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Chord construction simplified

Jerry

In a hurry?  Check the pre-requisites.  Start at the section ‘Chord construction.  The “Choose-skip” method’ .  Otherwise …

It takes time to build up a decent chord vocabulary, but it doesn’t take long to learn about the interval make up of different chord types, and hence make sense of the chord voicings you will encounter or discover. A beginner can easily understand this, although (s)he may not have the technique to play certain chords.    This post looks at a few chord construction methods based on selection of scale pitches, and the chord types created. By the end of this post you should understand the methods used to build chords in a few different ways, such as “stacking thirds” to create triads all the way up to thirteenths, or “stacking fourths” to build jazz voicings.  We’ll investigate these visually, no music notation involved.

All beginners learn a few chord shapes, such as G and Am, with no further explanation.  Each shape is a group of unknown notes, swimming in a sea of unknown notes on the fretboard between the nut and the third fret.  Beyond the third fret can only be dreamed of in the distant future.  There is no understanding that the A chord shape has had one modification to create the Am chord shape.  All the chords learned are perceived as unrelated other than they appear in songs.  Focused learning of any sort relies on building a mental framework of related concepts.  The above provides no framework.

With interval-based learning, the initial framework is present once intervals are understood.  Chords can then be perceived as a group of pitches layed out relative to the pitch of the chord root, determined by the intervals required for a chord typeThe chord roots themselves are perceived as being located at various intervals from the scale tonic.  Note names are not required to understand the chord’s construction. This is a very powerful framework to continue the study of music theory from, and more importantly, for creating tunes and for improvising over chord progressions.

Music theory is inherently independent of any instrument, giving guidance on note choice and rhythm.  In formal theory (schools, books) this guidance is usually expressed using examples of music notation. How these map to a given instrument is the musician’s problem to solve.

While reading music notation is required in formal theory, emuso.buzz further speeds up the learning process with a visual representation of the intervals involved is music constructs, such as a scale or chord. Our visual representation (a clock face) can be mastered in a few minutes.  The mapping from this representation to piano, or one string of a guitar, is trivial.

 

Pre-requisites

We’ve already discussed intervals, semitones, octaves in a previous post, including how an instrument can produce several octaves of pitches, with twelve pitches per octave, and how in any octave, these pitches are all a semitone apart in frequency, and music theory gives names to these frequencies.

Remember, the combination of tonic pitch (which is arbitrary) and required intervals (scale formula)  determines the scale pitches in one octave.  You can then use various octaves of these pitches, located on the guitar (using box shapes, CAGED system etc).

Contents

The major and harmonic minor scales are used as examples, but the exact same principle you learn today applies to any scale type, including modes.

A chord voicing is created by taking a chord formula, and applying this to the pitch chosen for the chord root.  This will result in pitches within two octaves at most above the root.  These pitches can then be rearranged and duplicated or moved to other octaves, to create a chord voicing, including chord inversions (which is when the chord root is not the bass note of the chord).  The resulting chord shapes are what you see in chord books.  We’ll provide a few voicings.

(If you are reading this inside emuso/Studio, these voicings are interactive, and can be dropped in Rhythm-X to listen to some chord progressions)

 

 

Introduction

A chord is a combination of two or more intervals.  Different combinations create different chord types with different sound flavours, and different musical uses.  Even in one octave,  there are twelve semitones and  a large number of permutations of intervals  from three to twelve, each producing a different sound.

However, many permutations are rejected as having no musical value, and the most common chord types are created from the seven or eight pitches found in a particular scale type.  Even here, there are still several permutations that are unused, due to the chord construction method used to select which pitches are involved.  We’ll be looking at some of these.

Classical composers used 7-note scales, and they avoided too much tension in the chord sounds they used.  This reflected the musical tastes of the time. The chords mainly had three or four intervals, chosen by combining scale pitches that were three or four semitones apart from each other, and then spreading these out into other octaves.   However, modern classical composers, and jazz musicians, were looking to expand the sounds they use.  They extended the classical system to build more complex chords, from five to seven pitches (still combining scale pitches that were three or four semitones apart from each other).  But other chord construction methods were invented, for example combining scale pitches that are mainly five or six semitones apart, much loved in jazz.  Musical tastes change!

One interval in a chord normally stands out to the ear.  One of the two pitches in that interval, known as the chord rootdominates what the ear picks out. This is entirely determined by the make-up of the chord; what intervals are present in it.

Watch this shortish video (11m 25s) … you will see and hear how the chord root dominates the chord.  As the chord is moved around, the shape may change, because of the guitar tuning.  The pitches involved will all change, but the intervals will not.

