Encoding

The encoding stage is the actual transfer of information from short term to long term memory, typically via the hippocampus. Short term memory is understood as being around 30 seconds, however the process of encoding information into long term memory can take much longer than that – perhaps over a few months depending on the nature and complexity of the information being stored. The hippocampus is believed to hold the information whilst it is being encoded into long term memory. It is also understood that the transfer of information from the hippocampus into longterm memory can happen subconsciously, “in the background”, and even during sleep. This explains why its important to take breaks during practice and why it is often easier to come back to a difficult task after a night’s sleep. Obviously any errors in encoding will hinder recall later on, so a key component of any good memorisation strategy is being thorough and accurate at the encoding stage.

Storage

This stage is where the information is kept in long term memory. However, provided that the information was encoded thoroughly, that reliable strategies for recall are in place, and that the brain remains healthy, there is very little that we can do to influence the storage component of memory; although periodically accessing the stored memory does seem to make future recall easier by helping to mitigate ‘trace decay‘. This is just another way of saying that regularly using the information will help to keep it fresh and easier to recall. Of course, it is also useful to continue to improve how deeply the information is encoded by regularly studying and reviewing previously learned information. Essentially, this amounts to use it or lose it.

Recall

Once we’ve successfully encoded and stored a memory, the final step in the memory process is recall – when we actually retrieve the stored information for use. The types of recall we are covering today are serial recall and cued recall.

Serial Recall

Serial recall refers to the ability to recall information in the order in which it was learned. For students who are overly dependent on only serial forms recall, it can be quite difficult to pick up a piece in the middle of a phrase, line or bar/measure. This can be particularly disastrous when a player loses their place during a performance, often having to ‘back-track’ to find a part that they are more familiar with first and then play from there. A good memorisation strategy then, should address the limitations of serial recall to help mitigate any occasional lapses in memory and to ensure that the performance goes on relatively uninterrupted. In practice, this means developing other recall processes so that one is not entirely dependent on only serial recall.

Cued Recall

A cue can be considered to be anything that may act as a reminder and prompt the recall of information. Any good approach to memorisation will have multiple, carefully planned and organised cues. The more cues that we have available to us, the less likely that the failure if any single cue will effect the performance.

Context-Dependent Cued Recall

Context-dependent cues are cues which depend on the environment or situation. For instance a particular smell may ‘trigger’ (that is, ‘cue’) a person’s early childhood memory of their mothers home cooking – this may even be a long “forgotten” memory, or may trigger the memory of information that the person was not even aware they knew.

An excellent example of this from my own life occurred when I was driving with my parents on an old, scenic country road. Due to the local vegetation and crops, this particular area had a subtle but distinctive smell, which triggered a memory of being there before. When I asked my mother when I’d been there, she replied that I was two years old at the time and travelling in a booster seat!

The physical environment can also act as a powerful cue even if we aren’t aware of it. As an example, many students tell me that they play better at home than they do in their lessons, which can point to a change in environmental cues effecting their recall. In the case of my previous story, there may also have been an element of environmental cues that prompted my spontaneous recall – I happened to be sitting in the centre back seat, which is the place that the booster seat used to go. Adults rarely sit in the centre back seat so it is likely that the majority of the memories associated with the centre seat were formed as a young child during my years in the booster chair.

The other side of the coin is how a lack of environmental cues can cause forgetting. I knew an extremely accomplished saxophonist and clarinettist who played in our local community concert band, and, depending on the availability of players, the scoring of the music, etc he would happily swap between instruments as necessary. On this occasion he was playing clarinet, but when the sax section asked him a question regarding fingering he completely blanked and couldn’t recall the correct saxophone fingering. However, once he had put down the clarinet and picked up a sax he immediately demonstrated the fingering. The presence of a clarinet in his hands cued memories of clarinet fingerings, whilst the sax was an environmental cue that was needed before his brain could ‘change gears’.

Accordingly its very important that our method of memorisation makes good use of contextual cues and accounts for any cues that may be unavailable during a performance context.

State-Dependent Cued Recall

Although the current understanding of state-dependent learning is still widely theoretical, it is generally understood that the emotional state or mental state of the person during encoding can be an important cue to recall. Information learned whilst happy for instance, can be more easily recalled during periods of happiness, or information whilst intoxicated can be better recalled when intoxicated than when sober.

