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.

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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.


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Fretography Zones

In the previous entry, you were introduced to the basic premise of Fretography; the mapping of the fretboard by means of systematically identifying significant landmarks. We looked at the three Axis positions which provide framework for a more detailed look at the overall note pattern.

Now we'll look at two of the five basic diatonic zones in the Fretography system. These zones are each named for the scale degree (numerical step of the scale) which is the lowest note in that zone. Because E is the 3rd scale degree in the key of C, and E is also the lowest note on the guitar, we begin with the III Zone (at the left of the diagram above). The next zone we will look at is the VII Zone, which is based on the note B, which is the 7th scale degree of the key of C.

There are three more zones, but these are the primary zones due to their symmetrical relationship to each other and the system as a whole.

Each of these two zones spans four fret spaces (including the open strings as a fret space). Because of this, it is possible to play all the notes in each zone without shifting the hand. Position the left hand so that there is a finger over each fretspace in the zone and play each note with the appropriate finger from the lowest to the highest, string by string.


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What is Fretography ?

The word Fretography was coined by Mark Newstetter as the name of a system of mapping the guitar fretboard. As a guitar teacher, Mark felt that there was something missing from the available guitar study materials and methods. While there are plenty of diagrams to be found showing numerous scales and chords, there just wasn't a system of connecting the standard Diatonic system of music with a set of diagrams that add up to provide the student with a complete and consistent map of the note patterns of each key as a whole.

In other words, rather than merely putting together a series of diagrams of chords and scales which are learned one by one, Fretography approaches the fretboard as a whole right from the start. This gives the student an iconic picture of the whole system of notes of every key which beginners and advanced players alike find extremely useful in finding their way around the fretboard.

Many guitar students struggle to understand how each scale and chord they learn are related to each other in a musical key. The very concept of keys is difficult enough for the beginner and is not made any easier by the usual piecemeal approach to fretboard patterns.

The fact is, there are important 'landmarks' on the fretboard which are completely overlooked in some methods and only given token significance in others. In Fretography, these landmarks given the attention they deserve; they are assigned names which correspond with their significance in standard music theory.

For instance; there are three places in the system where there is a note on each string at a particular fret. The open strings (EADGBE), the 5th fret (ADGCEA) and the 10th fret (DGCFAD). The 12th fret notes are the same as the open strings an octave higher, so it can be thought of as theoretically the same place.

Fretography gives each of these positions a name. EADGBE is the 'Phrygian Axis', ADGCEA is the 'Aeolian Axis' and DGCFAD is the 'Dorian Axis'. These names are based on the diatonic modes which stem from the top and bottom note of each position in the key of C: E = Phrygian mode (3rd step of the key), A=Aeolian mode (6th step), and D = Dorian mode (2nd step). These three Axis positions are found in all twelve keys and define the fret positions based on the 3rd, 6th and 2nd step of each key.

At first glance, the remaining notes of the key seem to be spread around in a random pattern. In fact there is a very precise symmetry in the pattern, but it is not immediately obvious. Fretography makes sense of the apparent disorder. After identifying the three axis positions, other landmarks are mapped and named.

Imagine trying to get from place to place in an unfamiliar city without a map that shows the overall boundaries of the city. Imagine having a map with no names for neighborhoods or streets. This is in fact how most methods approach the fretboard. Fretography assigns logical names to the various landmarks, patterns and zones of the fretboard which relate directly with conventional music theory so you have a dynamic way of learning how each scale and chord fits in with the whole of music theory. This ultimately makes it easier to learn music as well as improvise.


All contents of this blog are © Mark Newstetter