 

Visualising intervals

When explaining intervals required for an overall sound (like a scale or chord), we are not describing a scale shape or a chord shape. Obviously, these intervals need to be created on an instrument, maybe in several octaves. That is the separate problem of implementing a theoretical concept on-instrument.

emuso.buzz represents an arbitrary block of twelve pitches on a clock face, using circles  located at the clock times zero (midnight) to eleven AM on the clock face.  These times represent pitches that make intervals of 0 to 11 semitones with an arbitrary pitch denoted by time zero.  The pitches involved in some music construct, such as a chord, are represented as solid coloured circles, while pitches that aren’t used are shown as empty white-rimmed circles.

For example, the following diagram shows a scale whose tonic pitch corresponds to the pitch shown at time 0 AM, whose scale members are located at intervals of 0 2 4 5 7 9 and 11 semitones from the tonic.  This is the set of scale intervals  for the major scale.  It also highlights a subset of these pitches,  found at 0, 4 and 7 semitones from the tonic.

The clock representation is unchanged regardless if we’re discussing C major (the major scale built off the tonic pitch C), or Eb major etc.   The highlighted intervals correspond to a major triad rooted at the scale tonic.  The pitches involved in that triad are always located at 0, 4 and 7 semitones above whatever that tonic is. (Implemented on guitar, various voicings can provide these pitches, in more than one octave, but this is irrelevant to the theory of chord constuction).  You will see below why these pitches were selected, where you will also be given some tips on what to look out for in any clock diagram, to rapidly determine a chord type.

Here are two examples of this scale on the piano below, with different tonics.  Notice where 0,4 and 7 in each case.

 

Representing intervals greater than 11 semitones

Suppose we want to visualise the interval of 12 semitones above the pitch at 0 am.  This is also represented by the same time position (0 AM). Think of this as visiting pitches clockwise from 0, through 1, 2, 3 AM and so on,  around to 11 am.  This denotes 11 semitones higher.  Continue clockwise by one more semitone, and we arrive at 0 AM again (a total of 12 semitones).

So any clock time can represent both some pitch and its octave (and notionally any octave of that pitch).

Similarly, 14 semitones above the pitch at 2 am is visualised at 4 am (clockwise from 2 am to 2 am is 12 semitones, followed by an additional 2 semitones on to 4 am).  You’ll see later that “ninth” chords involve this interval, so, when we come to construct the ninth chord, we know to include a pitch that is 14 semitones above the root (or in even higher octaves).

 

 

Chord construction.  The “Choose-skip” method

Chord construction, is based around selecting a scale member as the chord root, then choosing other members at various semitone distances from this root. There are several methods for selecting these distances. Since, there are seven intervals in a 7-note scale, there are seven possible chord roots.

The most commonly used method to craft a chord is :

The above selects three scale members, which we call a triad. This method can be extended to determine up to seven scale members, creating the seventh,nineth,eleventh and thirteenth chord types.

With all 7-note scales in the major/minor system (major, harmonic minor, natural minor, melodic minor), and their modes, the above always results in chord members that are separated by 3 or 4 semitones (minor third or major third).  Each chord comprises a “stack” of thirds.  The same is true for 8-note scales.  Next we’ll look at what chords are found in the major scale, then harmonic minor.

 

Major scale

The major scale is defined by the intervals 0 2 4 5 7 9 11 semitones amde with the arbitrary choice of tonic pitch.

Below, where we mention  “4 AM”, say, we mean  “the pitch 4 semitones above the tonic pitch, represented by the coloured circle at time 4 AM”.

The major triads

If we apply choose-skip to construct a chord with three pitches, starting at 0 AM, we skip 2AM, choose 4AM, skip 5AM, and choose 7AM.  We get an interval of four semitones (a major 3rd) from 0 AM (solid red circle) to 4 AM (yellow circle) and three semitones from 4AM to 7 AM and hence seven semitones (a perfect 5th) from 0 to 7 AM.

This set of intervals (1, major 3rd, perfect 5th) is called a major triad.  Using interval symbols instead of interval names, the major triad is defined by the intervals (1 3 5).

Now let’s use the same method to build the chord rooted at 5 AM.

Starting at 5 AM, we skip 7 AM, and choose 9 AM, skip 11 AM, and choose 0 AM.  From 5 AM to 9 AM is four semitones (major 3rd), and from 9 AM to 0 AM is three semitones (minor 3rd), and in total, we have an interval of seven semitones from 5 AM to 0 AM (going clockwise).

Choose-skip produces a chord with intervals (1, 3, 5) again, rooted at 5 AM.  We have found another major triad can be created from pitches of the major scale, rooted at the fourth scale member.

