Omitting the Fifth

Usually one of the most unessential notes of any chord is the fifth. In these chords the fifth is essentially “inert”. It does not contribute to the sense of major or minor, nor does it add any interest (tension, dissonance or sense of forward movement) to the sound. Therefore it can typically be omitted quite safely without affecting the stability or tonality of the chord.

As an example, while a Cmaj7 would normally have the notes C, E, G and B, it is common to leave the G out, keeping only the C, E, and B. This is also true for dominant and minor type chords.

Of course, with chords which have a b5 or #5 (such as augmented and diminished type chords), it would normally be best to try to keep the fifth as these altered fifths do play an important role in the sound of the chord (they add dissonance and forward movement).

Omitting the Root

Omitting the root is also a possibility, though this is not nearly as straight forward as omitting the fifth. Like the fifth, the root is essentially inert and does not contribute any interest to the sound of the chord. The root does however, dictate the tonality of the chord and as such, we must exercise caution when employing rootless voicings.

For example, omitting the root from a Cmaj7 chord (C, E, G, B) would leave us with the notes E, G and B, which is the same as an E minor triad. We need a strong sense of harmonic context to prevent rootless voicings from sounding ambiguous or taking on the character of another chord. The following guidelines should help you in developing good taste when using rootless voicings.

• When playing in a band with a bass player or major harmonic instrument (such as piano), you will have more luck using rootless voicings since the other instruments will provide harmonic context, ensuring that the chord does not sound ambiguous
• If you are the only harmonic accompaniment rootless voicings will work better used part way through the duration of the chord. For example, two bars of Cmaj7 could possibly be changed to a bar of Cmaj and a bar of Emin. The initial bar of Cmaj will clearly provide the actual harmony and the Emin, will then simply sound more like a ‘passing chord’ and not take away from the intended harmony
• It is safer to omit either the root or the fifth. Omiting them both in the same voicing can sound very unstable. If you omit the root, try to keep in the fifth and vice versa

These guidelines are particularly important when creating rootless major or minor chords. Rootless dominant chords on the other hand can be used much more freely.

Rootless Dominant Seventh Chords

Unlike maj7 and min7 chords, dominant chords contain an interval known as a tritone. This interval is more or less unique to dominant chords, making it possible to fully imply dominant harmony with only two notes – the third and seventh in the chord. This means that the only ‘essential’ notes in a dominant chord are the third and the seventh, and that both the root and the fifth can be omitted freely without causing any tonal instability or harmonic ambiguity.

Being able to freely omit the root and the fifth gives us room to add in more harmonically interesting notes such as ninths and thirteenths. For instance rather than playing an unadorned C7 chord we could play a more interesting C13 (C, E, G, Bb, D, A). As it is incredibly difficult to play all of these notes together as a chord, we can instead omit the root and fifth (C and G) keeping only the other, harmonically more interesting notes – E, Bb, D and A.

Omitting Other Notes

Of course, we are not limited to omitting the root or the fifth. We are also able to omit tensions (such as the ninth or thirteenth) if necessary for practical reasons (such as fingering), or for musical reasons (such as needing a leaner voicing or barer harmonic texture). For instance, a Cmaj13th chord can have the ninth freely omitted, or, conversely the thirteenth could be omited and the ninth kept (which would effectively result in us playing a Cmaj9th chord).

Similarly it is sometimes desirable to omit the 7th from a major type chord (reasons for this will be discussed in a future post). So in the case of a Cmaj13th chord we may choose to omit the seventh, but keeping both the ninth and the thirteenth (effectively resulting in a C69 chord).

6th Chords

A major sixth chord is a major triad with a major sixth added on top. The formula for a sixth chord is therefore 1, 3, 5, 6. For a C6 this would mean adding an ‘A’ to the Cmaj triad which would give C, E, G, A.

Maj6th or Min7th?

Sixth chords are interesting in that they contain the same notes as a major seventh chord, but taking a different note as the root. In the case of a C6 chord, the C, E, G and A could be rearranged into thirds, with the A on the bottom. This gives us A, C, E, G which is an Amin7 chord.

For this reason some people prefer to think of sixth chords simply as inversions of major seventh chords (inverting a chord simply means that the lowest note is not the root – more on that in a coming post). So a C6 can be thought of as an inverted Amin7.

