Chord Formulas

[mr. beaumont]

Inspired by the "Why?" thread--You can figure out the notes in ANY chord you see by applying simple formulas to the major scale of the ROOT of the chord in question.

This goes for major or minor chords...bear with me, it's actually easy. You just need to know your major scales.If you don't know them yet, find them, print them out, and keep them by where you practice.

Then you number each note...1 2 3 4 5 6 7

Here's some formulas...

major: 1 3 5
minor: 1 b3 5
major 7: 1 3 5 7
minor 7: 1 b3 5 b7
dominant 7 (often just called "7") 1 3 5 b7
m7b5 (half diminished) 1 b3 b5 b7
diminished 7: 1 b3 b5 bb7 (that's not a typo, double flatted seventh)

extended chords, like the 9th, 11th and 13th are dominant chords which means b7. The 9th is the same note as the 2, 11ths are 4ths, 13 is the same as a 6 (it's like the numbering just kept going if you repeated the scale)
when you have an extended chord, it's assumed that all the extensions below it are present too (or at least fair game)

so 9: 1 3 5 b7 9

11th: 1 3 5 b7 9 11

13th: 1 3 5 b7 9 11 13.

You'll notice the 13th chord has 7 notes. Not going to happen on guitar...therefore guitar players will often make sure they're playing the most important notes...a common 13th chord voicing is 1 b7 3 6(13)

you can have major 9, 11 and 13 chords as well. These have a 7, not a b7.

11th chords are a little strange...we can go into that more later, but something like a maj11 chord is going to sound better with a b5. Let's not get too weird yet though, I'm trying to prove this is easy

So...if this interests you at all, throw a chord out there, one that looks really complicated, and we'll work through how to apply the formulas...

[tomh]

Looking forward to this. I was good on basic major and minor, but am recently getting interested in 6, 13, dominant 7 and major 7. If I can get those in my head I will be good for a WHILE. I am all about 3 chords and the truth but looking for a little flavor sometimes.

Thanks for posting. Very timely for me.

[mr. beaumont]

6th chords, 1 3 5 6

m6, 1 b3 5 6

Great sounds...and the 6/9!

1 3 5 6 9

The Beatles chord I call it.

[martingitdave]

Great post and thread. I’m going to print it out as a reference!

[rick-slo]

More voice leading opporunities is a plus for including extended chords in arrangements.

[Chipotle]

Diminished 7th is fun, because if you look at it in terms of intervals, each note is the same distance apart--interval of a minor 3rd.

Because the 3 half-steps of each interval evenly divide the 12 steps of the scale, it is "symmetric", if you will. If you move the chord up (or down) by 3 frets/half-steps... it's the same chord! Same notes, just in a different order now.

Even more fun, because of that symmetry, you can call the same chord by four different names:

Cdim7: C-Eb-Gb-A
Ebdim7: Eb-Gb-A-C
Gbdim7: Gb-A-C-Eb
Adim7: A-C-Eb-Gb

Which name you choose depends on how it's being used in the song and the chords on either side of it.

[JonPR]

Originally Posted by mr. beaumont

Then you number each note...1 2 3 4 5 6 7

Here's some formulas...

major: 1 3 5
minor: 1 b3 5
major 7: 1 3 5 7
minor 7: 1 b3 5 b7
dominant 7 (often just called "7") 1 3 5 b7
m7b5 (half diminished) 1 b3 b5 b7
diminished 7: 1 b3 b5 bb7 (that's not a typo, double flatted seventh)

You forgot m(maj7) : 1 b3 5 7

I'll add the following:

In jazz theory, the basic chord is the 7th, and there are six of those (the 5 you mentioned, and m(maj7). They break down as three types of triad (maj, min, dim) each with two kinds of 7th added:
MAJ with either minor 7 or major 7th
MIN with either minor 7 or major 7th
DIM with either minor 7 or diminished 7th
(The aug triad is not considered a foundational triad in jazz.)

These six they have the following basic functions in major and minor keys:

• Maj7 = I or IV in major key; bIII or bVI in minor key
• (dom)7 = V in major and minor key
• m7 = ii, vi and iii in major key; iv in minor key
• m7b5 = ii in minor key; (technically vii in major key but hardly ever used that way)
• dim7 = vii in minor; commonly borrowed as vii in major key
• m(maj7) = i in minor key

Obviously there are exceptions and additions. Minor key tonics can sometimes be m7 chords. More often (especially in older jazz) tonic chords in major or minor keys can have 6ths added instead of 7ths.

And then, of course, there are all the jazz "altered dominants"
1. four permutations of altered 5ths (b5, #5) and altered 9ths (b9, #9), often just called "7alt" in charts, because players can choose the alterations they want.
2."7b9", common as V in minor key, whith is the dim7 with V root. (E.g., in key of A minor, G#dim7 (G# B D F) is the vii chord, and if you add an E root it's E7b9.)
3. "7#11, 9#11, 13#11" = or "lydian dominant" chords, which are dom7 type chords, not used as V chords. E.g., if you see "G7#11" it probably won't be going to C or Cm; more likely it will be going to F#m, F# major or A major.
4. "7#9". In jazz, if used as a V chord, is usually short for a "7alt". But it can be used as a blues tonic chord, which we know in rock as the "Hendrix" chord.

