Fretography

3rd Rail Chord Symmetries (Part 4)

2011-12-20T14:16:00.000-08:00

Red diagonals indicate minor 3rds spanning the 3rd Rail. Roman numerals indicate their respective scale degrees.

Above you see the positions of the minor 3rds which span the 3rd Rail in the key of C. Each of these double-stops are at the center of a 7th chord. Two of them – the vi and the iii (dark red) – are each the center of a major 7th chord. The other two – the vii and ii (pale red) – are the centers of two different types of chords. The ii is the center of a B minor7 b5 (also called 'half-diminished') chord, and the vii is the center interval of a G dominant 7th.

In the diagram below, you see the two major 7th chords which pass through the above min3rd positions. The IV chord (F maj7) radiates from the a minor 3rd at scale degree vi, and the I chord (C maj7) radiates from the E minor 3rd at scale degree iii;

Roman numerals indicate scale degree of each major 7th chord root.

If we extend these 7th chord forms a 3rd above and below, we then have a set of minor 11th chords. Each of these extended forms radiates from a different part of the key, even though they have the same geometry;

Roman numerals indicate scale degree of each minor 11th root.

If we focus on these two extended arpeggios side by side, with some in-between frets removed for a better view, we see that their internal structures are identical. The form on the left is rooted in the second scale degree (D), the form on the right is rooted in the 6th scale degree (A)

The D minor 11th arpeggio (left) can be played from the open strings as indicated, or from the 12th fret.

The diagram below shows the centered interval structure of the two forms;

And here's where these two arpeggios are played on the piano keyboard;

The only way to distinguish one of these forms from the other from a geometric perspective is to look at the relationship between each of the arpeggios and the positions of the notes which surround each one. Because of their differing positions within the key, these 11th chord-arpeggio forms live in different surroundings on the fret board. We'll go more deeply into those relationships in a future post. For now, lets look at how each of these two big S shapes break into four triads;

Each three-note sequence in these forms is its own triad. Of the seven triads belonging to the key of C, six are present in these forms; C major, D minor, E minor, F major, G major and A minor. The remaining triad – B diminished – is found in both of the remaining 11th chord arpeggio forms.

Remember that the D minor 11th arpeggio can be played either rooted in the open string D or at the 12th fret.

Next: 3rd Rail Chord Symmetries (Part 5) – we delve into extended Dominant and Leading Tone Sevenths ...

3rd Rail Chord Symmetries (Part 3)

2011-12-19T15:00:00.000-08:00

So far we've examined the 7th chord forms which radiate around the 3rd Rail – that problematic nexus of the 2nd and 3rd strings. By treating it as a fulcrum or the center of gravity of the fret board, it becomes a useful organizing element. No longer a problem, but a solution.

Here's the interval structure of the four types of diatonic 7th chords in the major keys, based on the major and minor 3rds which occur between each chord degree;

Dotted line separates symmetrical and asymmetrical chords based on their interval structure.

Notice that the major 7ths and minor 7ths have opposite interval structures. The same opposing symmetry is true of the V and VII chords. Because these symmetries are integral to the chords' structure, it's logical that they play out on the fret board as geometrically symmetrical patterns.

The center interval in each of these 7th chords spans the 3rd Rail. Only the minor 7th chords have a major 7th in their centers. It takes a change in perspective to think of chords from the center outward, rather than from the bottom up, but it will give you a much more sophisticated understanding of harmony and a greater command of the fret board.

––––

The three minor 7th chords are rooted on the 2nd, 3rd and 6th scale degrees of a major key. The major 3rds at the center of these chords are rooted on the 4th, 5th and 1st scale degrees, respectively.

The I - IV - V center intervals on the 3rd Rail are essential landmarks on the fret board. We've already examined these positions in this post. The next diagram shows all the major 3rds spanning the 3rd Rail up to the 17th fret (If your guitar has 24 frets then you also get one there);

Roman numerals indicate repective positions of major 3rds rooted on 3rd string.

The minor 7th chords rooted on the 4th string all pass through the above positions;

Lower case Roman numerals indicate root positions of minor 7th chords rooted on 4th string.

If we extend these 7th chord forms a 3rd above and below, we then have a set of 11th chords;

Roman numerals indicate root positions of 11th chords on 4th string.

We have previously treated these low note extensions as integral parts of the 7th chords, but now we'll look at them in their own light. We'll start with the chord which radiates from the central axis position; the 5th fret in the key of C where the tonic major 3rd is positioned;

This chord form is only playable as an arpeggio because several notes are found on the same strings and it is spread out over too many frets, but an arpeggio is still considered a chord because of its harmonic structure

Here's the chord on the piano keyboard;

In this position – starting from the center and moving outward – we first find the C major 3rd (C-E), the A minor 7th chord (A-C-E-G), then the F major 11th (more precisely F major 7 #11), consisting of six notes (F-A-C-E-G-B). So this form is, starting from its lowest note, is the F major 11th chord – rooted in the fourth scale degree.

The F major 7 #11 can be broken into 4 triads;

The following diagrams show the shapes of the chords indicated in the notation above. Each three note sequence is a section of the overall extended 11th chord arpeggio;

The F major and E minor are only playable as arpeggios because they have two notes on a string, while the three notes of the C major and A minor can be arpeggiated or strummed or plucked together.

All seven of these extended arpeggio forms can be treated the same way. Play the notes of each form in consecutive three-note sequences (triads) starting from the low note, then from the highest note of each form.

Of course, any of these forms can also be played in other note grouping combinations. For instance, in addition to the triads shown above, each extended arpeggio form can also be split into three 7th chords – not just the central 7th chord we began with. Below is notation showing the three 7th chords within the F major 7 #11 arpeggio;

Lets look at the interval structure of all of the diatonic 11th forms based on their scale degrees;

The dotted line in the diagram above separates the first two chords from the next four because the IV, II and VI chords all have internally symmetrical interval structures, while each of the others is individually asymmetrical, though they are all part of a larger symmetry. Also notice that the only two which share the same interval structure are rooted in scale degrees II and VI.

Next: 3rd Rail Chord Symmetries (Part 4), we'll examine the triads if the major 7th extended forms which become the II and VI rooted 11th chords.

3rd Rail Chord Symmetries (Part 2)

2011-12-18T02:26:00.000-08:00

In the previous post, we examined the three minor 7th chords rooted on the 4th string and centered on the 3rd Rail, then added notes a third above and below the original four-note chord. The added high note is actually a 9th, and – since we are keeping the original chord root – the added low note can be thought of as a 6th (or a 13th).

Here's another example: If we take the tonic major 7th chord (C maj7) with the notes C-E-G-B as the Root-3rd-5th-7th respectively, the D added above the B of that chord is the 9th of the chord. The five notes comprise a C major 9th. The A added below the C is – theoretically – also a 6th above C. 6ths in chord structure are thought of as 13ths when added to 7th chords (or 9th chords), so the whole six-note sequence can be considered a C maj 9 add 13. And because the 13th (A) is now the lowest note in the chord, it may be called C maj 9 add 13/A. In chord naming, when a note other than the root is played as the lowest pitch, it is added to the chord name following a slash. The diagram below shows the relationships of these notes on the staff;

If we were to use the added low note as the root of these extended forms, we would call them 11th chords. For instance; A-C-E-G-B-D would be called an A minor 11th, F-A-C-E-D-G-B would be an F major 11th (actually, an F maj7 #11), etc. Of course, any three consecutive notes an a series of 3rds is a chord, so the sequence A-C-E-G-B-D contains four three-note chords; A min, C maj, E min, G maj. So you can choose to slice these patterns any way you want. However, the 7th chords comprising a single note on each of the four top strings are the most clearly symmetrical forms, and make a good core structure for purposes of study and practice, as well as providing clear landmarks for improvising and composing.

There are two major 7th chords in any major key. These are the 4th-string root position major 7ths in the key of C. They are F maj7 and C maj7, the I and IV chords of the key of C.;

The notes are shown in descending order on the staff because it visually follows their layout in the fretboard diagram.
Play the notes in ascending and descending sequences.

