About three weeks ago I discovered a simple system for producing chords with the same chord voicing/formula on different string sets. Think of it as a similar system to the CAGED system that we previously looked at, but instead of finding similar chords (different voicings) of the same root horizontally we try to find chords with the same voicing vertically but with different roots.
First however, I should go through some basics about string sets and how the standard tuning works.
A string set is a group of strings, normally three adjacent strings. The smallest chord is a triad (three notes) and two notes is a special case called an interval. So a natural way of grouping strings in string sets are (downwards from 1:st string (low E) to the 6:th (high E)):
- {1,2,3}: E-A-D
- {2,3,4}: A-D-G
- {3,4,5}: D-G-B
- {4,5,6}: G-B-E
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| The four basic triad string sets (right handed). |
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| The four basic triad string sets (left handed). |
So a triad on the first string set could be a C-major with fingerings 8-7-5 corresponding to the notes C-E-G.
Now, there is nothing that limits us to have string sets of more than 3 strings. We could use string sets of arbitrary size to give us richer chords (and more flexibility). Say we want to play a C9 chord. Then it could be played on the string set {2,3,4,5,6} which means it would be based on an A-shape (see the CAGED and chained for more information about chord shapes):
Now, the thing about the standard tuning. I'm not an expert on tuning systems and frankly, I stick to this tuning since I'm a little afraid of other tunings unless they are really called for. What I have realized about it though is that if you traverse vertically downwards from low E to high E, you will walk by fourths, but if you traverse vertically upwards then you will walk notes by fifths. Well, mostly. There is a special case as you probably have noticed, something happens at the step from the G-string to the B-string. This IMO ruins this otherwise so uniform and nice tuning. Why not EADGCF from low to high? Well, I really don't know, but a guess is that the idea behind it is to get as many root notes (open if possible) but maintaining a roughly regular fourths/fifths tuning. A nice thing about it though is that it avoids sharps and flats.
If you have ever played an octave interval between strings {1,3}, {2,4}, {3,5} or {4,6} (as made famous by Wes Montgomery by what he referred to as "the octave thing") then you have probably discovered this feature yourself.
So with this tuning in mind we can do pretty interesting things with a given chord. We can actually replicate a chord on an adjacent string set by using roughly the same fingering. Of course, when notes go beyond last string the chord will be truncated and lose one or more notes. Remember the CAGED system? We can actually deduce some chords from each other this way. Take the open G-chord, it starts with the root-position triad G-B-D then continues with G-B-G and the fingering would be (3,2,0,0,0,3) or the chord formula would be R-3-5-R-3-R. If you move this downwards vertically then you will get the fingering (X,3,2,0,1,0). Whoa, isn't this is an open C-chord?!! Yes it is... rather interesting yeah? But what happened there? Why is there a position 1 at string 5 and a position 0 at string 6? Well remember the little quirk in the standard tuning? This is exactly what it does to a chord that is moved down vertically (by fourths) in the standard tuning. Looking at the G-chord, the interval consisting of position 0 at string 4 and 0 at string 5 is a third interval and not a fourth interval which is evidenced by the notes G and B respectively, i.e. root and third. So since this chord has been displaced from a G-chord to a C-chord using the same chord formula the strings now represent a fifth and a root respectively. These notes instead forms a minor third interval, therefore the note on string 5 must have a note on the first fret. Note that the C-chord has the formula R-3-5-R-3 which is the same as the one for the G-chord but without the last root.
The same applies to the open E-chord on the string set {1,2,3,4,5,6}. This chord has the formula R-5-R-3-5-R and therefore the fingering is uniquely (0,2,2,1,0,0). If you move it one step down across the neck you will get an open A-chord but will lose the root at the end. The open A-chord has the formula R-5-R-3-5 and the fingering (X,0,2,2,2,0). Moving it one step downwards again will yield an open D-chord which has the formula R-5-R-3 and the fingering (X,X,0,2,3,2). So these three chords are very intimately related. On a side note, these chords are separated by fifths/fourths. E->A is a fourth and A->D is also a fourth due to how the standard tuning is set up.
Task: As an exercise, try figure out what open chord you will get when translating an open C-chord down one step. And if translating it down once more, can you see which of the other CAGED chord it is a subset of?
So, to pick another interesting example we can go back to that C9 chord and translate down vertically to make it an F9 chord. The colors match the respective intervals in the chord-formula (here R-3-b7-9):
The C9 chord was played on the string set {2,3,4,5,6} with the formula R-3-b7-9-5 and this chord (and the string set) has been translated to the string set {3,4,5,6} with the same formula but the last note R-3-b7-9 since the fifth has been truncated due to the translation. However this is OK since the fifth is less significant in determining the properties of a particular chord due to it's closeness with the root regarding to overtones.
With transposing we mean moving a chord in a given string set horizontally along the neck (sometimes with barre for practical reasons) and with translating I mean moving a chord in a given string set vertically across the neck to an adjacent string set. I.e. to a string set S that is translated up or down by N steps would become:
Snew = (S±N)∩[1,6].