Unfortunately for us, our emotional state is usually very different when performing than when practicing, which means that we will be lacking important state-dependent cues which can result in a memory lapse. For instance some people experience performance anxiety, nerves, excitement, stress, euphoria, or any of a number of other performance related changes in emotional state. In contrast we usually learn in safe, emotionally calm conditions, and in a relaxed non-demanding environment. During performance, many of the state-dependent cues that we are accustomed to during practice are no longer present, and can lead to poor recall. In developing approaches to memorisation we should therefore account for the emotional state during performance and attempt to mitigate any negative effects on recall. Where possible, we should also use learning environments that approximate performance conditions so that the emotional state during performance and practice might be more alike.

Other than state-dependent and context-dependent cues, other common memory aids can also be considered to be a cue. Unlike state- and context- dependent cues, we are often more aware of these cues and may even employ them deliberately as memory aids. Mnemonics, ‘cheat sheets’, dot points, cue cards and so on are all cue systems as they prompt or aid recall. There are many such devices which can, and should be employed in the memorisation of music. For instance, I always study the underlying harmony (i.e. the chord progressions) which I find makes it much easier to remember difficult passages. Rather than focusing on recalling complex fingerings, I simply need to memorise the progression which is often be sufficient to cue the correct fingering. Similarly, learning the structure of the piece makes it much easier to recall changes of key, mood, dynamics and phrasing etc.

Occasionally some students may find that they still need the music in front of them, but nonetheless play the music 95% from memory – only looking to the music at a few key points or for certain phrases. In this instance the music is acting as a set of ‘dot points’, where only a few bars are required to cue whole sections of music. In my experience this scenario can often be easily remedied by playing as much of the piece from memory as possible, and then noting any parts where the fluency falters. This helps to identify exactly what key phrases and important bars are acting as ‘dot points’. Once the student has found these key areas a little deliberate rote learning of those sections is usually enough to bring the entire piece together from memory. Using small sections of music to cue larger sections of music is a technique that I refer to as ‘sign posting’.

Another similar strategy which can help is what I call using a ‘trigger’. In complicated passages, or sections where my fingering can easily become muddled up causing a lapse in recall, I use trigger fingers to ensure that I adhere to the correct fingering. A ‘trigger’ may be something as simple as remembering to play a particular note with a particular finger or using an up stroke on a particular chord. Triggers are usually one or two notes, which, if played incorrectly, can quickly unravel the whole section. Playing these triggers correctly ‘sets me up’ in the correct hand position for the coming bars making recalling difficult sections easier.

Procedural Memory and Implicit Memory

Procedural memory is what many musicians term ‘muscle memory’ or ‘motor memory’ and refers to the brain’s ability to memorise processes. For musicians, procedural memory is typically the first way we learn to memorise music. By rehearsing music many times over, our brain gradually memorises the actions required to play the piece. Procedural memory is a form of implicit memory, meaning previous experiences aid in the performance of a task without conscious awareness of those experiences, or being consciously aware of the steps in the task being performed. Skills such as driving, tying shoe laces, and playing an instrument are typically remembered with procedural memory – we perform these skills automatically and without conscious thought. However, once again, an over reliance on a single mode of memory can make a person more prone to memory lapses. Engaging the declarative memory system an make recall significantly more reliable.

Declarative Memory and Explicit Memory

Where procedural memory is used for skills, declarative memory is the area concerned with memorising information, facts or events. Simply put, procedural memory is concerned with the how whereas declarative memory is concerned with the what.

Declarative memory is usually sub-categorised as episodic memory (memory of ones own life events, and of little use for memorising music), and semantic memory which concerns factual information – such as studying the harmony, structure, compositional devices etc. Declarative memory also differs from procedural memory in that it is an explicit form of memory – that is, it involves conscious recollection of information (i.e. its not automatic like procedural memory).

