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.

Chords

Generally, western music consists mostly of three basic chord qualities – major, minor and dominant seventh. The major chord formula is 1, 3, 5 while the minor chord requires a minor third so its formula is 1, b3, 5. Dominant seventh chords are a major triad with a b7 added on top, so the dominant 7th formula is 1, 3, 5, b7.

Of course, the major and minor chords can also be played as seventh chords, with a major seventh chord having the formula 1, 3, 5, 7 and the minor seventh being 1, b3, 5, b7.

All of these chords can be extended beyond the seventh with natural tensions up to a thirteenth – basically this means just stacking thirds above the seventh, without using flattened or sharpened degrees. The natural tensions above a seventh chord are therefore the 9th, 11th and 13th. We can add these notes to our major 7th, minor 7th and dominant 7th chords to create the major 13th, minor 13th and dominant 13th chords respectively.

Scale Choices

When choosing which modes to use over a given chord progression its important to always be aware that every mode implies a harmony, and that every mode co-exists with some sort of chord. One way of determining what chord relates with which mode, is to take the notes of the chord and rearrange them so that they fit into one octave – this means bringing the 9th down an octave to the 2nd, the 11th down to a 4th and the 13th down to a 6th.

Of course, we’ve already encountered these exact same formulas – but with different names. For instance the Maj13 formula is the same as the ordinary major scale/Ionian mode; the min13 formula is the Dorian mode, while the dominant 13th formula is the same as the Mixolydian mode.

This means that a Maj13th chord implies the Ionian mode. Similarly, a person soloing in a Dorian mode is implying min13th harmony. In fact, these modes and their respective harmony are so intertwined that its helpful to think of a maj13th chord as being meaning Ionian – and vice versa. Rather than thinking about chords and scales distinct from each other, its good to start thinking about ‘chord scales’ where terms like Ionian and major, or Mixolydian and dominant are two words for exactly the same concept.

‘Avoid’ Notes

An avoid note is a note of a mode, that creates an ‘unacceptable’ dissonance when held against the chord of the mode. For example, the Ionian mode is a suitable scale choice for a maj13 chord – but if you hold the 4th against a maj13 chord, the note will ‘need’ resolution if it is to sound ‘acceptable’. The sound of the 4th degree against a maj13 chord is almost universally agreed upon as sounding ‘wrong’ (or at least, not quite ‘right’).

Notes such as these are known as ‘avoid’ notes and need to be treated carefully when being used in melodic construction. Although they are called avoid notes, there is no need to avoid them completely – just use caution.

The Cause of Avoid Notes

Avoid notes are a result of the interval of a minor 9th (e.g. E to F, B to C etc). From the previous example, the reason the F sounds so unpleasant is because it clashes with the note E in the chord (a Cmaj7 contains the notes C E G B). Other instances of avoid notes include the 4th degree of a Mixolydian mode – e.g. a C over a G7 chord. G7 has the notes G B D F, but playing a C in the melody will clash with the B in the chord.

Dealing with Avoid Notes

Not all occurrences of a minor 9th will necessarily sound unmusical. Depending on the player, the voicing of the chord, and the expectations of the listener, its perfectly possible for an F to be played over a Cmaj7th chord (or a C over a G7 for that matter). Nonetheless, the minor 9th interval will typically sound unpleasant, so its important to be familiar with the common methods of dealing with these ‘clashes’.

The strident sound of avoid notes can be lessened by using the note as a ‘passing’ note. For our purposes, a passing note is a note which is usually of short duration and resolves stepwise to the note immediately below or above it. For example, in the case of an F over a Cmaj7 chord, keeping the F short and resolving it immediately to the E below, or the G above it would prevent the F from sounding ‘wrong’.

The other accepted way to deal with avoid notes is to raise them by a semitone – thus turning the ugly minor 9th interval into the much nicer sounding major 9th interval. In the case of the Cmaj7 chord this would mean raising the F to F#. This way the E in the chord will no longer clash with the melody note.

When raising notes to avoid the minor 9th dissonance it is important to be aware of the way that it will effect the ‘character’ of the melody. In ‘Top 40′ rock and pop songs or any music with a mostly static key centre, the raised note will sound like its ‘out of key’ – because, after all, that is exactly what it is. On the other hand, in many jazz tunes, some virtuoso rock guitar pieces, or any piece with ambiguous or changing key centres, or in a ‘modal key’, then the raised note may not sound so contrived or out of place.

