Natural Tensions

Adding notes above the seventh is as easy as extending the chord formula of seventh chords. The maj7 chord formula is 1, 3, 5, 7 so the next logical notes, would be 9, 11, and 13. Notes such as these, that are above the seventh, are known as ‘tensions’.

There is no need to add tensions above the thirteenth because, as can be seen in the image below, the fifteenth is the same note as the root, the seventeenth is the same as the third etc.

Maj9 Chords

Constructing a maj9 chord is as easy as starting with a basic maj7 chord formula and then adding a ninth on top. For example, building a Cmaj9 chord would mean starting with a Cmaj7 chord (C E G B) and putting a 9th on top. Our knowledge of intervals and scale degrees tells us that a 9th above C is D, so a Cmaj9 chord will be C E G B D.

Maj11 Chords

Adding an 11th on top of a maj9 chord gives us a maj11 chord. For Cmaj11, this means starting with a Cmaj9 (C E G B D) and then adding an F on top. However, bear in mind that maj11 chords are very rare due to the unpleasant dissonance created by the 11th clashing with the 3rd of the chord – in a Cmaj11 this would be the F clashing with E.

Maj13 Chords

Theoretically, a maj13th chord would be a maj11 with a 13th added on top. However, due to the dissonance associated with the 11th, it’s usual to omit it. This means that the real-world formula for a maj13 chord would be 1 3 5 7 9 13.

Extended Minor Chords

Adding extensions to min7 chords follows the same procedure as for maj7 chords. This means that:

• Adding a ninth to a min7 chord creates a min9 chord
• Adding an eleventh to a min9 chord creates a min11 chord
• Adding a thirteenth to a min11 chord creates a min13 chord

It is usual to include the eleventh in minor type chords, as there is no ‘clash’ between the eleventh and the minor third (the notes Eb and F in a Cmin chord). Therefore, while maj11 chords typically sound disagreeable, min11 chords sound perfectly pleasant. It also means that the eleventh is included in the formula for min13 chords.

Extended Dominant Chords

Adding extensions to dominant chords is essentially the same as with major and minor chords. However, since dominant chords have a major third, the eleventh will ‘clash’. Dominant 11 chords are therefore rare (in a C11 the F will clash with the E), and the eleventh should also be omitted from dominant 13 chords, for the same reason.

Other Extended Chords

The most commonly extended chords are based on the maj7, min7 and dominant 7 type chords, although it is also possible to extend min(maj)7 chords and min7b5 chords. Extensions cannot be added to diminished and augmented chords (not normally, anyway), because of the symmetrical structure of these chords – I’ll explore symmetrical chords (and scales) thoroughly in a coming post.

Because min(maj)7 chords and min7b5 chords are both minor-type chords, we are free to include the eleventh without creating a clash.

The first table shows the extensions for min(maj)7 type chords.

This table shows the extensions for min7b5 type chords.

Building Four Note Chords

Four note chords are built by stacking an extra third (major or minor) on top of the triads already covered in part 1. The table below shows every possible combination of four note chords built in thirds. (Although you will notice that that there is no augmented triad with a major third on top. This is because augmented chords are symmetrical chords, which is something that will be discussed in the next post.)

Major Seventh Chords

From chord theory part one we know that a major triad is constructed of a major third plus a minor third. Adding another major third on top will give us a major seventh chord. Therefore the interval structure of a major seventh chord is major third, minor third, major third.

The figure below shows the thirds structure applied to the note C, resulting in a C major seventh chord.

The following figure relates each note of the C major seventh chord to the root to find the chord formula. C is the Root; E is a major third above C; G is a perfect fifth above C; and B is a major seventh above C. This gives us the major seventh chord formula: 1, 3, 5, 7.

Dominant Seventh Chords

The dominant seventh chord is a major triad with a minor third on top. So the thirds structure of a dominant seventh chord is major third, minor third, minor third.

The figure below relates each note of a dominant seventh chord to the root note, C, giving us the dominant seventh chord formula: 1, 3, 5, b7.

Minor Seventh Chords

Taking a minor triad and adding a minor third on top creates the minor seventh chord. A minor triad is a minor third plus a major third, therefore the structure of a minor seventh chord is minor third, major third, minor third.