Here are the extended patterns of the above chords;

This pair of extended major 7ths have the unique characteristic of being the only two identical extended chord forms, and are each internally symmetrical – comprising two minor-major-minor-major-minor-3rd sequences.

Here's the extended 6th scale degree minor 3rd (A minor) between the two major 7ths;

F major 7th - A minor 7th and C major 7th extended arpeggio forms.

Here's the same configuration in the key of D;

G major 7th - B minor 7th and D major 7th extended arpeggio forms.

... and in the key of A;

F# minor is shown in the lowest and highest positions, around the A maj. 7th and D maj. 7th.

Returning to the key of C, here are the extended G dominant 7th (rooted on G at the 5th fret) and B minor 7 b5 (rooted on B at the 9th fret);

The extended dominant 7th becomes an E minor 11 b9 when the lowest note is taken as the root.
The extended B minor 7 b5 becomes a G dominant 11th when its lowest note is taken as the root.

These chords are shown below as they are positioned on the piano keyboard;

Here's the notation for these two extended chords. Notice that their interval patterns (and their geometry) are the exact opposite of each other;

Now let's look at the major 7ths, the dominant 7ths and the minor 7 b5 chords all together on the fret board;

These chord forms overlap in interlocking patterns, all based on the symmetry which is centered on the 3rd Rail. Remember that – by most accounts – the odd tuning of the interval between the 2nd and 3rd strings is a flaw – a glitch. But by treating that 'odd' interval as the fulcrum of the fret board, we see that there are very useful symmetries which stem from it.

In PART 3 we'll continue to explore the possibilities of these arpeggio forms.

3rd Rail Chord Symmetries (Part 1)

2011-12-17T19:28:00.000-08:00

Here's an set of patterns which make clear use of the 3rd Rail symmetry to simplify navigation. We can think of 7th chord arpeggios as spirals radiating around a central interval. For instance; the central interval (3rd–5th) in a minor 7th chord is a major 3rd. If the chord is rooted on the 4th string and played as a series of 3rds, the central interval will span the 3rd Rail and the overall shape of the chord will be perfectly symmetrical – therefore, easy to visualize. In Fretography this is the concept of 'centered chords'.

This diagram illustrates the basic principle. Starting with a 3rd interval as the center of the chord, we extend the chord an additional 3rd in both directions, so a 3rd becomes a 7th, then an 11th;

The chords we will study in this exercise are mostly arpeggios, which are chords that are played note by note rather than strummed. Knowing your arpeggios can really enhance your improvisations and your playing overall. Playing a chord as an arpeggio is necessary on the guitar when some of the chord's notes are on the same string and so can't be played at the same time. This is sometimes referred to as a "broken' chord. (We looked at some rudimentary arpeggios in a previous post.)

Below is the A minor 7th arpeggio of the key of C, rooted on the 4th string;

The notes are shown in descending order on the staff because it visually follows their layout in the fretboard diagram.
Play the notes in ascending and descending sequences.

See how the two minor 3rds within the chord radiate out from the central major 3rd. Now let's look at what happens if we add notes 3rd above and below this chord;

Italic numbers indicate fingering. Fret positions are indicated by bold non-italic numbers.
Original 7th chord tones are black, added notes are red.

The symmetry is clear. Of course, we can choose to make F the root of this new set of notes, in which case you are looking at an F major 7th sharp 11 arpeggio. But, for our purposes, we will treat the F and B as extensions of the original A minor 7th chord. Play this arpeggio slowly – ascending and descending – using the indicated fingering.

There are three minor 7th chords in any major key. They are rooted in the 2nd, 3rd and 5th scale degrees (D, E and A in the key of C). Though all three of these chords have the same interval structure, their positions in the key give rise to a different set of extended intervals for each.

Below is the extended minor 7th arpeggio rooted on the 3rd scale degree. Notice the same geometry of the central minor 7th chord (EGBD);

This is an E minor 7th, with diatonic 3rd extensions above and below. The C is a major 3rd below the root, and the F is a minor 3rd above.

There's one more minor 7th chord in the key of C. It is rooted on the 2nd scale degree, and it is D minor. The central minor 7th structure (DFAC) is the same as the two previous examples, but notice that it's the geometric and intervallic opposite of the iii chord – E minor.

Below are the three extended minor 7th arpeggios side by side. The vi chord is placed in the middle to emphasize their overall geometric symmetry. Remember that these forms will be in different fret positions in each key but will always retain their relative geometry based on their scale degrees.

Let's look at these chord forms as they are actually arrayed on the fret board.

Below you see the minor 7th arpeggio rooted on the 2nd scale degree. This time the chord is shown in its natural position on the fret board;

You can see that the geometry of this chord is the opposite of the previous example (the iii chord – E minor).

Here's the E minor again, with the whole fret board shown around it;

... and the extended A minor 7th;

Remember that these chords are extended versions of these minor 7th chords;

Here are all three extended minor 7ths in their actual positions in the key of C;

... and here's the same set of extended minor 7ths in the key of G;

Next we'll look at the four remaining 7th chords in the Key of C; C major 7th, F major 7th, G dominant 7th and B minor 7 b5.

The 3rd Rail ( The G & B Strings ) Part 2

2011-12-09T11:57:00.001-08:00

What's the best way to think of the 3rd Rail? How can you avoid hitting a wrong note when you move across it? Can't the guitar just be tuned so all the strings have the same intervals between them?

Actually there is a school of thought that a uniform tuning is the solution. Some tune the guitar to 'All 4ths' (E A D G C F) in order to avoid the issue of compensating for the odd interval. But - as stated in the previous post - most guitarists continue to use the standard E A D G B E tuning because it (probably) offers the best overall set of musical possibilities and because the vast majority of resources are available to guitarists in standard tuning. If you've found advantages to other tunings, more power to you. But if you are interested in getting the most out of standard tuning, then you'll want to come to terms with the 3rd Rail.

Think of it as a small hill. When you ascend from the 3rd to the 2nd string, you shift up a fret. When you descend from the 2nd to the 3rd string, you shift down a fret;

Because the interval of a Perfect 4th (W-W-H) is one half-step larger than a Major 3rd (W-W), shifting up one fret when crossing from the 3rd to the 2nd string will produce a Perfect 4th, while moving from the 3rd string to the 2nd string on the same fret produces a Major 3rd. Since there is a Perfect 4th between all the adjacent strings except the 2nd & 3rd, you can think of the Perfect 4th as the 'default interval' when crossing strings. So, when you cross from the 3rd to the 2nd string, think of a Perfect 4th as the norm. To do this, you only need to remember to shift up a fret when you go from the 3rd to the 2nd string, and go down a fret when going from the 2nd to the 3rd string.

Try playing all the notes on the 5th fret one by one from the lowest string to the highest; A - D - G - C - E - A. These are all 4ths except C - E, which is a major 3rd. If you were to play a series of 4ths starting from the same note, you would play the notes; A- D - G - C - F - Bb. Below is notation and tablature for this exercise;

Think of the 'Same Interval' sequence above as the default path for crossing all six strings.

Below is a diagram showing all the natural tone (key of C) Perfect 4ths on the fret board between adjacent strings, connected with green bars;

Notice that the diagram is divided between the upper four strings and the lower three strings. This is to emphasize the symmetries within these groups. Below are separate diagrams for each string group;

Upper String Group 4ths

Lower String Group 4ths

There are two notes on the fret board which are not part of these adjacent string 4ths; the F on the 1st fret of the 6th string, and the B on the 7th fret of the 1st string.

Also, within the Upper String Group, the F on the 3rd fret of the 4th string is isolated from the 4ths, but is a counterpart to the 1st string B. Similarly, the 4th string B in the Lower String Group is a counterpart to the 6th string F.

The interval from F to B is an Augmented 4th (W-W-W), which is a half-step larger than a Perfect 4th (W-W-H), so these two notes do not align when they are in adjacent string/fret positions.

Remember that starting from the middle (5th fret) and moving in both directions from there is preferable if you want to really absorb the symmetries.