In the context of learning music, engaging declarative memory involves analysing the music to have a more thorough understanding of the compositional devices including harmonic, rhythmic and melodic structures. Understanding the composition at a deeper level gives the information more meaning and significance. Meaning and significance are powerful cues to recall. For instance, recalling a random number is much harder than recalling a persons phone number; while a phone number is easier to recall if it belongs to a close friend rather than a random acquaintance. Similarly, a phone number that has sequential or repeated digits is usually more memorable because the phone number is no longer a collection of seemingly random numbers. Sequenced or repeated numbers are more meaningful and significant to us, and are therefore more memorable.

Till Next Time….

Now that we’ve covered the basics of exactly what memory is, the next post will cover how we can put this understanding to work and develop memorisation strategies. In developing these strategies the key points to remember are:

• Engaging the procedural memory process through rehearsal and practice
• Engaging the declarative memory process through compositional analysis
• Making strong use of contextual- and state- dependent cues to aid recall
• Accounting for any missing contextual- or state- dependent cues that may not be available during performance
• Developing other cues such as ‘trigger fingers’ or ‘signposts’
• Encoding the information accurately and thoroughly so as to allow dependable recall
• Encoding the cues accurately and thoroughly so as to develop dependable recall

Building Triads on Each Note of the Major Scale

Within the key of C major we have seven notes – C, D, E, F, G, A and B. We can take any one of these notes as a root note to build a chord on. For instance, building a triad on the note C gives us C, E, and G which is a Cmaj triad. Chords can be built from any note in the scale in the same way. Starting on the note E and including every second note from the scale would give us the notes E, G and B forming an Emin triad. Likewise, building a triad on the note G would give us a Gmaj chord with the notes G, B, and D.

We call the chord built on the first note of the scale the “Ⅰ” chord, the chord built on the second note of the scale the “Ⅱ” chord, and so on using Roman numerals to designate which degree of the scale the chord has been built upon. If the chord is a minor chord this can be indicated by using a lower case Roman numeral (eg ⅳ instead of Ⅳ) or can be indicated by adding a lowercase “m” after the Roman numeral (eg Ⅳm). In this post I use the more traditional convention of using lowercase Roman numerals for minor chords and uppercase Roman numerals for major chords.

The table below gives an example of all of the diatonic chords in the key of C major, each numbered with Roman numerals. The table also shows the corresponding mode beginning on each scale degree.

Building Sevenths and Extended Chords on Each Note of the Major Scale

Of course, we’re not restricted to building only triads (three note chords) on each scale degree. We can build four note chords (usually seventh chords), or ninth, eleventh and thirteenth chords if we so chose. Here is the same table again, but this time indicating the types of chords available using seventh chords. Note how the Roman numerals stay the same, however the number seven is added to indicate that it is representing a seventh chord. Also, for the B half-diminished seventh chord, a circle with a line through it (ø) is the standard symbol indicating half-diminished.

Chord/Scales

Back in part 6 of this series we learned about chord/scales. That post gave an introduction as to which mode suited which chord for the purposes of melodic construction, including improvisation. In that post I also provided a table showing which mode was appropriate for which chord. That table has been reproduced below for easy reference.

As we learned in part 6 and as you can see from the table above, Phrygian, Aeolian and Dorian all suit a min7 chord, however only the Dorian mode is ideally suited to min7 chords as both the Phrygian and Aeolian modes have avoid notes when used over min7 chords. However in this post, rather than looking simply at which scales suit which chords, we will investigate which scales suit which chord progressions. By looking at chords in a musical context (i.e. a progression), we actually find many circumstances where a Phrygian or Aeolian mode may be more suitable than the ordinary Dorian mode for minor seventh chords. Similarly, whilst the Lydian mode is considered to be the most consonant mode over major type chords, we will see that Ionian may often be a better choice in many situations.

The Ⅳ-Ⅴ-Ⅰ Progression

The Ⅳ-Ⅴ-Ⅰ progression is a hallmark of Western music. In the key of C a Ⅳ-Ⅴ-Ⅰ progression is Fmaj-Gmaj-Cmaj and using seventh chords the progression would be Fmaj7-G7-Cmaj7. As we know from part 6 of this series, the default mode for the major seventh type chord is the Lydian mode since, unlike the Ionian mode, Lydian has no avoid notes. Therefore, for Fmaj7 we would use the F Lydian mode.

