Chasmac is a semi-retired guitar teacher who has taught in various schools in London and elsewhere for over 30 years.
Learn the Formula Behind Chords
Although many musicians who play chordal instruments have a good knowledge of chord construction, many more rely purely on memory (or notation) to play them. While it's great to have a decent repertoire of memorised chords, understanding how chords are formed and named extends your chord knowledge considerably.
A knowledge of chord construction gives you the ability to play chords that you've never previously learned just by seeing the chord's name and understanding what the name actually means. It also allows you to modify chords based on 'sound' musical knowledge rather than guesswork.
For those who want to improvise over chord progressions, it's an advantage to know which notes belong to the chord being played and which don't. That way, they can target those essential chord tones accurately, and treat non-chord tones accordingly.
How Chords are Named
Chords are named in two main parts. The first part is simply the name of the note that the chord is based on (also known as the chord's ROOT). The second part refers to the type (or quality) of the chord. It contains words or numbers or both and describes how the other notes of the chords are chosen to go with the root.
For example, in the chord, C major 7th, the first part of the name (i.e., the root) is C and the second part (the type of chord) is major 7th. Similarly In the chord, F# minor 7th, the root is the note F# (F sharp) and the second part, minor 7th, is the type of chord. In the chord Bb major, the root is the note Bb (B flat) and the chord type or quality is major. As you probably know, when a chord is major, we usually drop the word major and just call it by its root name, (Bb in this case).
Finding the root note is easy enough as it's always given, but in order to know which notes are specified by the second part of the name, we have to do two things:
- Refer to the notes of the major scale that corresponds with the root. So for any chord with C as the root, we need to know the scale of C major.
- Next, we have to know the formula for that type of chord. That tells us which notes to select (or modify) from the scale.
Note* Referring to the major scale as a way to find the chord tones is purely a convenience. The chord tones don't actually come from the major scale or any scale; it's just a handy and familiar yardstick for applying the chord formulas. Any 'diatonic' scale would work just as well, but all the formulas would be different. The major scale is by far the best known of all the diatonic scales; that's why it's the only one used for this purpose.
The next part of this lesson lists the formula for each of the most common chord types. When you know the formula for any basic chord, it becomes easy to work out the notes of the more obscure chords as the clue is in the name.
Chord Formula List
Here is a list of chord types, each with its formula and example based on the root note C. It's not a complete list - that would be impossible, and it would also defeat the purpose of the lesson, which is to give you an understanding of how chords are formed, and how the name reflects the structure. More in-depth info for specific chords is given below the list. Hopefully, if you come across a chord type not mentioned below, you'll be able to make an educated attempt at finding the notes.
C major scale (2 octaves) > C D E F G A B C D E F G A B C
Chord Construction and Chord Formula List
|Chord type||Formula||Example in C||Notes|
1 3 5
C E G
Named after the major 3rd interval between root and 3
1 b3 5
C Eb G
Named after the minor 3rd interval between root and b3
1 3 5 b7
C E G Bb
Also called DOMINANT 7th
1 3 5 7
C E G B
Named after the major 7th interval between root and 7th major scale note
1 b3 5 b7
C Eb G Bb
1 3 5 6
C E G A
Major chord with 6th major scale note added
1 b3 5 6
C Eb G A
Minor chord with 6th major scale note added
1 b3 b5
C Eb Gb
1 b3 b5 bb7
C Eb Gb Bbb
Half diminished 7th
1 b3 b5 b7
C Eb Gb Bb
Also called minor 7thb5
1 3 #5
C E G#
1 3 #5 b7
C E G# Bb
1 3 5 b7 9
C E G Bb D
1 3 5 b7 #9
C E G Bb D#
The 'Hendrix' chord
1 3 5 7 9
C E G B D
1 3 5 9
C E G D
Chords extended beyond the octave are called 'added' when the 7th is not present.
1 b3 5 b7 9
C Eb G Bb D
Minor add 9th
1 b3 5 9
C Eb G D
1 (3) 5 b7 9 11
C E G Bb D F
The 3rd is often omitted to avoid a clash with the 11th
1 b3 5 b7 9 11
C Eb G Bb D F
1 3 5 b7 #11
C E G Bb D F#
often used in preference to 11th chords to avoid the dissonant clash between 11 and 3
Major 7th #11
1 3 5 7 9 #11
C E G B D F#
1 3 5 b7 9 (11) 13
C E G Bb D (F) A
The 11th is often omitted to avoid a clash with the 3rd.
1 3 5 7 9 (11) 13
C E G B D (F) A
The 11th is often omitted to avoid a clash with the 3rd.
1 b3 5 b7 9 11 13
C Eb G B D F A
Suspended 4th (sus, sus4)
1 4 5
C F G
Suspended 2nd (sus2)
1 2 5
C D G
Sometimes considered as an inverted sus4 (GCD)
5th (power chord)
Chord Formula Focus
Let's take a closer look at the formulas for major, minor, major 7th, 7th and minor 7th chords.