The Third Rail (The G & B Strings)

2011-12-04T13:28:00.001-08:00

What happens between the 2nd & 3rd strings on the guitar ... the G & B strings? There's a long and complex history behind the tuning of the guitar, which we won't go into here ... (google it) ... but to say that at some point the decision was made to tune the 1st & 6th strings to the same note, two octaves apart, and that those strings would be tuned to E. Because there are 6 strings on the guitar, there is no way to tune them all to the same interval and still have the same note on the highest and lowest strings. If most of the adjacent string pairs are tuned to Perfect 4ths, one of the pairs must be tuned to a Major 3rd. That major 3rd falls between the G (3rd) string and the B (2nd) string in standard tuning;

The result of this tuning is that scale patterns and chord forms are broken into various forms depending upon whether or not they cross between the oddly tuned strings. It's a compromise which makes barre chords possible, and it actually makes certain chords in the upper strings easier than they would be were the strings all tuned to 4ths. Of course not everyone accepts this tuning compromise, and there are numerous alternate tunings for the guitar. But the vast majority of guitarists are willing to work within the boundaries of the EADGBE or P4th - P4th - P4th - M3rd - P4th tuning.

In Fretography, the Major 3rd interval between the 2nd & 3rd strings in called the 3rd Rail. The 3rd Rail is a landmark on the fretboard map. It is a juncture – a turning point, or set of turning points. If you think of it the right way, it stops being an obstacle and becomes a useful navigational tool.

Remember that the 3rd Rail is the middle latitudinal axis of the upper string group's symmetry;

Any tonal interval occurring between any other two adjacent strings will be a different shape if it spans the 3rd Rail. For instance; a major 3rd played between the 2nd & 1st, 4th & 3rd, 5th & 4th or 6th & 5th strings will be a short diagonal, spanning two strings and two frets, while a major 3rd spanning the 3rd Rail will cross between the strings in a single fret position;

Compare the sound of the major 3rds in the upper string group (light blue). They are all the same pitches. The dark blue diagonals in the lower string group are an octave lower. All the major 3rds in both octaves are the same shape on the fret board except the one in the 3rd Rail.

There are three single-fret major 3rds in the 3rd Rail in the key of C: The G major 3rd of the open strings (and 12th fret), the C major 3rd of the 5th (and 17th fret), and the F major 3rd of the 10th (and 22nd fret). The symmetry of these positions is shown below;

These three fret positions are the three axis positions, which are indispensable in navigating the fret board.

Next post; The Third Rail - Part 2.

Voyage to the Bottom of the Staff - Part 2

2011-11-23T09:42:00.001-08:00

The Grand Staff is the standard system for written piano music. As a guitarist you may want to be able to read music written this way. If you already read guitar notation, you are used to reading in treble clef. You are also used to playing pitches an octave lower than their standard pitch because guitar music is written an octave higher than it sounds. So, reading in standard pitch, as you'll have do when reading music written for piano or voice, requires a change of attitude.

The diagram above shows all the notes on the grand staff in a symmetrical pattern. We use symmetry in the Fretography method because it strengthens cognition. When you study the note-pairs in the symmetry you'll be able to see connections between notes even when they are far apart in pitch. This is useful whether you are reading in standard pitch, or – more typically for guitar – transposed in treble clef.

The symmetries of the individual treble and bass clefs have been explored in previous posts. Now we are looking at the overall symmetry of the combined bass and treble staves. Pay special attention to the notes of the open strings on the staff as indicated at the right of the diagram. Of course these same pitches are found in various places on the fretboard. Learn to associate the each note on the staff with all of its fretboard positions starting with the notes of the open strings, then adding C and F.

Notice that C is the central note within the grand staff, and that middle C can be written one leger line below the treble staff and/or one leger line above the bass staff. Also note that the positions of B and D are mirrored between the two staves, as are E - A, and F - G.

Below is a comparison of the positions of middle C on the fretboard, the grand staff (standard pitch) and transposed for guitar on the treble staff;

We should mention that there actually is a special treble clef – the octave-down or octave-dropped treble clef – which serves the purpose of indicating that the notation is transposed;

The little 8 hanging from the bottom of the clef indicates that the notes on the staff are played an octave lower than written. You will occasionally see this clef used for guitar music, though the transposition is usually assumed even when a standard treble clef is used.

The more familiar you are with the positions of notes on the fretboard, the easier it will be to transpose.

Try playing melodies you already know in different octaves. One difficulty is that you may need to employ different fingerings when playing the same melody in a different octave. If you take a systematic approach, this will be less of an issue. The usual reason for fingering changes is that in one octave range, the melody may be within the four lower strings, and when it's transposed it crosses the 2nd and 3rd strings (what I call the 3rd rail.), thus requiring an adjustment to compensate for the different relative tuning between those strings.

Here's a simple rule; When you are ascending from the 3rd to the 2nd string, you must shift up one fret to maintain the same interval pattern of the lower 4 strings. When you are descending from the 2nd to the 3rd string, you must shift down one fret. In other words; when you go up you add a fret ... when you go down you subtract a fret.

We'll look at the shift between the 2nd and 3rd strings in greater detail in a future post.

Reading Notation: Voyage to the Bottom of the Staff

2011-11-22T09:06:00.001-08:00

Prepare yourself for a geeky look at a slightly obscure aspect of music theory for the guitar. What you are about to read, should you proceed beyond this introduction, will require both courage and patience - traits which are not often found in the same individual. But if you are one of those rare guitar players who is willing to stretch your synapses, read on.

Guitar music is usually written in the treble clef, transposed on the page an octave higher than its true pitch. For instance, the note pitch of middle C falls here in guitar notation;

... and here in piano notation;

Both of these notes are the same pitch on their respective instruments when played as written, but the piano follows the standard, so notation for the guitar is actually written an octave higher than standard. What this means in practice is that music written specifically for guitar will take into account the proper octave transposition - so the notes will be in their intended pitch, but if you play music written for piano or voice on the guitar, you will sound an octave too low, so you have to compensate by playing an octave higher than you would if the music was written for guitar.

For example; here is a melody written for piano;

First example.

... and the same melody written an octave higher on the staff for guitar but sounding the same pitch as if they were played on the piano from the example above (including tablature for reference);

Second example.

Both examples above will sound the same if played as written for each instrument. In other words, the pitch of the notes indicated on the tablature is actually the pitch of the notes indicated on the piano version of the melody in the first example. As you can see, the guitar notation places the notes higher on the staff. Notice that the Gs on the piano staff are two ledger lines below the staff.

If you were to play the melody notated for the piano in the first example as if it were written for guitar it would sound an octave lower;

Third example.

However, this would be wrong if you were trying to play what the piano was intended to play, since the intended pitch of the notation for the piano is an octave higher than the tablature shown here. As a guitarist reading notation for piano, you have to make the mental shift to the octave shown in the second example above, so it sounds an octave higher.

Here's the melody one more time with tablature indicating its 'true' pitch;

Fourth example.

As you can see, the true pitch of the notation of this melody on the fretboard is around the middle of the guitar's range – but low enough on the treble staff that going lower would require using the bass clef.

Here is the lowest note on the guitar (the open low E string) as written for guitar;

... and here is the same note as written for piano (its true pitch);

Piano music is written on the 'grand staff' which includes bass and treble clef.

As you can see, the open low E string on the guitar is quite low. So - as a rule - guitar notation is shifted an octave higher on the staff.

Now, suppose you have sheet music written for piano which you want to play on the guitar. You may have to make some changes in terms of chord voicings. But do you really have to re-write everything onto the treble staff, or should you just read it as it's written?

The great jazz guitarist and composer Johnny Smith is a firm believer that guitarists should read and write music on the grand staff, rather than transposing to the treble staff. Though this is not a majority view, there is certainly some merit to the idea. Being able to read in the bass clef has several benefits. Aside from being able to read piano music and play it on the guitar, you will be conversant with bass players, who read in bass clef. Interestingly, because the bass is so low, it also transposes, so the bass sounds an octave lower than written.