For the G7 chord we can use the Mixolydian mode, although it is important to remember that the natural fourth (the note C) in the G Mixolydian mode is an avoid note. As we know we can raise avoid notes by a semitone to make them more consonant. Raising the avoid note of the Mixolydian mode gives us the Lydian Dominant scale which was introduced in the previous post.

For the final chord, Cmaj7, the Lydian mode seems like a logical choice due to its lack of avoid notes, however most players would probably choose the Ionian mode instead, despite the presence of an avoid note. Why is that? Well, this progression is in C major (we know this because the Ⅰ chord is a C major chord). C Lydian, while certainly a possible choice, is actually derived from the G major scale, which is a completly different key centre. Using the F# from a C Lydian may sound like a ‘wrong note’ or it may suggest to listeners that you are modulating to the key of G major. Of course, experienced players may deliberately choose C Lydian as the #4 could prove more interesting. Typically speaking though C Ionian is the safer choice as it belongs to the the key.

Similarly, regarding the G7 chord, G Mixolydian belongs to the key (G Mixolydian is derived from C major), and may therefore be a better choice than G Lydian Dominant which is derived from an entirely different tonality. G7 is therefore the safer choice, however the #4 in Lydian Dominant may also be suitable for more colour, depending on the situation and player.

The ⅱ-Ⅴ-Ⅰ Progression

Like the Ⅳ-Ⅴ-Ⅰ progression, the ⅱ-Ⅴ-Ⅰ progression is one of the most common chord progressions in Western music. In the key of C major a ⅱ-Ⅴ-Ⅰ progression is Dmin-G-C, or, using seventh chords, Dmin7-G7-Cmaj7. The final two chords in this progression are G7 and Cmaj7, which is the same as the last two chords in the Ⅳ-Ⅴ-Ⅰ. Our mode choices are therefore the same, with G7 suiting either a G Mixolydian or G Lydian Dominant, and Cmaj7 fitting well with C Ionian or C Lydian. Once again G Mixolydian and C Ionian are safer choices in terms of adherence to the prevailing key, while G Lydian Dominant and C Lydian, are suitable if you are after a fresher/hipper sound, or prefer their lack of avoid notes.

For the ⅱ chord, Dmin, the obvious choice is the D Dorian mode. Dorian is the default choice for minor seventh type chords as it has no avoid notes. Also, because the D Dorian mode is derived from the C major scale, it belongs to the prevailing key.

The Ⅰ-ⅵ-Ⅳ-Ⅴ-Ⅰ Progression

The Ⅰ-ⅵ-Ⅳ-Ⅴ-Ⅰ is another hugely popular progression. In the key of C major this would be rendered as Cmaj-Amin-Fmaj-G7-Cmaj. As the first chord is a Ⅰ chord, we will be sticking with the mode built of the tonic – C Ionian. Also, the final three chords in this progression is the same as our Ⅳ-Ⅴ-Ⅰ progression above, so for those chords we will be using F Lydian, G Mixolydian and C Major respectively.

For the ⅵ, Amin, it would make sense to use either A Dorian, A Aeolian or A Phrygian as these are the main modes used for minor type chords. Since Dorian has no avoid notes, it would appear to be the obvious choice, however A Dorian is derived from the G major scale and will therefore contain an F#. F# is not a note that belongs in the key of C Major so it is very possible that choosing A Dorian may sound “off key”. A more reliable choice would be the A Aeolian mode as this mode is derived from the C Major scale and will therefore agree with the prevailing key which is C Major. Or course once again, choosing to use the A Dorian mode, with its non-diatonic F# is not necessarily “wrong”, just be aware that you may need to exercise more caution when using it.

Choosing Modes Based on the Prevailing Key

At this point it should be obvious that the main way to achieve a mode which complements and agrees with the progression is to choose a mode derived from the prevailing key. In effect, this means choosing the first mode of the key (Ionian) for the Ⅰ chord, the second mode of the key (Dorian) for the ⅱ chord, the fourth mode (Lydian) for the Ⅳ chord, the fifth mode (Mixolydian) for Ⅴ, and the sixth mode (Aeolian) for ⅵ. Accordingly the Phrygian mode would ideally suit the ⅲ chord, and Locrian will work well for the ⅶ.