Lydian Chords

As we know from the previous modes post the Lydian scale formula is 1 2 3 #4 5 6 7. Rearranging these notes into stacked thirds to create a chord and moving the 2, #4, and 6 up an octave we arrive at the chord formula 1 3 5 7 9 #11 13, which is the formula for a maj13#11 chord.

Of course its not necessary to use all of the possible notes to build chords. For instance using only degrees 1, 3 and 5 we can construct an ordinary major triad, or if we take degrees 1, 2 and 5 we can build a sus2 chord. More complex chords that can be derived from the Lydian mode includes the maj69 chord (1, 3, 5, 6, 9) or the maj7#11 chord (1, 3, 5, 7, 9, #11).

The most common chords that can be derived from the Lydian mode include maj, sus2, maj6, maj7, maj9, maj7#11, maj13, add9 and maj69 chords. As such Lydian can be a good choice for soloing over all of these chords.

Ionian Chords

The Ionian formula is 1 2 3 4 5 6 7. Rearranging these notes into stacked thirds to create a chord, we arrive at the chord formula for a maj13 chord, 1 3 5 7 9 11 13. Other chords which can be constructed from the notes in the Ionian mode are maj, sus2, sus4, maj7, maj9, maj11, maj13, add9, and maj69 chords.

You may notice that many of those chords can also be derived from the Lydian mode which means you have a choice of Ionian or Lydian as the mode to base your melodies on. Bear in mind though that the 4th degree of the Ionian mode will clash with the 3rd of the chord – i.e. the 4th note of the Ionian mode will be an avoid note. So be cautious, perhaps treating it solely as a passing note. Of course, you also have the option of raising the avoid note – but then you would just end up playing the Lydian mode anyway, since Lydian is essentially a major scale with a #4.

Mixolydian Chords

The Mixolydian formula is 1 2 3 4 5 6 b7. There are various chords which can be created from these notes such as the simple maj, sus2 and sus4 triads, and triads with added notes such as the add9 and maj69 chords. However, be aware of the natural 4th which will be an avoid note on the maj, add9 and maj69 chords. Of course, the sus chords do not have a third so there is no problem with an avoid note on those chords.

Mixolydian is ideal for dominant 11th chords (though to be honest these don’t come up often), and is also suitable over 7th, 9th and 13th chords – but again be aware of the avoid note. Mixolydian is perfectly suited to suspended dominant chords such as 7sus4, 9sus4 and 13sus4, because there is no avoid note.

Dorian Chords

The Dorian formula, when rearranged as a chord is 1 b3 5 b7 9 11 13, which is the chord formula for a min13th chord. The Dorian mode is therefore the perfect choice over most minor chords, min7, min9, min11 and min13 chords. Also, because the Dorian mode has a natural 6th (13th) it is perfect for min6 and min69 chords.

As the Dorian mode does not contain the major third, there is no danger of the natural 4th being an avoid note. This is also true for the Aeolian, Phrygian and Locrian modes since none of these modes have a major third.

Aeolian Chords

The Aeolian formula is 1 2 b3 4 5 b6 b7, which, when rearranged as a chord formula gives us a min7b13 chord formula, 1 b3 5 b7 9 11 b13. The only difference between the Dorian mode and the Aeolian mode is the presence of the b6 in the Aeolian. This makes Aeolian effective over min7, min9 and min11 chords, but will not work over min6, min69 or min13 chords as these chords all require the natural 6th/13th.

Also, even when used over basic min7, min9 and min11 chords we still have the issue of the b6 clashing with the 5 of the chord – i.e. the b6 is an avoid note. Because of this, it may be wise to stick to the Dorian mode over most minor chords. This is not to say that you can’t use Aeolian over min7 type chords – in fact, done carefully, I find that the b6 can be a beautifully ‘brooding’ note, providing that it is not held against the chord, and is used sparingly/tastefully.

Two chords which beg for the Aeolian mode to be used is the min7b13 and minb6 chords. Both of these chords a minor type chords, and both contain the b6/b13 note, so the Aeolian mode is the idea choice for these chords.

Phrygian Chords

The b3 and b7 indicate that the Phrygian mode is some kind of minor mode, however the presence of the b6 and a b9 (both avoid notes on min chords) makes it a less common choice over min7, min9, min11 and min13 chords. That said, used as passing notes the b6 and b9 make for a very dark, and, in my opinion, appealing sound, with a Spanish/Moorish flavour.

One chord that is particularly well suited to the Phrygian mode is the 7susb9. This chord is actually a dominant type chord – not a minor type chord – and it involves some fairly complicated theory to fully explain how and why this works. Unfortunately its well beyond the scope of this post, however later in the modes series we will look at it closer.

