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.


All contents of this blog are © Mark Newstetter

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.

____________________________________________________________________


All contents of this blog are © Mark Newstetter

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.


All contents of this blog are © Mark Newstetter

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).


All contents of this blog are © Mark Newstetter

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.


All contents of this blog are © Mark Newstetter

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.


All contents of this blog are © Mark Newstetter

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.


All contents of this blog are © Mark Newstetter