For example: A Gmaj7 could be the formula R-7-3 with the fingering (3,X,4,4,X,X) and would thus be on the string set S = {1,3,4}. If transposed three times you would get the translated string set Snew = ({1,3,4} + 3)∩[1,6] = {3,6,7}∩[1,6] = {3,6} and the fingering for the same formula but for this translated string set would be (X,X,X,3,X,5), however technically, this "chord" is not actually a chord anymore but rather regarded as an interval. :P
Of course, like CAGED you can transpose a translated chord so that you get the same root. Frankly, most of the time we deal with chords that are either of these shapes so linking them together is very easy if you have gotten the CAGED system under your fingers.
I hope this information will be useful to you and I encourage you to try to find new interesting chords and chord voicings.
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| A C-major triad on the 1st string set (right handed). |
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| A C-major triad on the 1st string set (left handed). |
Now, there is nothing that limits us to have string sets of more than 3 strings. We could use string sets of arbitrary size to give us richer chords (and more flexibility). Say we want to play a C9 chord. Then it could be played on the string set {2,3,4,5,6} which means it would be based on an A-shape (see the CAGED and chained for more information about chord shapes):
 |
| A chord played on a general string set (left handed). |
 |
| A chord played on a general string set (right handed). |
Now, the thing about the standard tuning. I'm not an expert on tuning systems and frankly, I stick to this tuning since I'm a little afraid of other tunings unless they are really called for. What I have realized about it though is that if you traverse vertically downwards from low E to high E, you will walk by fourths, but if you traverse vertically upwards then you will walk notes by fifths. Well, mostly. There is a special case as you probably have noticed, something happens at the step from the G-string to the B-string. This IMO ruins this otherwise so uniform and nice tuning. Why not EADGCF from low to high? Well, I really don't know, but a guess is that the idea behind it is to get as many root notes (open if possible) but maintaining a roughly regular fourths/fifths tuning. A nice thing about it though is that it avoids sharps and flats.
If you have ever played an octave interval between strings {1,3}, {2,4}, {3,5} or {4,6} (as made famous by Wes Montgomery by what he referred to as "the octave thing") then you have probably discovered this feature yourself.
So with this tuning in mind we can do pretty interesting things with a given chord. We can actually replicate a chord on an adjacent string set by using roughly the same fingering. Of course, when notes go beyond last string the chord will be truncated and lose one or more notes. Remember the CAGED system? We can actually deduce some chords from each other this way. Take the open G-chord, it starts with the root-position triad G-B-D then continues with G-B-G and the fingering would be (3,2,0,0,0,3) or the chord formula would be R-3-5-R-3-R. If you move this downwards vertically then you will get the fingering (X,3,2,0,1,0). Whoa, isn't this is an open C-chord?!! Yes it is... rather interesting yeah? But what happened there? Why is there a position 1 at string 5 and a position 0 at string 6? Well remember the little quirk in the standard tuning? This is exactly what it does to a chord that is moved down vertically (by fourths) in the standard tuning. Looking at the G-chord, the interval consisting of position 0 at string 4 and 0 at string 5 is a third interval and not a fourth interval which is evidenced by the notes G and B respectively, i.e. root and third. So since this chord has been displaced from a G-chord to a C-chord using the same chord formula the strings now represent a fifth and a root respectively. These notes instead forms a minor third interval, therefore the note on string 5 must have a note on the first fret. Note that the C-chord has the formula R-3-5-R-3 which is the same as the one for the G-chord but without the last root.
The same applies to the open E-chord on the string set {1,2,3,4,5,6}. This chord has the formula R-5-R-3-5-R and therefore the fingering is uniquely (0,2,2,1,0,0). If you move it one step down across the neck you will get an open A-chord but will lose the root at the end. The open A-chord has the formula R-5-R-3-5 and the fingering (X,0,2,2,2,0). Moving it one step downwards again will yield an open D-chord which has the formula R-5-R-3 and the fingering (X,X,0,2,3,2). So these three chords are very intimately related. On a side note, these chords are separated by fifths/fourths. E->A is a fourth and A->D is also a fourth due to how the standard tuning is set up.
Task: As an exercise, try figure out what open chord you will get when translating an open C-chord down one step. And if translating it down once more, can you see which of the other CAGED chord it is a subset of?
So, to pick another interesting example we can go back to that C9 chord and translate down vertically to make it an F9 chord. The colors match the respective intervals in the chord-formula (here R-3-b7-9):
 |
| The C9 chord translated to a F9 chord (right handed). |
 |
| The C9 chord translated to an F9 chord (left handed). |
With transposing we mean moving a chord in a given string set horizontally along the neck (sometimes with barre for practical reasons) and with translating I mean moving a chord in a given string set vertically across the neck to an adjacent string set. I.e. to a string set S that is translated up or down by N steps would become:
Snew = (S±N)∩[1,6].
For example: A Gmaj7 could be the formula R-7-3 with the fingering (3,X,4,4,X,X) and would thus be on the string set S = {1,3,4}. If transposed three times you would get the translated string set Snew = ({1,3,4} + 3)∩[1,6] = {3,6,7}∩[1,6] = {3,6} and the fingering for the same formula but for this translated string set would be (X,X,X,3,X,5), however technically, this "chord" is not actually a chord anymore but rather regarded as an interval. :P
Of course, like CAGED you can transpose a translated chord so that you get the same root. Frankly, most of the time we deal with chords that are either of these shapes so linking them together is very easy if you have gotten the CAGED system under your fingers.
I hope this information will be useful to you and I encourage you to try to find new interesting chords and chord voicings.
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