names the notes of the four top strings so as to emphasize the symmetry within this string group.

If you have a piano, compare the pitches as shown in the diagram.

You can see that moving from lower string/lower fret to higher string/higher fret will quickly get you to higher pitches, while moving from higher string/lower fret to lower string/higher fret will enable you to change fret positions while essentially staying within the same tonal range.

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Half Step Cluster Paths

The half-step clusters can be played as a set of two patterns - or paths - running from the lowest string to the highest and, in the key of C, from the open strings to the 13th fret. The term path is used because it best describes the linear nature of these patterns.

Try playing the paths using this fingering (lowest string first, slashes indicate string change);

Phase One: [ 0, 1 / 2, 3 / 1, 2 / 3, 4 / 1, 2 / 3, 4 ]

Phase Two: [ 1, 2 / 1, 2 / 3, 4 / 1, 2 / 3, 4 / 3, 4 ]

The first path, called Phase One, ascends from the open 6th string, beginning on the IIIrd scale degree of the key (bottom E) and ends at the 8th fret of the 1st string at the Tonic (C). Phase Two ascends from the 7th fret of the 6th string on the VIIth scale degree (B), and ends at the 13th fret of the 1st string, on the IVth scale degree (F). Notice that the fret positions of the end of Phase One coincide with the beginning of Phase Two, and that the end of Phase Two at the 12th and 13th frets on the 1st string coincides with a repeat of the same two notes on the 6th string. These bottom string notes then become the beginning of Phase One again.

If we transpose the pattern into other keys, the geometry remains the same, though the fret positions change accordingly. So, in the key of A, for example, Phase One, which begins on the IIIrd scale degree, would originate at the 9th fret of the 6th string (C#), while Phase Two would start out at the 4th fret of the 6th string (G#).


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Fretboard Symmetry

The diagram above shows the tones of the key of C as they are arrayed on the fretboard from the open strings to the 10th fret. There are no tones in the key on the 11th fret, and the system begins again at the 12th fret. By splitting the system into two groups of strings, upper and lower, we can see the clear embedded symmetry.

The 'upper string group' comprises the top four strings (D, G, B, E from low to high), the 'lower string group' comprises the three bottom strings (E, A, D from low to high), the 4th string (D) is shared by both groups.

The three half step clusters in the upper string group each comprise the same four pitches - middle B, C, E, F on the piano - shown as VII, I, III, IV in the diagram. The two clusters in the lower string group contain the same four tones and octave lower. Also, each of the string groups contain two partial clusters with two tones in each.

Just as the repeating pattern of black and white keys on the piano is essential in understanding and accessing the tones on the piano keyboard, this method of mapping and diagramming the guitar fretboard has real advantages over the conventional linear approach.

Every scale, mode, interval and chord can be understood more comprehensively with the help of the symmetrical approach offered by Fretography. Regardless of the style of music you play, your understanding of music theory as applied on the guitar will be enhanced.

Take some time to study the diagram above. Find your way around the fretboard using it as a guide. Let yourself meander, don't try to play scales, but treat the diagram as a roadmap and learn the terrain the way you would make your way around if your were visiting a new city.

You might start with the central half step cluster, positioned at the 5th fret, and then venture out from there in all directions, returning to the center again. Remember that the symmetry is based on two separate string groups, so stay within the top four strings for a while, then the lower three, before crossing between the two groups.


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Half Step Clusters

In the diagram above, dark ellipses indicate the positions of the diatonic half steps. The lighter gray regions are the zone patterns we have discussed previously. Notice that each of the two zone patterns contain two half step clusters consisting of four notes, and one 'partial cluster' consisting of two notes. There is a skewed cluster at the center of the system between the two zones.

Notice that this diagram replaces alphabetical note names with Roman numerals. C=I, D=II etc.

Learning the positions of these clusters will go a long way toward helping you to be able to clearly visualize all the note positions as you play. Memorize the fret and string positions of each cluster. Once you've done this you will know the positions of 4 of the 7 tones in the key of C. The remaining three tones are all whole steps apart, so you can navigate from any half step cluster in either direction on any string and play either two or three whole steps to get to the next cluster. More precisely, there are two whole steps going up from the highest tone in the cluster (IV), and two whole steps going down from the lowest cluster tone (VII) before arriving at the next cluster.