While the treble clef is a stylized letter G, The bass clef is a stylized letter F. The two dots on the clef surround the line of the staff assigned to the note F. Below you see the names of the notes on the bass clef;

Notice that the central note of the bass clef is D, also that E is one leger line below the staff and C is one leger line above.

The diagram below shows the symmetry of the notes on the bass clef;

Interestingly, the symmetry of the bass clef is centered around the note D, just like the Fretographic symmetry of the guitar fretboard.

Notice that the true pitch of the open strings of the guitar brings them will into the bass staff. Only the notes of the open 1st and 2nd strings are placed above the staff.

Now let's compare the bass symmetry with that of the treble staff;

(To review the treble staff symmetry in depth - read the previous entry here)

The respective symmetrical note-pairs are shown in boxes above the treble and below the bass staves. The diagonal dotted lines in the middle are connecting the equivalent central notes of the two staves to draw attention to their symmetrical positions across both staves. The note positions of the open strings are indicated to the right. Notice that the upper part of the bass and lower part of the treble staff include the same notes. For instance; the lowest E on the treble staff (below the 3rd leger line) is actually the same pitch as the E in the center of the bass staff. Likewise, the highest A indicated on the bass staff (above the 3rd leger line) is the same pitch as the A in the middle of the treble staff.

In piano music, the bass staff is used to indicate notes which are played with the left hand on the piano. The treble staff indicates notes played with the right hand. The two staves may therefore overlap so that the left hand can occasionally move into the territory of the right hand and vice versa.

Being aware of the note relationships on the staff, with or without the guitar at hand, will widen your musical horizons. Spend some time just studying the treble and bass staves. Memorize the note positions so that you can close your eyes and picture them. That's the first step to being able to connect the concept of music as sound with music as written language.

Still with us?

To be continued ....

iPhone App Now Available!

2011-11-17T19:10:00.000-08:00

Download FretApps: Modes 101 now from the Apple App Store, or visit the FretApps Blog for more information.

A highly useful instructional tool for learning the structure of mode patterns on the guitar. Based on the Fretography Method.

The App covers the symmetrical Mode Forms, called 'Modules' in the Fretography method, some of which are detailed in this blog here, here, here, and here, and adds interactive elements and sound to the experience of studying modes.

Features include;

* Every mode in every key, with note names and scale degrees

* Fingering for each mode scale, in both moveable and open-string positions
* Full 24-fret "pinch-to-zoom" guitar fretboard
* Superb graphics in portrait and landscape views
* Displays note names and scale degrees on the whole fretboard
* All the 27 most practical 3-string/single-octave mode forms
* Built-in browser access to FretApps blog featuring the pioneering Fretography Guitar Method

Reading Notes: Staff Symmetries

2011-11-09T15:36:00.000-08:00

The natural key symmetry of the diatonic treble staff is an interesting counterpart to the symmetry of the same diatonic key on the fretboard. We have examined the fretboard's symmetry in a number of posts. Now we are seeing how the specific patterns of notes on the staff have their own rules of symmetry. Whereas on the guitar fretboard (and the piano keyboard) the central note is D, on the treble staff, B is the central note - or fulcrum around which other notes are arrayed.

The symmetry of the fretboard is based on the intervals within the key. The pattern of half-steps ascending from D is a mirror image of the intervals descending from D. On the treble staff, the note B is the central note from a graphical or visual perspective.

When we look at the staff, there is no indication where the whole-steps and half-steps are to be positioned. Just a set of five lines and the spaces between them;

The seven notes of the key of the natural key, ABCDEFG, are assigned to these lines and spaces, sequentially from the bottom up;

Notice that the note in the space below the staff is D and the note in the space above the staff is G, and that B is the central note on the staff.

Additional notes are added above and below the staff when higher or lower notes are to be played. Short lines (leger lines) are used for individual notes;

Remember that you always have a reminder of where the note G is on the staff, because the clef itself is actually a stylized letter G. The belly of the clef encircles the G line on the staff;

Since the notes are alphabetical, it's only logical that we tend to think of them in that order. The ascending scale is usually the first exposure we have to music theory. Chords are thought of as starting with the root note and rising from there. Of course, scales descend as well, and chords don't have to be played from the lowest note first. Notes can be played in any order at any moment.

Here's another way to look at the way notes are arrayed on the staff; instead of a linear progression, you can think of the staff as a symmetrical array with the note B as the fulcrum.

If we look at the staff from the center first, the symmetry emerges;

Look carefully at the diagram above. study the symmetrical relationships of the notes from the center up and down. Study the positions of the note B, then the notes A/C, then D/G, then E/F. B forms its own symmetry, A and C are symmetrically arrayed - C is one leger line below the staff, A is one leger line above ... A is two leger lines below the staff, C is two leger lines above. D/G and E/F follow the same principle.

Below is another version of the same diagram. The notes are connected by dotted lines which clarify the symmetry;

Learning these connections will help you identify notes on the staff more quickly.

Reading Notes: Those G-D notes

2011-11-08T20:29:00.000-08:00

Here is the staff symmetry for G and D;

The reciprocal relationships of these two notes is clear. They are in opposite positions, equidistant from the center line of the staff.

The solid colored D and G are the notes of the open 4th and 3rd strings, respectively. But these same two note pitches are also found elsewhere on the fretboard. The diagram below shows all the D and G positions from the open strings to the 12th fret;

The pattern is highlighted to bring out certain symmetries. The notation represents those same symmetries so you can connect the note positions on the fretboard with the notes on the staff.

Because of the interval relationships of G and D, they align on the same fret positions in most instances. The are a perfect 5th ( G -A-B-C- D ) or a perfect 4th ( D -E-F- G ), depending on which note you count from. Since this is the interval tuning of most of the guitar's strings, these two notes are aligned except between the 2nd and 3rd strings, where the tuning is a major 3rd - thus the D and G are skewed one fret apart.

Reading Notes: E-F-ing

2011-11-08T19:14:00.000-08:00

The lowest note on the guitar in standard tuning is an E. Always one fret away from E is, by a happy coincidence, the next letter of the alphabet; F. It's also a happy coincidence that these two letters are similar in appearance, because - like A&C - they are symmetrically distributed on and around the staff;

The four Es and Fs in the diagram above are shown in all their color coded glory on the fretboard in the diagram below;

As you can see, the symmetry of these notes on the staff has a fairly straightforward relationship with the note positions on the fretboard. Notice how each of the three shaded diagonal blocks connect the same sets of notes. Also notice that the block furthest to the right (block 3) spans an additional fret. This is due to the difference in tuning between the 2nd and 3rd strings. The block of notes which does not cross between those two strings has a slightly different geometry than the other two, both of which cross the 2nd and 3rd strings.

As with the two previous note reading exercises, play through these patterns slowly and say the note names out loud as you play.

Reading Notes: AC Current

2011-11-08T16:29:00.000-08:00

A and C The positions of these two notes on the staff is symmetrically reciprocal. In other words, moving away from the center line of the staff (B), A and C are in opposite positions. C is in the space below the center line, A is in the space above the center. C is the first leger line below the satff, A is the first leger line above;

The distribution of these notes on the fretboard - from the open strings to the 13th fret - is shown below, along with notation. The notes have been color coded to clarify their geometric relationships;

Reading music is not all about scales. Using symmetrical relationships, you can learn to identify wider tonal ranges. Get to know the positions of these two notes, naming them out loud as you play them. Try connecting them in different ways.

Reading Notes: The Importance of B

2011-11-08T12:49:00.000-08:00

When we think about music theory, we usually start with the letter C, which is the tonic of the key of C, which is the 'natural' key - having no sharps or flats. But if the key of C begins with C, it ends with B.

In keeping with the basic principle of Fretography®, we'll look at how notes are arranged symetrically on the staff, and examine how the staff's symmetry relates to the fretboard.