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The formula for major chords is 1 3 5. That means if we want to know how to make the chord of C major, we would take the 1st, 3rd & 5th notes of the C major scale. Similarly, if we wanted to build the chord of G major, we would use the 1st, 3rd & 5th notes of the G major scale.
Let's take a closer look at both the scale and chord of C major.
The scale of C major consists of the notes: C D E F G A B C
So applying our 'major chord' formula (1, 3 & 5) to that scale, we get the notes C, E & G.
Play them all at the same time (or even one after the other) and we have the chord of C major. We can duplicate any of the notes to make the chord fuller sounding. For example, we can have C E G E G C, or any other arrangement that our instrument allows.
We can play the notes in any order, but usually we want the lowest pitched note (the bass note) to be the root. If the root is the lowest note, we say the chord is in ROOT POSITION. If any other note is the lowest sounding note, we say the chord is inverted. Chords in root position tend to sound more stable and balanced than when they are inverted. Inverted chords have a more subtle, less definite harmonic effect. Both types (root and inverted) have their place in music.
It also depends on whether another instrument is playing a bass note that is lower than the bass note of the chord. For example, if a guitarist plays the chord C major with E as the lowest note, the chord is said to be in first inversion. However, if at the same time a bass guitarist is playing the root note (lower than the E played by the guitarist), the chord will again sound stable because the overall sound of the chord (bass plus guitar) to any listener will be in root position.
The formula for minor chords is 1 b3 (flat 3) 5. It's similar to the major chord except that the middle note has been lowered. In other words the distance (or interval) between the root and the 3rd is smaller than in the major chord. That interval is called a minor 3rd and that's why the chord is called MINOR.
To get that b3rd note in order to make the chord of C minor we take the 3rd note of the C major scale and lower it (keeping the same letter name). So instead of C E & G, that the major chord formula gave us, we get C Eb (E flat) & G.
Major 7th Chords
The formula for major 7th chords is 1 3 5 7. In other words, it's a major chord with the 7th note of the scale added. So the chord of C major 7th consists of the notes: C E G & B. Note that the word major in this type of chord isn't referring to the fact that this is a major type chord but is referring to the chord's 7th being a major 7th interval above the root This distinguishes it from the 7th chord below, which uses a flat 7th - the 7th note being a minor 7th above the root.
The formula for 7th chords (also called dominant 7ths) is 1 3 5 b7.
Applying this formula to the C major scale, gives us the chord C7, consisting of notes C E G & Bb.
Note* Be careful using the term 'dominant 7th' as it has another, more official, meaning, which is 'the 7th chord built on the 5th (dominant) note of major or minor scales'. It's actually referring to a chord function, but in modern times the term has been hijacked to name any chord with the formula 1-3-5-b7 regardless of key or scale.
Minor 7th Chords
The formula for minor 7th chords is 1 b3 5 b7. So C minor 7th consists of the notes C Eb G & Bb. It's a minor chord with a flat 7th added.
You may have noticed that the chords we've dealt with so far have used alternate notes of the major scale. That is, we took the first note, missed the second, took the third, missed the 4th, took the 5th, and so on, all the way up to the 7th. We can describe this by saying that most chords are built in thirds. In other words, the spacing (or interval) between each note and the next covers three letter names.
Here's the C major scale again with the chord C major 7th outlined in bold.
C D E F G A B C
C to E is the interval of a 3rd because it encompasses three letters: C, D & E. Similarly, E to G is a 3rd too, because it spans 3 letters: E, F & G, and G to B is also a 3rd as it spans 3 letters G, A & B. They're not all the same size of 3rds; E to G is a minor 3rd as it's one semitone smaller than the other two, which are major 3rds, but, regardless of size, they're all 3rds because they all span 3 letters.
We can extend the notes even further than the 7th by continuing to add more notes spaced by intervals of a 3rd, but we need to extend the scale beyond an octave to see this. Here is the C major scale written out over two octaves. The notes in bold are all spaced a 3rd apart and the final note is D which is the 9th note of the scale. This gives us the chord C MAJOR 9th with formula 1 3 5 7 9. As mentioned previously in the 'major 7th' example, the word major here is referring to the 7th being a major 7th interval above the root. and not being lowered to a flat 7th.
C D E F G A B C D E F G A B C
As you can see, the 9th note (D) is the same as the 2nd, but we prefer to call it a 9th to show that it has been arrived at by stacking notes spaced by intervals of a 3rd. The same applies to the other notes. The actual pitch (register) of the notes doesn't matter; they could be at opposite ends of a piano. Further extended chords can be formed by continuing this process, giving us 11th and 13th chords. That's as far as we can go. If we add another 3rd to the 13th scale note, we arrive back at C, two octaves above our starting note. So you won't see any number higher than 13 in reference to chords.
It's worth mentioning here that it's possible, and often desirable, to omit certain notes from chords. For example, 13th chords have 7 notes, (with formula 1 3 5 b7 9 11 13). We often omit the 11th because it can clash discordantly with the 3rd. We can also omit the 5th as it doesn't add much to the chord's overall sound. In fact, to convey the essential sound of a 13th chord, all we really need are the notes: 3, b7 & 13. Even the root can be implied just with that 3-note combination.
