To begin with, we will need the 12 Major Scales (to build these
refer to the Circle of Fifths lesson).
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Chords are most easily built using simple formaulas. Each chord has a specific formula. The formula ia applied to the major scale sharing the same root note as the chord that is to be built. For instance, if we wanted to build an E minor chord, we would apply the formula for the minor chord to the E major scale.
On the following page is a reasonably comprehensive list of chord formulas (there are literally thousands of chords, this is a selection of the more common ones).

Now, with the fairly extensive list of chord formulae you can work out the notes of around 500 chords.
Determining the notes of the chords is straight forward. Before we try a few examples I’ll explain the "extensions" (i.e. 9, 11, 13 etc.) and how to find them.
1 2 3 4 5 6 7 8
Root
Root
These are the first octave scale tone numbers, the scale tone numbers of the next octave are numbered as such:
8 9 10 11 12 13 14 15
Root
Root
So let’s have a look at the C Major scale over two octaves with it’s respective scale tone numbers:
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Now to try a few examples:
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The next thing we require is the formula for the chord type we want to determine, in this case, the formula for the minor chord:
1 b3 5
So the 1 is C, the b3 is Eb (3 is E then flatten it as directed by the b3), the 5 is G. Therefore, the notes of the C minor chord are: C Eb G
Simple!
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The formula for the minor seventh chord is:
1 b3 5 b7
The 1 is F#, b3 is A natural, 5 is C#, b7 is E natural, Therefore, the notes of the F#m7 chord are: F# A C# E
Another aspect of chord construction etc. is determining the name of a chord written in standard notation from the notes it contains. (Basically, the examples we’ve just covered but in reverse order).
The simplest chords to work out this way are those in root or first inversion. This means the notes of the chord are stacked from the root note up.
For instance:

This is a root or first inversion of a chord. Because we can clearly see the root note we can work out the name of the chord by comparing the notes of the chord with the major scale sharing the same root note as the chord.
The root note is G, so the major scale to work from is the G major scale:
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The notes of the chord are: G Bb D and F#. The G is 1, the Bbis b3, the D is 5, and the F# is 7. So the formula for this particular chord is: 1 b3 5 7.
Locate this formula on the chart of formulas.
Found it? It is the formula for the minor major seven chord. Therefore the chord is Gm(maj.7).
The difficulty of this principle arises when chords are written in different inversions to the one just examined. Here is the same chord written in 3 different inversions:

1st inversion 2nd inversion 3rd inversion
The notes are the same but the chord is stacked from a different note for each inversion. A fairly straight forward process, if the notes are stacked from the second note of the chord (in this case Bb), it’s a first inversion of the chord. If the notes are stacked from the third note (D), it’s a second inversion, and so on.
This makes it a little more difficult to determine the root note but not impossible. You need to be able to picture the inverted chord in a more regimented order (i.e. all notes on lines, all notes in spaces, or as close to this as you can reasonably get), then see if the root note becomes clearer. Whatever note you determine to be the root note will also be the major scale you use to work out the chord formula and, therefore, the chord name. If the formula you conclude seems too weird or bizarre, decide on another note within the chord to be the root note and go through the process again. Continue this until you have what you consider to be the most feasible formula.
The more of these types of chords you work out, the more chords you’ll see that share the same notes but different names. This is not at all uncommon.
Improving your ability to construct and/or name chords requires practice. The more chords you work with the more chords you’ll remember and recognise (the notes or the names) from sight. You’ll also be able to work out the most difficult of chords quickly. This is especially useful when transferring chords written for one instrument onto another (i.e. piano chords played on guitar - you have 8 fingers and two thumbs you can use on a piano, but only a maximum of 6 notes on a guitar, you must decide which notes to omit and how to invert them so you can play them comfortably on the guitar). This ability is also useful for, among other things, playing chords you’ve never played before quickly, to improvising over difficult passages of music using the notes of the chords instead of a scale.
Try every formula on the chart with a couple of different root notes. Try looking at some sheet music you haven’t learnt and work out the names of the chords written in standard notation. Here’s a few examples to try:

Answers:
Copyright, 1999
Shane Bailey