Locrian Chords

The Locrian formula is 1 b2 b3 4 b5 b6 b7, the notes of which build a min7b5 chord or simply Ø (meaning half-diminished). Since the half-diminished chord has a b5 (rather than a natural 5) there is no danger of the b6 being an avoid note as it was in the Aeolian and Phrygian modes. The only avoid note in the Locrian mode is the b9 which clashes with the root note. As with all other avoid notes mentioned in this post, this note is usually ‘brushed over’ as a passing note, or raised up to a natural 2nd.

In Summary

Today we’ve covered a LOT of material, so hopefully this table might make the most important things a little easier to digest.

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.

What are Intervals?

An interval is simply the distance between two notes. For instance what is the distance between C and F? Or G and A#? Well that’s what we’re going to find out (and more). Intervals can be melodic if the two notes are played successively, or they can be harmonic if the notes are played together.

Tones and Semitones

The most basic intervals in music are tones and semitones (whole-steps and half-steps for those in the U.S.). A semitone is a distance of one fret or one key on a piano.

A tone is twice the interval of a semitone, and is a distance of two frets on the guitar and two keys on the piano.

So to answer the questions at the start of the page, what is the distance between C and F?

As you can see, C and F are five keys apart, telling us that they are five semitones apart (don’t count the C but count every other key from C to F including the black keys).

What about G and A#? Well they are three keys apart which means they are three semitones apart.

All of the more complex intervals, such as a minor third or an augmented fourth, are simply combinations of multiple tones and semitones.

Larger Intervals

Intervals are designated a quality and a number. For example, a “major 6th” is an interval of a 6th and its quality is major. First we are going to have a look at the number component of interval names, before looking at the quality component.

The number of an interval comes from the number of letters (note names) that separate two notes. For example, C and D are two letter notes apart and is therefore an interval of a second. F and A would be an interval of a third since they are three notes apart. C and A are six letters apart and is therefore an interval of a sixth.

As we’ve learned in reading the notes part 1 a D# and an Eb are the same pitch. However it’s important to realise that, although a C to a D# is the interval of a second, a C to Eb is an interval of a third. What is important here is how many letter names apart the notes are.

Interval Quality

C and D, C and Db, and C and D#, are all intervals of a second, as they are all two letters apart. Interval quality is what sets them apart from each other. For instance C to D is called a perfect second, C to Db is a minor second and C to D# is an augmented second. A major second requires a distance of two semitones, a minor second requires a distance of one semitone, and a augmented second requires a distance of three semitones.

This table below lays out all common intervals with their name and distance in semitones. I don’t expect you to go through this table and try to memorise it by rote. Instead I suggest that you print it off for later (or better yet, save paper by just bookmarking the page in your browser). That way you’ve got the table for reference when you need it.

Also the table might seem hard to digest right away so here are a few pointers to make it easier.

• Augmented intervals are one semitone larger than a perfect or major interval
Diminished intervals are one semitone smaller than a perfect or minor interval
• Major intervals are one semitone larger than minor intervals
• Minor intervals are one semitone smaller than major intervals
• Fourths, fifths, unisons and octaves are never major or minor – but they can be perfect
• Seconds, thirds, sixth and sevenths are never perfect – but they can be minor and major

Also, it’s worth noting is that any interval can be augmented or diminished.

(Astute readers will notice that I missed a few intervals from the table – such as ‘augmented sixths’, ‘diminished octaves’ etc. Although these intervals exist in theory, in reality they are hardly ever needed, so I thought it best to limit the table to the more common intervals. Besides, if you do get to such an advanced level of theory that you do find yourself using augmented sixths then you should already have enough musical knowledge to figure it out by yourself )

Complementary Intervals

Complementary intervals have the same letter names but occur in the opposite direction. For instance C to E is a third (three letter names), however, E to C is a sixth (six letter names). Complementary intervals have some interesting characteristics, such as:

• The complement to a minor interval is major – i.e. minor becomes major
• The complement to a major interval is minor – i.e. major becomes minor
• The complement to a perfect interval is perfect – i.e. perfect remains perfect
• The complement to a diminished interval is augmented – i.e. diminished becomes augmented
• The complement to an augmented interval is diminished – i.e. augmented becomes diminished
• Adding the numerical value of two complementary intervals always adds up to nine

For instance,

• C to E is a major third. The complementary interval is E to C which is a minor sixth (major has changed to minor, and three plus six equals nine)
• C to A is a minor sixth. Its complement, A to C, is a major third (minor becomes major, and 6+3=9)
• C to G is a perfect fifth. Its complement, G to C, is a perfect fourth (perfect interval remains perfect, 5+4=9)
• C to G# is an augmented fifth. Its complement, G# to C, is a diminished fourth (augmented becomes diminished, 5+4=9)
• C to C can be an octave, or a unison. Octaves and unisons are both perfect intervals (perfect remains perfect) and their numerical values add up to nine (8+1=9)

Scale Degrees

We can also use the interval nomenclature (major third, augmented fourth etc) and their abbreviations to label the degrees of scales. Note how the root is usually marked with an R, as opposed to P1 which we use for intervals.