Relating every note to the root, we arrive at the chord formula: 1, b3, 5, b7.

Minor-major Seventh Chords

Minor-major seventh chords are a minor triad with a major third on top. The interval structure of a minor-major seventh chord will therefore be minor third, major third, major third.

From this C minor-major seventh chord we can derive the minor-major seventh chord formula: 1, b3, 5, 7.

A min/maj seventh chord gets its name from the fact that it is a minor triad, but unlike the minor seventh chord it has a major seventh on top.

Half Diminished (Minor Seventh Flat Five) Chords

Stacking a major third on top of a diminished triad creates the half-diminished chord – also known as a “minor seven flat five” chord. A diminished triad is constructed of two stacked minor thirds, so the structure of a half-diminished chord is minor third, minor third, major third.

From this C Half-diminished seventh chord we arrive at the chord formula: 1, b3, b5, b7.

The name minor seventh flat five comes from the fact that the chord formula is the same as the chord formula for the regular minor seventh chord but with the fifth flattened (the minor seventh formula is 1, b3, 5, b7, whereas the minor seventh flat five is 1, b3, b5, b7)

The name half-diminished comes from the similarity of the chord formula with the diminished seventh chord formula (shown below). The diminished seventh chord has two diminished intervals in its chord formula, however the half-diminished chord only has one diminished interval (the b5) – making it only ‘half’ diminished compared to the regular diminished seventh chord.

Diminished Seventh Chords

A diminished triad plus a minor third creates the diminished seventh chord. Every interval in a diminished seventh chord is a minor third, so the structure is minor third, minor third, minor third.

When building a C diminished chord it is very important that the top note is written as a B double flat. Chords are built in thirds, and a Bbb is accordingly a minor third above Gb (three letter names). Spelling the Bbb as its enharmonic equivalent, the note A, will cause problems later when the theory gets more involved (Gb to A is not a minor third, it is an augmented second).

From this C diminished seventh chord we arrive at the chord formula: 1, b3, b5, bb7.

Note that the seventh degree is a double flattened seventh (bb7). Double flattened sevenths are also known as diminished sevenths, and is where this chord gets its name from.

Augmented Major Seventh

Starting with an augmented chord and adding a minor third on top results in the augmented major seventh chord. The thirds structure of augmented triads is two stacked major thirds, so adding a minor third on top to create an augmented major seventh gives the structure major third, major third, minor third.

The chord formula is therefore: 1, 3, #5, 7.

Looking at the chord formula we can see that the augmented major seventh is a regular augmented chord but with a major seventh on top. This is what gives the augmented major seventh its name.

Summary

Here’s a table showing everything covered in this post.

Know Your Intervals

Chords are built by stacking intervals on top of each other, so you’ll need to make sure you know your intervals first. You can find out all about them in my intervals lesson and even if you do know your intervals, it might be worth having that page open for reference – it has a big table which shows the number of semitones for any interval.

Stacking Thirds

Typically, chords are created by stacking thirds (either major or minor) on top of one another. For instance, in a C major chord, we have the notes C, E and G.

The interval from C to E is a major third (4 semitones), and the interval from E to G is a minor third (three semitones).

So the chord construction for a major triad is a major third on the bottom (C to E), and then a minor third on top (E to G).

As another example, the Cmaj9th chord has the thirds structure of major third, minor third, major third, minor third.

Chord Formulas

Another way of conceptualising the structure of chords is with a chord formula. A chord formula does not relate each note to its surrounding notes, but instead relates everything back to the root note. In the case of the Cmaj chord, the chord formula is 1, 3, 5. The number 1 refers to the root note (in this case C), the number three indicates a note a major third above the root which is E, and the number 5 indicates a note a perfect fifth above the root, which is G.

Here’s is the same principle of chord formulas, this time applied to the Cmaj9th chord. This gives us the maj9th chord formula which is 1, 3, 5, 7, 9.

Triads

Triads, as the name suggests, consist of three notes. Triads form the basis of western harmony, the most ‘basic’ (at least in terms of structure) are the major, minor, augmented and diminished triads.

Together these four chords cover every possible three note combination of stacked major and minor thirds, as shown in this table.

Using this information, we can stack thirds to create the C major, C minor, C augmented and C diminished chords. We can then count up the semitones to arrive at the chord formulae.