Minor 6th Chords

A minor sixth chord is a minor triad with a major sixth added on top. The formula is therefore 1, b3, 5, 6 so a Cmin6 would be C, Eb, G, A.

Just as the C6 is an inverted Amin7, a Cmin6 is an inverted A half-diminished chord.

Add9 and Min Add9 Chords

Adding the major ninth to a major chord creates an add9 chord. The add9 chord formula is therefore 1, 3, 5, 9 which can also be thought of as a regular maj9 or dominant 9 chord with the seventh left out.

Adding a major ninth to a minor chord formula gives the madd9 formula: 1, b3, 5, 9. This is the same as a min9 chord but with the seventh omitted. Madd9 chords can be safely used in place of min9 chords when a simpler, ‘leaner’ chord voicing is required.

69 and Min69 Chords

The sixth and the ninth are two of the ‘prettiest’ chord tones in any chord – they are colourful without being dissonant. By adding both of these notes to a basic major triad, we are able to arrive at full, ‘fleshed out’ chord voicings, without the dissonance that could occur if we included the major seventh. The chord formula for a maj69 chord is therefore: 1, 3, 5, 6, 9.

In minor-key jazz tunes, min69 chords are also a great chord to use on the tonic minor. They are more colourful than the tonic min6, but not as strident as the min/maj7.

Suspended Chords

The only difference between a major and minor triad is the type of third in the chord. The presence of a major third indicates that the triad is major, while a minor third indicates a minor triad. For instance a Cmaj triad has an E natural whereas a Cmin triad has an Eb.

In short, the third is what we use to identify the quality of the chord – i.e. whether it is major or minor (of course the fifth will determine whether a chord is augmented or diminished but that is a topic for another post). In contrast, suspended chords do not contain a third. This means that suspended chords cannot be major or minor, and therefore do not have a ‘quality’ in the traditional sense – although they do have their own unique and appealing sound.

Like major and minor triads, suspended chords do still have a root (obviously) and a perfect fifth, but the third is replaced with another note. In suspended fourth chords the third is replaced with the perfect fourth (the note F in the key of C), and in suspended second chords, the third is replaced with the major second (the note ‘D’ in the key of C). This gives us the formulae 1, 4, 5 for suspended fourth chords, and 1, 2, 5 for suspended second chords.

In classical harmony, a ‘suspended’ note is a note which replaces a chord note. Therefore, suspended chords are best thought of as ordinary major or minor chords but where the third has been ‘suspended’ (i.e. replaced) with the second or fourth of the scale.

Sus4 Chords

Suspended fourth chords have the third replaced with a perfect fourth. Suspended fourth chords are usually abbreviated to ‘sus4′ or occasionally just ‘sus’.

A sus4 chord should be thought of as a either: (1) a major triad with the third raised by a semitone, or; (2) a minor triad with the third raised by a tone.

Sus2 Chords

Suspended second chords have the third replaced with a major second. On sheet music, the abbreviation for suspended second is always ‘sus2′ (never just ‘sus’).

A sus2 chord should be thought of as a either: (1) a major triad with the third lowered by a tone, or; (2) a minor triad with the third lowered by a semitone.

Suspended Seventh Chords

Adding a minor seventh above a suspended fourth chord creates a suspended seventh chord. Major sevenths are never added to sus4 chords because they create a tritone with the fourth in the chord (such a chord would therefore be better thought of as a dominant-type chord, built from a different root – a more detailed explanation of dominant chords, and the importance of the tritone will be covered in a future post).

It is also uncommon to add a seventh to a sus2 chord. Sus2 chords do not have the harmonic momentum found in sus4 chords – adding an extra note on top would only further weaken the suspended effect and harmonic momentum. Therefore, the only real-world suspended seventh chord, uses a minor seventh on top of a sus4 chord. The formula for a 7sus4, or simply 7sus, chord is therefore 1, 4, 5, b7.

Of course, we can build 9sus4 (1, 4, 5, b7, 9) and 13sus4 (1, 4, 5, b7, 9, 13) chords as well – though its impossible to have an ’11sus4′ because the eleventh and the fourth are the same note. It is also common to flatten the ninth of a suspended seventh chord, to increase its harmonic momentum, as is the case in 7sus4b9 (1, 4, 5, b7, b9) and 13sus4b9 (1, 4, 5, b7, b9, 13) chords.

Table of Suspended Chord Formulas

The following table summarises everything covered so far in this post.

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.