For instance, here is a C major scale with the notes labelled according to their degree.

Similarly, say we flatten the seventh and third degrees. We can use the lowercase m’s or b’s to represent the minor seventh and minor third.

Being able to label scale degrees this way means that, we can easily refer to particular notes in a scale of chord. For instance: “I’ll play the root and the fifth, you play the third and the sixth on top of that”, or “Gimme an F major chord but put a #4 and a ninth on top or colour”.

Beyond the Octave

So far we’ve only looked at intervals and scale degrees within the confines of an octave, however occasionally (and especially when studying chord theory) its necessary to be familiar with intervals greater than an octave. Of course, by going beyond the octave we end up creating extra labels for notes which already have a label. For instance a 9th and a 2nd are the same note (but an octave apart), as are the 10th and the 3rd, the 11th and the 4th, the 5th and the 12th, and the 6th and the 13th.

Of all of these possible ‘extra’ intervals/scale degrees only a few are particularly common – such as the 9th, 11th and 13th – so it’s probably worth becoming familiar with those first, rather than trying to learn everything at once. Also, the qualities of augmented, diminished, major, minor and perfect, apply to these upper octave scale degrees, exactly the same as they were applied to the lower octaves.

Relative Mode Theory (aka ‘Modes in Series’)

So far we’ve been mostly using relative mode theory – e.g. where C Ionian and A Aeolian share the same notes, but have different roots. But now we are going to learn to use our modes in parallel. In contrast, parallel modes have the same roots but different notes.

Where C Ionian and A Aeolian are relative, C Ionian and C Aeolian are parallel modes. F major and F minor can be called parallel scales (or even parallel keys).

Comparing the Major & Natural Minor Scales

In the figure below, we can see that the first, second, fourth and fifth notes of these scales are the same…

…but, because of the different tone-semitone structure, the third, sixth and seventh notes are all one fret lower. Notes that are one fret lower are said to be ‘flattened’ and are represented with a ♭.

In the following diagrams I have numbered each scale degree with a number for easier reference. Sticking to convention, the first and last notes are still being labelled as R, rather than 1 and 8.

We can relate all modes back to the major scale in this way. Using ‘♭’ to represent ‘flattened notes’, and ‘♯’ to represent ’sharpened notes’ (i.e. notes that are one fret higher).

Comparing the Modes with the Major Scale

When analysing the modes in parallel we find that the modes are all pretty similar to each other. In fact, each mode is only one note different to another mode. For instance Lydian and Ionian are only one note different. The same is true for Dorian and Aeolian. The following images show each mode, with an arrow indicating the note that has moved.

Here’s the same information collated into an easier-to-read table.

(NB: If you’ve never encountered such things as “♭3s” or “♯4s” before, or used scale formulas like those in the table I suggest that you hone up on your scale degrees and intervals before moving on with the rest of the modes series.)

The Character of Each Mode

Play through the modes in this order – starting with Lydian and then progressively lowering one note each time until you arrive at Locrian. You should find that Lydian is the ‘brightest’ or most consonant mode, and that, each mode is progressively darker than the last, until you get to the Locrian mode which is extremely dark and dissonant.

This table has the brightest modes on the left and the darkest modes on the right. Each mode gets progressively darker as you flatten more notes.

I strongly urge you to play through each of these scales and find your own description of each mode. The following list is how I think of each mode, and should help get you started.

• Lydian Very consonant
• Ionian Sweet and cheerful
• Mixolydian Bright like the major scale, however the b7 lends it a more ‘bluesy’ edge
• Dorian Not particularly bright or dark. Popular for jazz-tinged blues.
• Aeolian The natural minor scale, it typifies ’sad’ songs
• Phrygian Dark and ‘characterful’. The b2 gives it a distinct ‘Spanish’ flavour.
• Locrian Dissonant

Tones and Semitones

Scales are sets of notes arranged into tones and semitones, also known as whole-steps and half-steps. Simply put, a tone (whole-step) is a distance of two frets, while a semitone (half-step) is a distance of only one fret.