The Major Chord Formula

The thirds structure of a major chord is a major third on the bottom and a minor third on top. Taking C as our root we find the next note by going up a a major third to the note E, and a minor third above the E to G. Therefore a C major chord uses the notes C, E, and G. C is the root and is marked as 1 (or R) in the chord formula; E is a major third above C which is marked as 3 in the chord formula; and G is a perfect fifth above C so it is marked as 5, which gives us the chord formula: 1, 3, 5 or R, 3, 5.

The Minor Chord Formula

From the table we know that a minor chord has a minor third on the bottom and a major third on top. Again, taking C as the root we find the next note by going up a a minor third to the note Eb, and a major third above that to G. Therefore a C minor chord uses the notes C, Eb, and G, where C is the root; Eb is a minor third above C and is written as b3 in the chord formula; and G is a perfect fifth above C so it is marked as 5. This gives us the minor chord formula which is: 1, b3, 5 or R, b3, 5. It is the minor third (b3) that gives the minor chord its name.

Augmented Chord Formula

Using the table to find the thirds structure we see that an augmented chord is built with two stacked major thirds. Starting on the note C we have the notes C, E, and G#. It is important that the last note is labelled G# not Ab. This is because, although G# and Ab are the same pitch, Ab is not a major third up from E – since E to A is four letter names, Ab would be a diminished fourth above E, not a major third above E.

The C is the root and marked 1 or R, the E is a major third from C and is marked 3; and the G# is an augmented fifth from C. This results in the augmented chord formula which is 1 3 #5 or R 3 #5. The augmented chord gets its name from the augmented fifth on the top of the chord (#5).

Diminished Chord Formula

Using the table, a diminished triad is two stacked minor thirds. Starting with C, Eb is a minor third up, and Gb is a minor third above that. So a C diminished chord contains C, Eb and Gb. Again, be careful that the top note is spelled Gb not F# since an F# is an augmented second above Eb not a minor third. Simple triads are always built in thirds.

So the chord formula for diminished chords will be 1 b3 b5. It is the diminished fifth on top (b5) which gives the diminished chord its name.

Major Seventh Chords

These are the most basic major seventh chords, in open position.

Using the CAGED principle we can turn these into moveable chord forms, which will allow us to use the chords anywhere on the neck – not just as open chords.

Minor Seventh Chords

Here are the minor seventh chords, again in open position.

And here are the moveable CAGED shapes based on those open shapes.

Dominant Seventh Chords

The following diagram shows some of the most common open position dominant seventh chords. Note that although there are other possible chord grips, only these five conform with the CAGED system.

And here are the moveable CAGED shapes:

If your wondering which of these CAGED shapes you should learn first, its probably a good idea to make sure that you know the A and E shapes first and then learn the C and D shapes. The G shape is very rarely used in its entirety, so it is probably the least important – although there are some very useful ‘chord fragments’ which can be taken from the G shape, so don’t discount its usefulness out of hand, either.

Sorry, but I haven’t quite figured out how to do 4, 5 and 7 string blank TAB for guitar and bass – I’ll post them as soon as I can…

• Standard Notation with Treble Clef
TAB
• Hybrid with Both Standard Notation and TAB
• Chord Boxes
• Full Page Fretboard Diagrams

Prerequisites

To make full use of this article you should first have a basic knowledge of common open position chords – especially C, A, G, E and D major chords – and have at least a vague understanding of barre chords, what they are and how they work. Its also helpful if you know what notes in each of these open chords are the root. Beware that this is not necessarily the lowest note in each chord, and that most chord shapes have the root occurring simultaneously in different octaves (more on that later).

But for those who need a refresher, here are the basic chords you’ll need.

The roots in each chord are marked ‘R’. The note names of the roots are the same as the letter name of the chord – so the root of a C major chord, is C and the root of A major is the note A etc.

Benefits of the CAGED System

The CAGED system is a simple way of visualising how common chord shapes, scale shapes and arpeggios inter-relate and overlap with one another. The CAGED system works for all chords, scales (including the blues scale) and even modes, and works in both major and minor keys. It gives us a way of linking up smaller shapes into a larger ‘fretboard map’.