B is the central note on the staff. The B line is the middle of the five lines. And going up or dawn an octave from the middle B will bring you to a space equidistant from the center of the staff;

These three Bs have more than three positions on the fretboard;

To memorize these note positions, it will help you to understand how they are related to each other, rather than just treating them as separate isolated positions. Look at the lowest (burgundy) B. Notice that its two positions are a span of 6 frets, from the 2nd to the 7th fret.

Now look at the middle (black) B. From the open 2nd string, there is a 5 fret span to the next position on the 4th fret. Then a 6 fret span to the 9th fret, and another 6 fret span to the 14th fret.

The high (brown) B starts on the 7th fret of the 1st string and there's a 6 fret span to the next B on the 12th fret of the 2nd string, then a 5 fret span to the 16th fret of the 3rd string.

As you can see, the 5 fret spans are always between the 2nd & 3rd strings, and the 6 fret spans fall between the other adjacent string pairs. This pattern of fret spans is true for every note on the fretboard, but only the note B is positioned so symmetrically on the staff.

Reading notation requires that you can easily connect the notes on the page with their positions on the fretboard. So understanding the unique geometric character of each note is very helpful.

In the next posts, we'll look at symmetrical pairs of notes.

Reading Notes: Arpeggios

2011-11-07T12:49:00.000-08:00

One of the daunting tasks guitar students face is learning to connect notes on the staff to positions on the fretboard. It is particularly difficult when the notes are not scale based, since there may be an irregular pattern in both the notation and the fretboard.

The notes shown on the staff in the diagram below – including the a few notes above and below the five lines of the staff which are attached to short additional lines (called leger lines) – are the notes which will be used in the exercises which follow;

The notes are simply in alphabetical order from the bottom up as you go from line to space to line to space; C-D-E-F-G etc.

The lowest note shown here (C) can be played on the 3rd fret of the 5th string, or the 8th fret of the 6th string. The highest note (B), can be played on the 7th fret of the 1st string or the 12th fret of the 2nd string;

One way to open the door to reading non-scale patterns is by reading arpeggios, which are simply chords which are played note by note. The simplest chord forms are just sequences of 3rds; C-E-G-B etc.

This exercise covers a wide span of the fretboard, from the 8th fret of the 6th string - across to the 1st fret of the 1st string and ending on the 5th fret of the 1st string.

By positioning a series of 3rds starting with C in such a way that the notation and the strings of the fretboard align, you can see the relationship between the staff and the fretboard note positions. The total set of notes comprise a C major 13th chord arpeggio. Notice that all the notes fall on lines of the staff, not the spaces. Whenever you play a series of 3rds, they will all be on either lines or spaces, depending on the specific set of notes - but there will never be a mix of lines and spaces.

Follow the fingering (italic numbers) carefully;

The grey numbers below the fretboard are fret positions. Numbers in squares are chord degrees; R is the chord root, 3 is the 3rd above the root, etc. The piano keyboard shows the sequential relationship of the notes from left to right. (If you play piano, you'll notice that the notation for the guitar sounds an octave lower than the same notation written for the piano.)

Memorize the positions of these notes on the staff and the fretboard. Say them aloud as you play them They can serve as reference points to find other notes.

Here's a similar exercise based on D;

This is a D minor 13th arpeggio. Notice that all the notes are in spaces on the staff, not lines.

An interesting thing about these arpeggios, is that each contains all seven notes of the key of C. Hopefully these two examples will give you some insight into the relationship between standard notation and the fretboard. More to come.

Parallel 3rds (Symmetrical Pattern)

2011-10-29T18:39:00.000-07:00

This pattern divides the 3rds of the key of C into two zones within the top four strings. One lower zone spanning from the open strings to the 5th fret and another higher zone from the 5th to the 10th fret. Each 3rd in the pattern comprises two notes separated by one string and one fret. This is an easy pattern to remember due to its clear symmetry.

The lower zone runs in a descending order from the Tonic 3rd (C-E on the 2nd and 1st strings, respectively) to the IV (F-A on the 4th and 3rd strings). The upper zone ascends from the Tonic (C-E on the 4th and 3rd strings, respectively) to the V (G-B on the 2nd and 1st strings).

In the diagram below, fingering is shown below the notation as italic numbers. The Roman numerals are the corresponding scale degrees. The green bars are major 3rds / The purple bars are minor 3rds. Notice all the connected notes in the pattern between the 2nd and 3rd strings (B-G) are minor, and the rest are major.

Once you have practiced the pattern as written, try reversing direction, playing the first part as an ascending sequence from IV up to I, and the second part descending from V down to I.

(Fretboard note positions outside the notated pattern (grayed out) are shown in the diagram for reference.)

The Center of the Fretboard

2011-10-28T16:00:00.000-07:00

Have you ever pondered the question of where exactly, is the 'middle of the fretboard?' Maybe 'center' is a better word than 'middle'. One certainty is that there is no clear comprehensive answer. The best answer is probably;"It depends."

If what it depends on is the Diatonic Key, then the answer can be more precise;

In Fretography, the center of the fretboard is considered the center of the key (and vice versa). So, in the key of C major/A minor, the center of the fretboard is the 5th fret between the 2nd & 3rd strings (G and B string). The 2nd and 3rd strings form what is, in Fretography, the "Third Rail." This refers to the 3rd interval between those strings. Since the tuning relationship between these strings is unique, they are given special focus. They become the pivotal strings around which all the note patterns revolve. The principal of rotating symmetry becomes quite clear when you focus on this position before exploring the rest of the fretboard.

The four encircled tones in the diagram above are the four compass points to the rest of the fretboard. In the key of C, they are B-C-E-F. The 7th, Tonic, 3rd and 4th of the key, respectively.

Below, the same pattern in the key of D;

Notice that the four center notes are now C#-D-F#-G. These are the 7th, Tonic, 3rd and 4th of the key.

This cluster of tones, VII - I - III - IV are positioned on a fret which forms an Axis. Notice that there are three unique Axis frets on the fretboard in the above diagrams. There are four actual Axes, but in both of the keys shown above, there are two with identical note names; EADGB. These matching fret positions can be considered the same theoretical Axis.

If we ignore the far right Axis in the first diagram (Key of C, 12th fret) and the far left Axis in the second diagram (Key of D, Open Strings), then we have a set of three Axes, with the target notes in the Center Axis.

This Axis is shown below with Roman numerals which represent the scale degrees which apply to every key, regardless of which fret position the Axis is placed;

The four notes of the Center Cluster can be found in three places within the span of the four top strings;

The same notes, an octave lower are positioned as shown below with blue targets;

Let's see where these notes fall on the piano keyboard. The diagram below shows the BCEF clusters in three octave positions on the fretboard and piano. Also shown is the very low EF 'semi-cluster' - the two lowest notes on the guitar (in grey), as well as the high BC semi-cluster on the 7th & 8th frets of the 1st string (yellow) and the low EF semi-cluster on the 12th & 13th frets 6th string (blue);

These notes are not only the tonic, 3rd, 4th and 7th of the key – as such, they are also the half-step positions. Learn the positions of these four notes. They are the compass points which show the way to the whole system.

4-String Modes Rooted on the 6th String, Key of Bb

2011-10-21T00:45:00.000-07:00

Here are the same lower string modes in the key of Bb. Notice that the symmetry is clearer in this key;

4-String Modes Rooted on the 6th String, Key of C

2011-10-21T00:40:00.000-07:00

The lower four strings are all tuned in 4ths (E-A-D-G from low to high) which yields symmetrical patterns. The following diagrams show all the 4-string modes in the key of C;

4-String Modes, Rooted on 5th String

2011-10-21T00:35:00.000-07:00

When 4-string mode forms are rooted on the 5th string, they lose their symmetry. This is because the interval pattern of the strings is asymmetrical. That is, the interval pattern of the upper four strings (4-3-2-1, from low to high), the interval pattern is Perf. 4th / Maj 3rd / Perf. 4th, which is symmetrical. However the interval pattern of the four middle strings (5-4-3-2) is Perf. 4th / Perf. 4th / Maj 3rd, which is asymmetrical. So the patterns which span these four strings are asymmetrical.