Recognising Chord Progressions

Unless you are a session player, you’ll rarely encounter chord progressions written out as numbers or Roman numerals like I have done in this post. Usually chord charts are only written with their actual names, such as Cmaj, G6/9 etc. This means that, in order to use the information presented above, you’ll need to develop your familiarity with chord progressions and learn to recognise certain progressions when they appear. For instance Fmin-Bb7-Ebmaj immediately screams ⅱ-Ⅴ-Ⅰ in the key of Eb major.

The only way to really develop this automatic recognition is to analyse LOTS of charts until it becomes automatic. Of course, its important that you also have a good grounding in chord progression theory before you try this, so if you feel like your knowledge of progressions is lacking, then you’d better enter a few search terms in a search engine!

Minor Key Chord Progressions

So far we’ve only really touched on modes as they relate to chord progressions in major keys. Progressions in minor keys are slightly more complicated so for now it may be wise to limit your study of chord charts to songs in major keys. Minor key songs can become very complicated very quickly, so we’ll look at those specifically in the next post.

Like the major scale, we can form modes from the Melodic Minor scale, by changing which note is regarded as the root. For instance, by taking the notes of C Melodic Minor but starting on F we will have the F Lydian Dominant scale: F, G, A, B, C, D, Eb, F.

The First Mode of the Melodic Minor Scale

The first mode of the Melodic Minor scale is the Melodic Minor scale. Unlike the major scale which has the modal name Ionian, there is no alternative modal name for the Melodic Minor scale.

As we know, the formula for Melodic Minor is 1, 2, b3, 4, 5, 6, 7 so a C Melodic Minor scale would contain the notes C, D, Eb, F, G, A, B, C. If we take a fretboard diagram and mark a dot at each of these notes everywhere on the fretboard, we arrive at a fretboard map that looks like the diagram below (if you need help finding the notes on the fretboard, you may find my ‘Finding the Notes’ series helpful).

To make this giant fretboard map more digestable and user-friendly we can divide it up into five CAGED shapes.

The Dorian Flat 2 Scale

The mode starting on the second degree of the Melodic Minor scale is the Dorian b2 scale. Taking C Melodic Minor as our parent scale, but starting on the second note, we get the D Dorian b2 scale.

Of course, since D Dorian b2 and C Melodic Minor contain the same notes, but with different roots, the fretboard maps are identical but with the root notes in different places.

To understand why this scale is called Dorian b2, its useful to compare the D Dorian, and D Dorian b2 scales side-by-side.

As you can see, the two scales are identical except the Dorian b2 has its second notes lowered – hence the name Dorian b2. As we know from part 2 of this series, the Dorian scale formula is 1, 2, b3, 4, 5, 6, b7. This means that the scale formula for Dorian b2 will be 1, b2, b3, 4, 5, 6, b7.

Lydian Augmented

The third mode of the Melodic Minor scale is the Lydian Augmented scale, and is formed by taking the notes of the Melodic Minor scale, but defining the third note as the root. If we use the C Melodic Minor scale as the parent scale, the related Lydian Augmented scale will be Eb Lydian Augmented.

As with D Dorian b2, Eb Lydian Augmented shares the same fingering patterns as C Melodic Minor however it is important to remember that the position of the roots will be different.

Comparing the Eb Lydian Augmented scale with the regular Eb Lydian, shows us what is meant by the term Lydian Augmented.

As you can see the only difference between these two scales is that Lydian Augmented has its fifth note raised by a semitone, from Bb to B. The term Augmented is borrowed from the Augmented chord, where the word is used to denote chords which have had their fifth note raised. Where the regular Lydian scale formula is 1, 2, 3, #4, 5, 6, 7, the Lydian Augmented scale formula must have a #5 and is therefore 1, 2, 3, #4, #5, 6, 7.

Lydian Dominant

Taking the fourth note of the Melodic Minor scale as the root gives us the Lydian Dominant scale. Taking the C Melodic Minor scale, but begining on the fourth note we arrive at the F Lydian Dominant scale.

Once again, because C Melodic Minor and F Lydian Dominant are relatives of each other (that is they share the same notes), this also means that the fingering patterns will be the same. Of course, the important difference is that the position of the roots are not the same.