 

Starting at 7 AM, going clockwise, we choose 7 AM, skip 9 AM, choose 11 AM, skip 0 AM, and choose 2 AM.  This shows intervals of four semitones from 7 AM to 11 AM, and three semitones from 11 AM to 2 AM (in the next octave).  Once again, choose-skip produces a chord with intervals (1, 3, 5), the major triad, this time rooted at 7 AM.

We now know that we can construct three major triads in the major scale, rooted at 0 AM (the first scale member, the tonic), 5 AM (the fourth scale member, located five semitones above the tonic), and at 7 AM (the fifth scale member, located seven semitones above the pitch).

For example, we could choose an arbitrary fret on an arbitrary string, for example, the 3rd fret on the bass A string, which produces the pitch C3, and play the major triad rooted there (so we’re playing a C triad), and play another major triad rooted five frets higher, at fret 8 (so we have F triad) and rooted at fret 10 (7 semitones above the first chord so we have G triad).  These chords would all belong to the C major scale.

The minor triads

If we apply choose-skip, starting at 2 AM, we get a different chord type.  Let’s have a look.

We choose 2 AM, skip 4 AM, choose 5 AM, skip 7 AM, and choose 9 AM.  This time, we have a chord with an interval of three semitones (a minor 3rd) from the chord root at 2 AM to 5 AM), and an interval of four semitones(a major 3rd)  from 5 AM to 9 AM.

This combination of intervals, (1 b3 5), defines the minor triad.  The chord symbol is either “m” or “-“, as in Am or A-

Try applying choose-skip yourself, from 4 AM for one chord, and from 9 AM for another chord.  You will find these are also minor triads.

Finally, let us apply choose skip to 11 AM.  We get a different chord type.  We choose 11 AM, skip 0 AM, choose 2 AM, skip 4 AM, and choose 5 AM.  From 11 AM to 2 AM (clockwise) is an interval of three semitones (a minor 3rd).  From 2 AM to 5 AM  is another interval of three semitones.    From 11 AM to 5 AM is in interval of six semitones, known as the diminished 5th (b5).

This set of intervals (1 b3 b5) defines the diminished triad.  The chord symbol is either “dim” or “o”, as in Bo.

 

 

The major scale triads

We have just seen there are three major triads (intervals required: 1 3 5) rooted at the tonic, fourth and fifth scale members.  Putting this another way, the fourth and fifth scale members make intervals of a perfect 4th (5 semitones) and perfect 5th (7 semitones) with the tonic.

So, once we know the tonic pitch, we can use the interval shapes for a perfect 4th and perfect 5th to locate the roots of these major triads, along with the major triad rooted at the tonic.

We also know there are three minor triads (intervals required: 1 b3 5) rooted at the second, third, and sixth scale members.  These make intervals of a major 2nd (2 semitones), major 3rd (4 semitones) and major 6th (9 semitones) with the tonic.  We can use these interval shapes to locate the roots of these minor triads.

Finally, we know there is a diminished triad (intervals required: 1 b3 b5) rooted at the seventh scale member, which makes an interval of a major 7th (11 semitones) with the tonic.  Its root, an octave lower, is found one semitone lower than the tonic.

 

Visual tip:  two pitches making a major 3rd are separated by three circles, while two pitches making a minor 3rd are separated by two circles.  This means you can look at any potential chord root, and look clockwise to the next but one scale member, and visually determine whether this chord has a minor 3rd or a major 3rd.

 

Seventh chords

By using choose-skip to select four pitches from a scale, we get some kind of “seventh” chord, so-called because the chord contains an interval of a minor 7 (10 semitones) or major 7 (11 semitones) made with its root, as we’ll now see.

In this example, we start at the tonic, choose it, skip 2 AM, choose 4 AM, skip 5 AM, and choose 7 AM.  This has selected the major triad we saw above.  Now we continue, skip 9 AM, and choose 11 AM as our fourth pitch.  From the tonic to 11 AM is 11 semitones (a major seventh).

This collection of intervals (1 3 5 7) defines the major seven chord, whose chord symbol may be “maj7” or an upside down triangle, maybe followed by the digit 7.

If we choose 5 AM as the chord root, then we get 5 AM, 9 AM and 0 AM, the major triad, and continuing from 0 AM, we skip 2 AM, and choose 4 AM.  Moving clockwise from 5 AM around to 4 AM is an interval of 11 semitones (a major 7th again).  So, we can construct a major seventh chord rooted at 5 AM.

But if we start at 7 AM as the chord root, we get a different chord type. As before, we get the major triad pitches at 7 AM, 11, AM and 2 AM.  Continuing from there, we skip 4 AM and choose 5 AM.  Moving clockwise from the root at 7 AM, around to 5 AM, is an interval of 10 semitones (a minor 7th). 