Interestingly, three of these patterns - Mixolydian, Aeolian and Dorian - though lacking the rotational symmetry of the standard module forms, share the same silhouette;

The diagram above shows the key of G. Below you can see the Dorian and Mixolydian modes in the key of C;

The Ionian and Phrygian modes, which are a symmetrical module in the upper and lower strings, are very different in the middle four strings;

Likewise, the Lydian/Locrian module becomes a mixed bag;

4-String Mode Forms

2011-10-21T00:30:00.000-07:00

The simplest single octave mode forms span three strings. We have looked at all of these forms in previous posts, and they are included in the iPhone App, Modes 101. All of the 3-string modes are played starting from the 1st or 2nd finger (or an open string). Now we'll examine some mode forms which span four strings.

It may be more practical within a particular riff to begin the mode on the 3rd or 4th finger, because of the hand position dictated by a previous chord or riff. All the 4-string mode forms begin on either the 3rd or 4th finger, and cannot start with an open string (but may begin with the 2nd finger if the mode includes open strings).

Let's start with the Ionian/Phrygian module spanning the upper four strings. The symmetry is clear;

Notice that the Phrygian mode begins with two notes on the lowest string of the pattern and ends with one note on the top string. The Ionian mode is exactly the opposite.

Next, the Mixolydian/Aeolian module;

These forms overlap in this view. Notice that the silhouettes of the modes are identical. They both begin and end with a single note on the low and high string. Starting on the 4th finger and ending on the 1st.

And here are the 4-string mode forms in the Lydian/Locrian Module on the 4 upper strings;

Dorian Mode, in these 4-string upper forms, would be rooted in the 12th fret or on the open 4th string in the key of C, which is not a very practical position. Below, it's shown in the key of G where it is rooted on the 7th fret;

Symmetrical Blocks

2011-05-20T16:33:00.000-07:00

Here's another Fretography exercise which brings out the diatonic symmetry of the four top strings in the key of C.

The diagram above shows all the notes of the upper string group from the open strings to the 10th fret. The note positions are highlighted in colors which correspond with their intervallic symmetry. Below is notation for playing the indicated blocks in a symmetrical sequence. The notes of the Axis positions (amber verticals) are not included in the exercise, but are shown for reference.

The purpose of an exercise like this is to visualize the note positions between the axes. Notice that each side of the overall pattern spans four frets. All the notes of the top four strings which fall between the axes are accessed within these two positions. This is simply a way of learning the positions of the natural tones which is not based on a scale pattern, but rather - upon a symmetrical array.

The diagram below shows the same kind of symmetry within the lower 3-string group.

Here's the notation for playing the lower string pattern;

Modes 101

2010-12-06T17:16:00.000-08:00

What are modes and why does it matter?

Understanding the relationship between the guitar and the diatonic system would be significantly more difficult without an understanding of modes. In a sense, the seven diatonic modes are key to the fretboard.

This is true because of the way the modes are aligned within the fretboard's systematic grid of strings and frets. Something which is widely misunderstood.

Keep in mind that everything you play on the guitar can be understood better if you can recognize the modal elements in the music. If that last sentence is puzzling to you, consider that you already are using modes if you are playing any scale. If you play a major scale you are in a 'major mode.' If you play a minor scale you're in a 'minor mode.'

You already know two modes. Now you need to learn the other five. And remember ... it actually gets easier.

In the next post we'll revisit modes from a really fundamental place. Meanwhile, you can review some earlier posts on the subject ... here, here, here, and here.

Double Helix Pattern (Tritones and Major 3rds)

2010-09-20T10:23:00.000-07:00

The C and E at the 5th fret comprise a major 3rd. B on the 4th fret combines with F on the 6th fret to form a tritone. Study the diagram and notation above. Think of the 5th fret as the starting point, notice the symmetry.

This is an essential exercise in Fretography. The fingering of the pattern is indicated by the italic numbers above and below the notes. The first double-stop, C-E, is played at the 5th fret with the 2nd and 3rd fingers, the second double-stop , F-B, requires the 1st finger on F and the 4th finger on B, 4th and 6th frets respectively.

In each of the double-stops, the right hand thumb plucks the lower string and the index finger plucks the higher.

Play it slowly and be careful to follow the indicated fingering.

Also, study the symmetry of the pattern carefully. Notice its relationship to the surrounding note positions within the upper four strings, particularly the two BC/EF clusters in the upper left and lower right of that part of the diagram. Then study positions of the remaining three tones: ADG. You'll see that the all the positions of the A's and the G's are exactly opposite, and the Ds form their own rotational symmetry.

The Philosophy of Fretography - Part II

2010-09-19T16:51:00.001-07:00

Here are a few concepts which are essential to, and form the basis of the Fretography method;

- Symmetry is inherently part of the standard tuning of the guitar.

- The study of the fretboard begins at the 5th fret (not the nut).

- The symmetries on the fretboard, which correspond with those of the standard diatonic system, are centered around the 5th fret.

- The key of C is the template for the patterns in Fretography which, once learned, can be applied to every key.

- The three axes in the key of C (Open Strings=EADGBE/5th fret=ADGCEA/10th fret=DGCFAD) and the positions of the natural half-steps (B-C and E-F ) should be learned first.

- The four top strings (DGBE), as a group, comprise one aspect of the symmetry, the three bottom strings (EAD), as a group, comprise another aspect. These two symmetries are studied separately, then combined. These lower and upper string groups can be thought of as analogous with the left and right hands of the piano, respectively.

- Scales, modes, double-stops, triads and extended chords are all found in symmetrical positions.

- Additional symmetries are present, which are learned once a satisfactory comprehension of the above concepts has been achieved.

Regardless of the style of music being played, the mapping of tones in Fretography remains consistent. Just as the pattern of black and white piano keys is no different whether one is playing Ludwig van Beethoven or Thelonius Monk, Fretography can be applied to classical, jazz, rock, folk, blues etc.

The Philosophy of Fretography

2010-09-07T16:22:00.000-07:00

One of the dangers of challenging the norm in any field is being misunderstood. The salvation from this fate, should it befall one, is the realization that the 'norm' is also misunderstood. Since no one really understands the norm, it's not abnormal to be misunderstood. That people don't understand something doesn't say too much about the truth or falsity of that thing.

Most beginners don't understand the way the fretboard really works. Not just from a mechanical, physical perspective, but a musical one as well. Presented with a diagram showing, say, the positions of the notes of the key of C on the fretboard, most would say that there doesn't appear to be a discernible logic to the positions of the notes.

What one comes to understand is that what is 'discernible' may not be obvious. You have to know how to look at things.

The trick is to have a reason for choosing a particular way of looking at something. Music is not merely based on a set of arbitrary choices. The fixed tonal relationships of the diatonic system reflect natural harmonic principles. When you hear music, you are sensing vibrations (and you are vibrating). These vibrations are recognized as 'music' because they follow identifiable patterns.

If you watch ocean waves rolling to the shore, you can see complexity in a single wave.

Each wave is really a combination of smaller waves. The white foam at the crest of a wave is where turbulence forms to scatter the light enough to turn transparent water opaque. Millions of tiny waves within the bigger wave. The waves come in rhythmic patterns. Some waves are smooth and don't break until they hit the sand. Some waves break before reaching the shore and are absorbed into bigger waves.

This is the ocean singing.

Music is streams of invisible waves, no less real than those in the ocean, which fill the air and set your tissues vibrating in sympathy. There is symmetry and structure inherent in the experience of music, so there is symmetry and structure in the musical tones as they are arrayed on the fretboard. That it appears at first to be a random array is a matter of perspective. There is, of course, randomness within order,

......

I began playing the guitar at age 9, had two formal lessons and decided to find my own way with the instrument. Consequently I took what I think of as 'The Long Slow Path.' What I had, and hope I still have, is diligence.

I also had somewhat formal music training in the New York public schools I attended, in which I learned to play the recorder and the viola. My mother, and some aunts, uncles and cousins played piano, so I learned a few things from them. I felt prepared to figure out the fretboard using the theory I'd learned in school, the left hand technique I was acquiring on viola in Junior High, and the chord structure I studied on the piano.