Augmented and Diminished Chords
So far, all the chords have used note 5 straight from the major scale, but there are two other important chord types that modify note 5, by raising it or lowering it.
If we take a major chord (1 3 5) and raise the 5 to #5, we get an augmented chord. As C major consists of C, E & G, then C augmented consists of C E & G#
We can sometimes see other chords that contain that #5 note. For example, C major 7 #5. As we saw earlier, C major 7th consists of C E G & B, so C major7#5 consists of C E G# & B
Augmented chords have the symbol +, e.g., C+ means C augmented
If we take a minor chord (1 b3 5) and we lower the 5 to b5, we get a diminished chord. So, as C minor consists of C Eb G, the chord, C diminished consists of C, Eb & Gb.
As with augmented chords, diminished chords can be extended too. There are two important ones, namely: Diminished 7th and half diminished 7th.
The diminished 7th chord has a strange sounding structure because it consists of notes: 1 b3 b5, like the simple diminished chord, but it also includes a 7th note which has been lowered twice!! We call that note a double flatted 7th (bb7). So, the formula for this chord is 1 b3 b5 bb7. The chord, C diminished 7th consists of C Eb Gb and... wait for it... Bbb. Bbb sounds the same as A of course, but to be correct within our chord naming system, it has to be called Bbb to show that it's a kind of 7th chord.
The half diminished 7th chord is similar to the (fully) diminished 7th, except that the 7th is lowered just once instead of twice. Its formula is 1 b3 b5 b7, and C half diminished 7th consists of the notes: C Eb Gb & Bb. This chord is also called minor 7thb5 because, as you can see, it's similar to a minor 7th chord but with a b5 instead of 5.
Diminished chords have the symbol ° e.g., C°7 means C diminished 7th.
Half diminished chords have the symbol Ø7 (or sometimes just Ø by itself) e.g., CØ7 means C half diminished 7th.
If you can see the logic (such as it is) in the chord naming system, then you can more easily work out any chord construction problems you come across. Memorise the formulas for the important and well-used chords, and you'll find it easy to construct the more obscure ones because they're all just extensions or modifications of the important ones. The clue is almost always in the name.
Questions & Answers
Question: Where is add2? I guess I can play Cadd2 in the key of C. Can you help me?
Answer: Add 2 chords are just another name for add 9 chords because the 2nd note of a scale is the same as the 9th note. C add2 / C add 9 = C E G & D
Question: Isn't the "7th #11" and "7th b5" the same chord? Or are the 7th#11 and 7th b5 different because the 5 is still present in a 7th #11 chord? If you then omit the 5 in a "7th #11" is it called a "7th b5"?
Answer: It's the context of the music that determines the most appropriate name of the chord. Compare C7b5 (C E Gb Bb) with C7#11 with a missing 5th (C E (G) Bb F#). In the first case, C-Gb is a tritone interval. If it resolves in the music in the standard way by going to Db-F) then the Gb really is a Gb (falling to F) and not an F#, and the chord is best called a 7b5. If in a 7#11 that same note has a rising, leading note quality rising to G in the next chord, then it really is an F#, not a Gb. If the music proceeds to the next chord in a non-standard way, or nonfunctional way then choosing the most logical name requires other factors to be taken into the account such as the key of the music and the neighboring chords, etc.
Question: Can a pianist play 7th chords with both hands on a piano keyboard?
Casey on July 24, 2020:
"Note* Referring to the major scale as a way to find the chord tones is purely a convenience. The chord tones don't actually come from the major scale or any scale; it's just a handy and familiar yardstick for applying the chord formulas. Any 'diatonic' scale would work just as well, but all the formulas would be different. The major scale is by far the best known of all the diatonic scales; that's why it's the only one used for this purpose."
Dude this is EXACTLY what I came here to figure out. Thank you so much for writing this part, it makes so much sense now. I was sitting here wondering if there were like, minor chord formulas or something.
Chas Mac (author) from UK on June 27, 2020:
The fingers you use depends on the instrument - piano, harp, guitar, ukulele, etc.
Constant on June 14, 2020:
How to place the fingers by just seeing the formulas,not with the diagram?
Chas Mac (author) from UK on November 21, 2019:
Slash chords are normal chords built on top of a bass note, usually as part of a melodic bass run. Am/G is A minor(A-C-E) with the non-chord tone G in the bass. Am7/G is Am7 (A-C-E-G) built on top of the chord tone G. If the G has no melodic function then it's just Am7 in 3rd inversion (G-A-C-E).
Chas Mac (author) from UK on November 21, 2019:
Yes - it's an add 9 (1359) or minor add 9 if the 3rd is a flat 3rd (1-b3-5-9) The order of notes doesn't change anything so it doesn't matter where the 3rd is - it will cancel any sus effect.
Dave.. on November 20, 2019:
How are slash chords constructed? and how are they used, thanks..
Zack on September 10, 2019:
What if you have a suspended 2 chord but have the third above the octave is it still an add chord?