This combination of a major triad plus a minor 7 (1 3 5 b7) defines the dominant seven chord.

Here’s a really useful visual tip for determing if a chord with  a major or minor seventh interval can be constructed from its root, using choose-skip.

Instead of moving clockwise around the clock, look counter-clockwise by one or two hours (e.g from 7 AM to 6 AM, or from 7 AM to 5 AM) to see if there is a scale member there.  If it is adjacent (e.g. at 6 AM),  the chord would contain a major seventh interval.  If it is one time further back (e.g. at 5 AM), the chord would contain a minor seventh interval.

Given this, look at 2 AM.  If we choose this as a root, the nearest scale member counter-clockwise is at 0 AM, which is two hours back.  From above, we know that there is a minor triad rooted at 2 AM.  With this visual tip, we now know we can build a minor triad with a minor seventh from the root as well.  (As a reminder, starting at 2 AM, we choose 2 AM, skip 4 AM, choose 5 AM, skip 7 AM, choose 9 AM (we now have our minor triad), skip 11 AM, and choose 0 AM.  From 2 AM clockwise to 0 AM is 10 semitones.  But using this viusal tip, we can just “see” there is an interval of 10 semitones present, if we choose four pitches)

The intervals (1 b3 5 b7) define the chord type known as minor 7.  Its symbol may be -7, m7 or min7.

Using this same visual trick, we can look at 4 AM as the chord root (we know this yields a minor triad), and see there will be minor seventh involved when we choose 4 pitches from there.  Ditto, when we look at 9 AM as the chord root.

That is, the major scale contains three minor seven chords, rooted at 2, 4 and 9 semitones above the scale tonic.

If we apply this trick to the chord root at 11 AM, its nearest counter-clockwise time is 9 AM, so this chord will include a minor 7th interval from its root, if we choose four pitches from that root.  This is another chord type, comprised of a diminished triad and the minor 7th interval.

The intervals (1 b3 b5 b7) define the minor 7 flat 5 chord, whose symbols may be -7b5, m7b5, min7b5, or a circle with a slash through it.

Ninth chords

We can continue in this same vein, using choose-skip to choose five scale members for the chord.  When the is done, the final interval added is either a major 9 (14 semitones) or minor 9 (13 semitones).  Of course, this interval is added to the seventh chord we saw above.  Hence the generic name “ninth chords”.

The visual tip here is to look clockwise from the root to the next scale member.  If this is one hour ahead, the chord will include an interval of a minor ninth (start at the root.  Go fully around the clock to end up at the root again (an ocatve higher).  Continue one more semitone.  If this is two hours ahead, the chord will include an interval of a major 9th.

Look for yourself at each possible chord root of the major scale shown below.  Which ones have chords that include a minor 9th?  These are the roots at times 3 AM and 11 AM.  All the rest have chords that include a major 9th.

This now gives us the following ninth chords:

For example, here is the minor 9 chord rooted at 2 AM.

We can continue like this, to choose six scale members (the “eleventh” chords), and finally all seven scale members (the “thirteenths .

So, the principle of chord construction like this is simple, just adding more and more intervals, producing more and more complex chord sounds.

Choose-double-skip

However, we can change the choose-skip method, to skip over two scale members each time, instead of one.  Now we get an entirely new set of chord types, where the chord members are separated by 5 or 6 semitones, having a very different set of sound flavours, adored by jazz players, in addition to the above.

 

Wrapping up

The main point is that these methods provides various  well-organised systems for creating chords from a scale, that sound good, and work well with melodies based on the scale members as well.

When chord progressions are created, we don’t always stick with just these chords.  For some additional energy, we may slightly change the expected chord type rooted at a scale member to something different.  We may even include chords rooted at non-scale members, for some additional ear-candy.

The above methods are not the only ways to construct chords.  There are several others, some of which create really tense sounding chords.  For example, starting at some chord root, select it and the next three scale members (no skips).  These are used in jazz, on piano, but they are impossible to play on guitar, as the finger stretch required is immense.

In reality, depending how we put chords together, what we choose as our “root” for the purposes of construction, may actually not be the root at all, sonically.  But using stacked thirds, in the vast majority of cases, the chosen “root” really is the sonic root.

Players keep discovering new ways to put chords together.  Here is one I just thought of, looking for ways of using pitches that are a semitone apart.  It is a very ambiguous sounding chord.  For me,this works well as a chord rooted off the tonic of jazz minor, though its no good as a resting chord.  That would need the minor triad at its tonic.

 

 

 

 

 

 

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