I could play scales, picked up chords quickly, and figured out how to sing and strum in two different rhythms at once.

But, like most guitar players, I avoided written music of any kind. But, I enjoyed training my ear to match the tones I'd hear on records with the guitar as I played. It was a great puzzle to try and solve.

That's where it gets confusing.

That the guitar fretboard is somewhat puzzling is common knowledge - especially among novice guitarists. The guitar student has to make sense of what seems to be an almost random invisible array of notes on the grid of the fretboard.

First of all; it's facing the wrong way! You have to be curious to play the guitar, because it plays hard to get. You can't get face to face with the guitar when you play. Because it's difficult to reconcile the 'upside-down' view one has of the fretboard when playing with the way it's represented on the page, reading for the guitar is a challenge for most students.

If you play for a while, you'll likely reach a point when you'll want to know something about the music theory you've avoided. Especially if you find yourself jamming with people who play other instruments.

Since players of other instruments aren't faced with the convoluted maze of fingering patterns that guitarists have to wrestle with, they have more time to come to terms with the link between notation and vibration. You'll probably be the worst reader in the room. You may end up having the piano player tell you the names of the notes your playing.

Avoidance is not a solution. Yet there are no shortage of workarounds available. Methods based on short cuts. Tablature is the most common short cut. No question that tablature is useful. It's a great form of short-hand. But it doesn't translate. Only a guitar player can make sense of tablature. Players of other instruments read the same basic standard music notation, not tablature. It's a given that if you take piano lessons, or violin lessons, or saxophone lessons, that you'll be taught to read notation.

Not so for the guitar. Students know that lots of famous guitar players get by just fine with little or no formal music theory. Guitar teachers, if they read music themselves, have to accommodate students who are hooked on tablature before they walk in the door.

Where tablature falls short is that it reveals essentially nothing about the relationships between the fret and string positions of notes and their musical identities, either in terms of tonality or rhythm.

Interval relationships are clear in notation. The timing and dynamics of notes is clear in notation. And notation is shared by many many instruments, bringing the guitarist 'into the fold.' Also, because notation is a true language, not merely typography, it can be verbalized and used to enhance communication between players. Tablature can't be read off the page verbally to coherently express the musical ideas it is supposed to represent. All you'd have is a series of string and fret numbers, which would be as meaningless to players of other instruments as the tablature itself.

Tablature does nothing you can't do with notation, though it does provide you with what amounts to a set of map coordinates which simplifies the process of knowing where to put your fingers and which string to pluck in what sequence. Sure it works as advertised, but that's not all there is to music, and the more you play, the more you begin to realize that.

Now, if tablature is an inadequate method of written guitar music, and you want to learn standard notation for the guitar while staying sane, what's the best way to go about it?

The classical method is basically to learn the notes in each fret position from the open strings to the 1st fret, to the 2nd fret, and on up, one by one. Become familiar with the open string position, then the next hand position, then the next. So that you become intimately familiar with the notes of the first three or four frets before moving up a fret.

... Though this works for millions of people, it's somewhat tedious to learn this way. And you never really get a clear picture of the overall note array on the fretboard.

This wouldn't matter if the fretboard was devoid of any recognizable symmetry in the way the notes are distributed. It's not. There is a recognizable, symmetrical pattern to the notes on the fretboard which can be used the way a piano player uses the pattern of black and white piano keys to navigate the keyboard.

It's recognizable ... once you see it. The image below is an expression of the symmetry of the guitar fretboard I call The Spiral Galaxy Pattern The essential elements are the clusters of half-steps, the natural tone axis positions and the central spiral pattern which connects the remaining note positions.

An animated version of the pattern can be seen here.

But unfortunately, it's invisible on the guitar. You have to imagine it as you play. When you do, finding your way around the fretboard becomes almost as easy as finding notes on the piano. And the logic of the pattern conforms nicely with standard music notation, which is the goal.

When you have a pattern in your mind, you can find your way around better. Using tablature is a little like having a map with nothing but a grid and no geographical features. You know the latitude and longitude of each location, but you can't see the roads or the land masses and the oceans.

Without a picture of the 'geography' of the fretboard, you are wandering aimlessly. With that picture, you are communicating with the guitar and it is communicating with you. The journey becomes the destination.

Fretography challenges the norm in saying that the fretboard begins in the middle, not at the open strings. There's a good reason for this. It's because, if you start in the middle it gets easier faster than if you start with the open strings.

The conventional bias toward learning the guitar from the open strings first, then moving up incrementally has understandable origins, and it's clearly the best way to learn un-fretted instruments like the cello and violin, since, without frets, the only 'fixed' tones are the open strings. When the open string is the only absolute reference point for pitch on each string, every note you finger on a fretless instrument has to be learned in reference to the open string. On the guitar this matters not at all.

Since the frets take care of the intonation of each note you play on the guitar, you don't have to worry that your finger is exactly, precisely, in the perfect spot, as long as it's next to the correct fret on the correct string. If you're playing a cello or violin, then finger position is absolutely critical.

So why start with the open strings? I believe that the standard method is an anachronism which is long overdue for an upgrade.

.... To Continue ....

What is Fretography ?

2010-07-26T13:36:00.000-07:00

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.

Twelve C Major Scales

2010-04-26T14:41:00.000-07:00

Most tones on the guitar can be found in several positions on the fretboard. Because of this there are numerous ways to play any scale. Below are twelve versions of the same C major scale, the first four are rooted at the 3rd fret of the 5th string. Pattern 1 and 3 include open strings and each spans 4 strings. Additionally, pattern 3 comprises 2 notes per string. Pattern 2 is played in a single hand position spanning three strings, and pattern 4 comprises 4 notes on each of two strings;

The next four are rooted on the 8th fret of the 6th string. Pattern 5 and 7 each span 4 strings. Additionally, pattern 7 comprises 2 notes per string. Pattern 6 is played in a single hand position spanning three strings, and pattern 8 comprises 4 notes on each of two strings;

Pattens 9 and 10 are both based on the same fingering, 9 is rooted on the 3rd fret/5th string, and 10 is rooted on the 8th fret/6th string. Patterns 11 and 12 are each played on a single string;

Pay close attention to the indicated fingering, being careful to use the same fingering ascending and descending.

Crazy Zig-zag Lightning Bolt Major Scale

2010-04-24T12:40:00.000-07:00

Deconstructing the contrary motion pattern in the last entry, we can see that the lower line is actually an interesting scale form in its own right.

You can think of this zig-zag pattern as a lightning bolt. What's nice about this pattern is that it moves in the opposite direction of most scale patterns in that the higher pitched notes are lower on the fretboard.

Looking at the pattern in the key of C as a descending line, it begins at the 5th fret, 3rd string; what, in Fretography, is called the Center C. From there you play B on the same string, then two notes on each string to the low C as shown in the diagram and notation.

The 2-note-per-string approach to scales can be applied to all seven modes of every key.

Organizing the scale this way connects fret positions in an unusual way. You shift up the frets while moving lower in pitch. It is one of twelve standard Fretography® fingering patterns for the C major scale in this octave. In the next entry we'll look at all twelve patterns.

More Contrary Motion

2010-04-09T19:28:00.000-07:00

Here's another way to play a contrary motion scale. Unlike the previous pattern, the note positions are not symmetrical, but it is possible to play all the notes in groups of two within accessible hand positions. Let's call this an 'asymmetrical pattern - rooted on the 3rd string.'

The diagram below shows how the pattern is arrayed on the fretboard.

Because it is so complex, a single diagram cannot adequately illustrate the sequence of this pattern. Below is a step by step diagram of the entire scale (click on the image for a larger version);

And finally, here is tablature and notation for the pattern including fingering;

Contrary Motion

2010-03-31T13:16:00.000-07:00

When the pitches of two musical lines move in opposite directions their movement is said to be contrary. On the guitar can be difficult to play two separate lines, let alone have them go in opposite directions. But developing this technique can really enhance your playing.