The table below shows the regular F Lydian scale, compared with the F Lydian Dominant scale. As you can see the only difference between these two scales is that the Lydian Dominant scale has its seventh note flattened by a semitone. The term Dominant has been borrowed from chord terminology, where the term is used to denote chords with a major third and a minor seventh, which is the case with the Lydian Dominant scale.

The scale formula for the regular Lydian mode is 1, 2, 3, #4, 5, 6, 7. Adding a b7 gives us the Lydian Dominant formula 1, 2, 3, #4, 5, 6, b7.

Mixolydian Flat 6

The fifth mode of the Melodic Minor scale is Mixolydian b6, also known as the Hindu scale. Using the notes of C Melodic Minor but regarding the fifth note, G, as the tonal centre we have the G Mixolydian b6 scale.

As with the previous examples the fingering patterns for the G Mixolydian b6 scale and the C Melodic Minor scale are the same, however the position of the roots are different.

The name Mixolydian b6 implies that it is the same as a regular Mixolydian scale but with the sixth note lowered. This can be confirmed by comparing Mixolydian b6 and regular Mixolydian with each other. Accordingly we can find the Mixolydian b6 scale formula by begining with the formula for the regular Mixolydian mode (1, 2, 3, 4, 5, 6, b7) and then lowering the sixth, which gives us 1, 2, 3, 4, 5, b6, b7.

Half-diminished Scale

The Half-diminished scale is the sixth mode of the Melodic Minor. Taking C Melodic Minor as the parent scale but starting on the sixth note, gives us the A Half-Diminished scale. As always, since C Melodic Minor and A Half-diminished share the same notes, they will also share the same fingering patterns, just make sure that you are aware of which note is considered to be the root.

A half-diminished chord is a chord with a b5 and a b7. The notes in an A Half-diminished chord are A, B, C, D, Eb, F, G. The interval between the root and the fifth is a diminished fifth (i.e. b5) and the interval between the root and the seventh is a minor seventh (i.e. b7). The half-diminished scale gets its name from the fact that, like the half-diminished chord, its characteristic notes are the b5 and b7.

While the term Half-diminished is my prefered term for this scale, other standard terms include Locrian #2 or Aeolian b5. Comparing this scale with a regular Locrian scale reveals that it is the same but with the second note sharpened (i.e. #2).

Comparing this same scale with the Aeolian mode reveals why it may also be called the Aeolian b5 scale. The table shows that the Aeolian b5 is the same as the regular Aeolian scale but with the fifth flattened.

The scale formula is for the Half-diminished scale is the same as the formula for the Aeolian scale but with the fifth note flattened. Therefore, where the Aeolian scale formula is 1, 2, b3, 4, 5, b6, b7, the Half-diminished scale formula will be 1, 2, b3, 4, b5, b6, b7.

Superlocrian

Superlocrian is the seventh and last mode of the Melodic Minor scale. If we take C Melodic Minor to be the parent scale and take the seventh note as the root, we will have the B Superlocrian scale. As with every example in this artcle, the fingering maps are the same, however the key difference is that the roots are not the same.

Comparing Superlocrian with the regular Locrian scale shows the Superlocrian to be the same as a Locrian scale but with a ‘flattened fourth’.

Where as the formula for Locrian is 1, b2, b3, 4 b5, b6, b7, the formula for Superlocrian must be 1, b2, b3, b4, b5, b6, b7. In reality the Superlocrian scale is rarely considered viable – since the ear will always hear/interpret a flat fourth as its enharmonic equivalent, a major third. However, enharmonically re-spelling the notes of the formula as 1, b2, #2, 3, b5, #5, b7, gives us what is known as the Altered scale.

While this means that the Altered scale and Superlocrian will both contain the same pitches, conceptualising the scale in this way makes it far easier to understand how the scale is applied. This is a source of great confusion for some students so I will investigate the Altered scale and its uses thoroghly in a later installment of this series.

Summary

This table shows each of the Melodic Minor scales and their respective formulae covered in this post. I have also included some common alternate names used for the modes, and written out the Tone-Semitone formula of each mode for those who are interested.

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.

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.