It may appear that the patterns are only roughly symmetrical. However, as well see in the next entry, there is a very precise symmetry embedded in the fretboard if you know how to look at it.


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Tetrachords

The tetrachord is a group of four tones spanning a perfect 4th. It is the basis of the Diatonic system, and it is the basis of the Fretography method.

A perfect 4th is an interval of two whole-steps and one half-step. For instance; C-D-E-F, which is based on the intervals; W W H (W=Whole-step, H=Half-step). So the first four notes of a major scale (in this case; C major) form a tetrachord. The next four notes in the scale; G-A-B-C are based on the same interval pattern; W W H, so it is a tetrachord identical in structure to the first. There is a whole-step between the two tetrachords, resulting in the pattern below;

tetrachord I - tetrachord II

C (W) D (W) E (H) F (W) G (W) A (W) B (H) C

This interval pattern is the same for every key. It can be expressed in terms of scale degree where a Roman numeral is used for each tone instead of an alphabet letter;

tetrachord I - tetrachord II

I (W) II (W) III (H) IV (W) V (W) VI (W) VII (H) I

One way to apply this principle to the fretboard is to locate the positions of the half-steps within a key. By memorizing the pattern of half-step positions on the fret board, all the note positions can be learned more easily since the remaining notes will all be based on whole-steps.

In other words, simply by knowing that half-steps are III-IV (E-F) and VII-I (B-C) you have learned the precise positions of four of the seven tones of the key, and the other three tones pretty much fall into place.

In the next post we'll look at the position of the half-steps on the fretboard.

All contents of this blog are © Mark Newstetter

The VII Zone

Because the Zone patterns in Fretography are named for their Diatonic position, you always know where you are within any key. In the key of C major, the 7th scale degree is B. By a happy coincidence, B is found on the 7th fret of the 1st and 6th strings, so the VII Zone in the key of C is based on the 7th fret.

If you position your 1st finger at the 7th fret the next three fingers align with the next three frets and stay that way when you play this pattern. Playing the pattern from low to high gives you the following fingering;

string > finger

1st > 1 - 2 - 4

2nd > * - 2 - 4

3rd > 1 - 3 - 4

4th > 1 - 3 - 4

5th > 1 - 2 - 4

6th > 1 - 2 - 4

*There are only two notes on the 2nd string in this pattern.

The bold numbers indicate the positions of the tonic.

By grouping the strings in pairs; low, middle and high, we can see the symmetry of the pattern more clearly;

1st > 1 - 2 - 4

2nd > * - 2 - 4

---------------

3rd > 1 - 3 - 4

4th > 1 - 3 - 4

---------------

5th > 1 - 2 - 4

6th > 1 - 2 - 4

Learn the pattern string by string from bottom to top, starting with B on the 6th string - ending with D on the 1st string. Notice that the two bottom strings (5 and 6) have the same fingering. Likewise, the fingerings on the two middle strings (4 and 3) are identical. Of the two top strings, the 2nd string has only two notes which are played with the 2nd and 4th fingers, and the 1st string fingering is 1 - 2 - 4.

Study the diagram, giving special attention to the positions of the half-steps, B - C / E - F. Notice that they form clusters on the two bottom strings at the 7th and 8th frets, and on the two middle strings on the 9th and 10th frets. There is also a half-step on the 1st string at the 7th and 8th frets which duplicates the pattern on the 6th string.

The VII Zone is the simplest and fastest way to play diatonic scales across all six strings since it has such clear symmetry and does not involve a shift of hand position. Playing the complete pattern will take you from the 7th scale degree of the key of C, to the 2nd scale degree, two octaves higher. The total range of the VII Zone is two octaves plus a minor 3rd.

A two octave C major scale is played by beginning with C on the 6th string and ending on C 1st string. For single octave C major scales, play from C 6th string to C 4th string, or C 4th string to C 1st string. Whenever you play any part of this Zone pattern, be sure to use the same fingering, keeping your fingers aligned with the frets as described above. By doing so, you'll be able to find the note you need, when you need it.


All contents of this blog are © Mark Newstetter