Here is a pattern which is based on ascending and descending lines played in an alternating sequence, moving further apart as you go along;

Here's the notation for the pattern;

Follow the fingering carefully, play the pattern legato with no gaps between the notes. Notice that the first five measures are contained within a five-fret span. It is possible to simultaneously finger both notes in each of these measures. In the 6th measure, it will be very difficult to reach from the low E to the high C. If you can't connect them, get as close as you can. When you've played the pattern as written, try reading (and playing) it in reverse.

Lower string group symmetries

2010-03-18T19:34:00.000-07:00

The lower three strings have their own symmetry. The center of this symmetry is a group of tones I like to call 'The Big Box'.

The nine notes of this pattern, with D at the center, are aligned on the 3rd, 5th and 7th frets across the 4th, 5th and 6th strings. Looking at the remaining tones within the lower string group, you can see their rotational symmetry around the big box.

There are two complete mode scales in the big box. Ascending from G and descending from A it can be treated as an ascending Mixolydian mode from G to G, and a descending Aeolian mode, from A to A.

This pattern also fills the space between the Phrygian and Ionian modes on the same three strings;

So all the key of C note position on the lower three strings can be learned by studying these three patterns.

Total Modal Symmetry

2010-03-18T16:06:00.000-07:00

The diagram above shows all seven Diatonic Modes. They are shown in the key of C, divided into two groups; Primary Modes and Mixed Modes. The three primary modes are each made up of two intervalically identical tetrachords. The four mixed modes each contain two differing tetrachords. There is symmetry within each of these two mode groups. Study the Whole-step / Half-step patterns of each mode and each group of modes, looking at them from the center outward.

Knowing the tetrachord structure of each mode greatly simplifies the learning process. In addition, the three mirror mode sets we looked at earlier enable you to learn two modes simultaneously. As we've seen, the mirror mode principle organizes the tones of specific modes into symmetrical patterns on the fretboard. This is simply an expression of their innate musical symmetry within the diatonic system.

Ionian mirrors Phrygian, Lydian mirrors Locrian, Mixolydian mirrors Aeolian, and Dorian mirrors itself.

There's really no reason to treat modes as mysterious, yet many guitarists are confused by them. Part of the reason for this is the tendency for scale patterns to be learned haphazardly. If your study of scales overlooks tetrachords and their symmetry, modes will be baffling.

Wikipedia has an interesting entry on modes; http://en.wikipedia.org/wiki/Properties_of_musical_modes

Tangentially ...

2010-03-18T13:24:00.000-07:00

In case you're joining us mid-blog, this may help you catch up to the story line;

The previous entry ended, "In the next entry, we'll sum up the overall structure of modes within a given key...."

... And it's true. In the next post we'll get back to modes. Right now it may be a good idea to restate just what is the point of this method.

Diatonic Symmetry

The Fretography® method debunks the myth that the guitar fretboard is asymmetrical. It approaches the fretboard from the middle, not from the open strings and the first fret 'up'.

Fretography doesn't assume you are trying to avoid conventional music theory, nor does it require you have a music degree to understand it, only a basic knowledge of fundamental music theory concepts is required. If you're a beginner, you can use Fretography to actually help you learn how music theory concepts apply to the guitar, which will enable you to communicate with players of other instruments like piano or sax. If you're an experienced guitarist, you'll find this method will augment your existing knowledge regardless of the style of music you play.

If the concepts and diagrams in this blog seem unusual it's because this method is not found elsewhere. The principle of fretboard symmetry is expressed and explored by means of Fretography. This principle is overlooked in other methods. In fact, the idea of symmetry on the guitar fretboard is usually treated as non-existent, or only approximate. Fretography shows that there is in fact a precise symmetry that can be learned and visualized, providing a highly useful tool in learning and playing the guitar.

You may want to read the first entry; http://fretography.blogspot.com/2009/06/what-is-fretography.html

and progress from there. Or just browse around. Welcome to Fretography®

Next ... back to modes....

Dorian Mode ( Upper Strings / 3-String Form )

2010-03-17T13:03:00.000-07:00

The only perfectly symmetrical mode is the Dorian mode. Based on the second scale degree, the interval pattern of the Dorian mode is;

If you look at this mode from the center whole-step and go both directions from there, you'll see that the intervals mirror each other. As a result of this, the Dorian mode appears in opposition to itself on the fretboard as seen in this diagram;

In the next entry, we'll sum up the overall structure of modes within a given key.

Lower 3-String Modes

2010-03-14T17:37:00.000-07:00

Our next modes are Lydian and Locrian, modes IV and VII, respectively.

These modes are also paired symmetrically. They differ from all other modes in that the central interval in each of them is a half-step.

More 3-String Mode Forms

2010-03-14T15:59:00.000-07:00

The next two modes we'll examine are the Mixolydian and Aeolian modes, the Vth and VIth modes, respectively.

Like the Ionian and Phrygian, these two modes are mirror image interval patterns;

Study the diagram at the top of this post. Notice that the modes are geometrically opposite.

As with all patterns on the guitar, there are various forms for playing each mode. The specific forms in these diagrams are chosen because they clearly illustrate the symmetry of the patterns. This is a useful way of learning modes, because you can learn two at a time while also achieving a better understanding of their tonal character.

Remember that symmetry is an inherent element in the diatonic system. ( Review the blog entry on this subject ) Just as specific tones are arranged in geometrically opposing pairs, so are modes.

Modes ( 3-String Forms )

2010-03-11T16:52:00.000-08:00

When you play a major scale you are in fact playing a mode. Any time the tones of a key are played in sequence spanning an octave, it's a mode. For example; the sequence C D E F G A B C, usually referred to as a major scale, is also known as the Ionian Mode. The sequence D E F G A B C D is the Dorian Mode, E F G A B C D E is the Phrygian Mode.

Modes are useful for playing harmonies and are important in understanding how melodies work. Songs don't all begin and end on the tonic.

Two modes are shown above; Ionian and Phrygian. Notice that the note positions in one are the exact opposite of the other. The interval structures of these two modes are mirror images of each other;

Each mode contains all the tones of the key, but they each begin and end on a different tone. Play each mode and you'll find that they have their own individual musical character. These two modes harmonize because they are a 3rd apart. If two guitars each play one of these modes in synch with each other, the result will be a harmonious scale.

There are seven modes, one for each scale degree. Below is a list of the modes and their interval structures;

I = Ionian Mode;

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

II = Dorian Mode;

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

III = Phrygian Mode;

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

IV = Lydian Mode;

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

V = Mixolydian Mode;

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

VI = Aeolian Mode;

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

VII = Locrian Mode;

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

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

We'll look at the symmetrical relationships of the other modes in the next posting.

Spiral Galaxy Pattern

2009-10-11T14:03:00.001-07:00

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.

Pentatonic Axis Positions

2009-09-29T11:21:00.000-07:00

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;

[perfect 4th]

[major 3rd]

[perfect 4th]

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.

____________________________________________________________________

Symmetrical Root Position Triads

2009-09-29T10:24:00.000-07:00

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.

More Symmetrical Triad Inversions

2009-09-28T15:28:00.000-07:00

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).

Symmetrical Triad Inversions

2009-09-28T01:21:00.001-07:00

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.

Black Key Chords

2009-09-19T15:22:00.001-07:00

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.

The Circle of Fifths

2009-09-18T20:11:00.000-07:00

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.

11th fret Symmetry

2009-09-18T16:27:00.000-07:00

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#.

Black Keys /Accidentals in C

2009-09-18T09:54:00.001-07:00

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.

Tritones and Major 3rds

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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.

Diatonic Symmetry 2

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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.

Diatonic Symmetry

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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;

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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

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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.

Middle C

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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.

Half Step Cluster Paths

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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#).

Fretboard Symmetry

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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.

Half Step Clusters

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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.

Tetrachords

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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.

The VII Zone

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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.

Fretography Zones

2009-06-03T20:35:00.000-07:00

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.

What is Fretography ?

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