For those that know a little about piano, a tone is one key apart, while semitones are adjacent keys.

The Interval Structure of The Major Scale

The notes of the Major scale (Ionian mode) are spelled out as Tone, Tone, Semitone, Tone, Tone, Tone, Semitone. Since a tone is two frets, and a semitone is one fret, a major scale could look like this, along a single string. (Of course, we would rarely use a scale laid out on a single string – but mapping it to the fretboard like this does make it easier to see the intervals (fret-distance) between each note.)

Realise that I haven’t just pulled this fretboard map out of thin air. It’s been taken from the regular C Ionian/Major scale (covered in Modes Part 2). In case you can’t see the connection, here is the full fretboard map with the other notes ‘greyed-out’.

The Interval Structure of The Modes

As we learned in Modes Part 2, a mode is little more than a major scale starting in a different place. This means that finding the interval ‘formulas’ of the other modes is as simple as starting the Tone, Tone, Semitone, Tone, Tone, Tone, Semitone formula at a different place.

For instance to get the Dorian mode formula, we will start at the second interval of the formula, since Dorian is the second mode of major. This would give us the Dorian interval structure as being Tone, Semitone, Tone, Tone, Tone, Semitone, Tone. Similarly, the formula for Phrygian, the third mode, would start at the third interval of the major scale formula, giving us Semitone, Tone, Tone, Tone, Semitone, Tone, Tone.

I’ve provided a table below for easy reference, but you should make sure that you can work out the formulas yourself.

And in case you’re a more visual person, here are those same modes mapped out along single strings.

CAGED Revision

Thinking back to the second CAGED post, you will recall that the CAGED system refers to the root shapes and the way that they lay out, and overlap, on the fretboard. Obviously, its important to understand how the CAGED system works with basic scales, before we apply it to the modes, so look back at that article if you need a refresher. Even so, I’ve reproduced the root shapes here for easier reference.

NB: Remember that the terms ‘A shape’ and ‘C shape’ etc only refer to the root shapes – don’t think that ‘A shape’ has anything to do with the note ‘A’ or that ‘C shape’ refers to the note ‘C’. If you mix this up things can quickly become very confusing .

CAGED

Lets begin with the C Ionian and D Dorian modes that were introduced last week.

Although the C Ionian and D Dorian patterns are exactly the same, the roots have moved. This has the effect that CAGED naming scheme will be different depending on what mode we are using. For instance, the ‘A shape’ C Ionian pattern, has the same fingering as the ‘C Shape’ Dorian pattern.

Conversely, the ‘E shape’ Ionian mode looks like this:

Whereas the ‘E shape’ Dorian mode is completely different:

Furthermore, since it is the placement of the roots which dictates what mode is being used, a fretboard diagram without the roots shown is absolutely meaningless.

For instance, this figure…

… could be known as the ‘E shape’ Ionian if the roots were placed like this:

But could also be the ‘G shape’ Dorian if the roots were placed like this:

Thinking Modally

Until now, we’ve been thinking entirely in ‘C major’. If we wanted a G Mixolydian, we would think of the C major scale but visualise the new position of the root. Effectively we’ve been thinking “C major”, but calling it something else. As you can see, though, when we start giving them CAGED names it quickly becomes difficult to ‘think in C‘ but play a G Mixolydian mode with the ‘A shape’ pattern. Working with three different letter names is asking for trouble. We need to streamline things if we want to actually use modes in real-world playing.

To play modal tunes, and improvise creatively with modes it’s impossible to calculate the parent major scale, figure out the new position of the root, and then choose the most convenient CAGED shape on the fretboard in an instant. Music should speak emotionally not intellectually, and unless you like sounding formulaic, you don’t want to be thinking formulas, either .

So if we want to play modally, we need to think modally by internalising the modes with the same thoroughness and completeness as any other scale. If you want to actually use modes in your playing, and not just think of them theoretically, you’ll need learn and practice each mode as if it were an entirely new scale. Modes are independent scales in their own right, so learn them as such. We want to think of the mode, not its parent major scale.

So Which Modes Should I Learn, First?

That’s a tough question. For instance, if you’re interested in jazz you might like to start with the Dorian or Mixolydian modes, or if you’re into Steve Vai then maybe starting with the Lydian mode would be a good idea. Over the next few modes posts, we’ll look at how each mode is used and in what styles. This should give you an idea which modes are most useful for you, so you can focus on mastering those modes, first.