If you want to easily navigate the neck then the CAGED system is a good place to start (though there are other more complicated ways of visualising the fretboard)

The Caged System

If you hadn’t gathered by now, the CAGED system is an acronym of the C, A, G, E and D chord and scale fingering patterns. Each of these open chords has a movable barre chord shape. The most common barre chord shape being the ‘E shape’ barre chord, which can be found by taking the regular open E chord, moving the chord up a fret, and adding a barre behind it.

If you are familiar at all with barre chord construction it should be clear how these two shapes are essentially identical. Note that when you play the ‘E shape’ barre chord, although it is known as being an ‘E shape’, its actual root (letter name) will change. For instance an ‘E shape’ barre chord at the first fret is an F chord, while an ‘E shape’ barre chord at the fifth fret is would be an A chord.

If this sounds like double dutch read the Wikipedia entry for barre chords first.

Barre Chords for the Other Shapes

All common open chord shapes can be made into a barre chord, simply by moving the shape further up the neck, and laying a barre behind it in lieu of the nut. The barre chord shapes of C, A, G, E and D are listed below (click the pic for a larger and clearer view).

Also, note that even though the ‘D shape’ chord isn’t technically a barre chord (since it doesn’t actually use a barre), it is still a movable shape, and can be treated exactly the same as the actual barre chords.

Mapping the Fretboard

Now, for simplicities sake lets begin mapping the fretboard for the D major chord, beginning with a D major chord at the second fret using the ‘C shape’ barre chord.

We could also play a D major chord using the ‘A shape’ at the fifth fret.

Note that both the ‘C shape’ and ‘A shape’ D major chords are built off the same root, D, on the fifth string. Its good to draw both of these shapes on the one fretboard diagram. This way we can easily see how the two chord shapes relate to one another, and we can see that the two shapes overlap at the root note on the fifth string.

As well as having a root on the fifth string, the ‘A shape’ barre chord also has a root on the third string. The only other barre chord with a root on the third string is the ‘G shape’ barre chord. Since the ‘A shape’ and ‘G shape’ barre chords share the same root they can also be drawn together on a single large fretboard diagram.

As well as having a root on the third string, the ‘G shape’ barre chord also has a root on the sixth string. The ‘E shape’ barre chord shares this root on the sixth string.

Finally, the ‘E shape barre chord’ share its root on the fourth string with the ‘D shape barre chord’.

Of course, we can also arrange all of these chords onto a single large fretboard diagram (click the image for a larger view).

And there we have it – every common chord shape laid out in a key on the fretboard with all roots overlapping. And, as we would expect, the chords came out in the order C-A-G-E-D giving us the CAGED system. Of course, when you get to the end of the word CAGED the process just repeats itself in the next octave – the image above shows how the final ‘D shape’ links onto the next ‘C shape’.

So to easily remember how all of the chord shapes inter-relate and overlap with each other, you can recite the letters of the word CAGED to quickly recall the sequence.

These diagrams have six lines representing the strings, and the diagram is oriented as if the guitar is standing up in front of you.

Since the guitar is oriented as if standing up, the thickest string is on the left and the thinnest string is on the right. The nut is usually represented with either a double line or a single bold line, at the top of the diagram.

And the horizontal lines represent the frets.

Dots show where you need to place your left hand fingers.

Often the dots are numbered to show you which fingers you should use; where the 1 is the index-finger, 2 is the middle-finger, 3 is the ring-finger, and 4 is the little finger.

X’s are used to indicate strings which you should not pluck (or should mute). 0′s indicate notes which you should pluck and are to be played ‘open’. This means that you do not need to fret the string with your left hand – just pluck the string without fretting.

When a single finger is used to fret more than one note, it needs to be barred. A barre is represented with a solid line.

Sometimes chord/scale diagrams will indicate positions further up the fret board. In this case the nut is not drawn in. Instead, a normal horizontal fret is drawn, and a roman numeral indicates the fret that the diagram is drawn at.

So this figure means that the index finger is to be placed at the fifth fret, and the ring finger at the seventh fret.

Lastly, chord diagrams are occasionally tipped on their side. When this happens the nut is always on the left, and the string at the top of the diagram is therefore the thinnest string, and the string at the bottom is the thickest. The following two images show the same fingering for the same chord – one diagram is drawn standing up, and the other, lying down.