OK, that's enough JAZZ.....

[JonPR]

OK, here's my $0.02 on 9, 11 and 13 - which Jeff sensibly avoided...

(OK, I'm going in... if I'm not back in 24 hours, call a search party...)

9ths can generally be added to any chord type, if they are major 9ths (whole step above the root). If the 7th is omitted - as is very common in rock, folk and pop - they are called "add9".
This is an inconsistency in chord symbol shorthand. The original idea was that the most common chord types would get the shortest symbols (by assuming vatious default intervals); but that was at a time when full "9" chords were an extension on a 7th chord. Now, in rock music, it's a lot more common to add a 9th to a triad. So a "9" chord has more notes in it than an "add9" chord.

"A(add9)" = A C# E B; "Am(add9)" = A C E B.

The "9" doesn't have to go on top of the chord. It can go low in the chord. E.g., A B C# E is still "A(add9)" not "A(add2)". (Calling it "9" is another hangover from the 1 3 5 7 9 11 13 stacking principle).
IOW, as with all chord symbols (except slash chords), it only tells you the notes you need to include in the chord; not the order you have to arrange them. I.e., in theory "A(add9)" means "A C# E B"; but in practice you can stack those notes in any way you like - except with B on the bottom (because that makes it sound like a different chord.

In jazz, you sometimes get b9s on V7 chords - as mentioned in the last post. It's a strong dissonance (with the root), but dissonance is kind of the point with V7s, so it's OK.

"11" and "13". In theory, these just indicate the last note added to the complete stack, making 6-note or 7-note chords. But - as Jeff says - in practice they are almost never complete, for various reasons. Obviously with a 7-note chord there is the practical issue for 6-string guitarists! But even a pianist is highly unlikely to play every note of a "13" chord. (There is an exception, which I'll come to.)

11ths. The one kind of 11th chord that can be a complete stack is a "m11" chord. Am11 = A C E G B D. The 9 (B) is optional, but if you can get it in there it sounds fine. As many of you will know, the open strings of the guitar form an "Em11" chord, missing the 9th (E G B D A); you could add the 9th (F#) as 2nd fret on the 1st string. But as you see, EGBDA is 5 notes from Am11 too! (Technically A9sus4, but it shows how chord identities start to become blurred the more notes you add...)

Adding 11ths to major chords means (almost always) omitting the 3rd. So "A11" - technically A C# E G B D - is often used as shorthand for A9sus4 (A E G B D), because everyone knows (or should...) that "A11" will not include the C#. The interval C#-D is known in jazz as an "avoid note", because of the awkward (unhelpful or confusing) dissonance it makes. So you leave out one or the other.

On a maj7 chord, an 11 causes an additional issue. A C# E G# B D makes an E7 chord on top of an A major chord! A V chord and I at the same time! I.e., a harmonic mess.

13ths. With either "13" or "maj13", the 11th will be omitted (for the above reasons). The 9th is also optional. And in jazz, seeing as perfect 5ths are also often omitted, a "13" chord only needs 4 notes: root-3rd-7th-13th. An "A13" chord might only contain A C# G F#. Of course, the E helps confirm the root (if you can get it in there), while the B will help fill it out. But on guitar, x-0-5-6-7-x makes a perfectly good "A13".

Maj13" chords are rarer, but still possible. "Amaj13" = A C # E G# B F#. Try this: x-0-6-6-7-7 (add the open 6th if you want to include E).

13ths can be added to m7 chords, but it's very rarely done. E.g., in theory you can have a complete 7-note "Am13" chord: A C E G B D F#. (F#, notice, not F. Added 6ths and 13ths are always major.) But the problem - as with any chord using the whole scale! - it could be almost any other chord! But even if you left out the B and D, so it was more clearly Am7 with F# added, it sounds too close to the chord most likely to follow, which would be D7. IOW, when we use Am7-D7, one of the most important moves is from G on Am7 to F# on D7. If we add the F# to Am7, obviously it spoils that resolution. That doesn't mean that m13 chords sound bad in themselves; try x-0-5-5-7-7.

13sus4 chords are quite possible, and not uncommon. "A13sus4" = A D E G B F#. Think of it as "Em9/A" if you like, or "Gmaj7/A" if you miss the E (which is not essential). x-0-5-7-7-7, or x-0-2-0-3-2. (follow that with Dmaj9, x-x-0-2-2-0.) The 9th is also optional.

Getting back to 11ths, the "avoid note" issue can be "avoided" not only by omitting the 3rd, but by keeping and 3rd raising the 11th.
Here are some #11 chords:

Amaj7#11 = A C# E G# D#
Amaj9#11 = A C# E G# B D#
Amaj13#11 = A C# E G# B D# F#
A7#11 = A C# E G D#
A9#11 = A C# E G D# B
A13#11 = A C# E G D# B D#

So, there are two potential 7-note chords which work (in theory anyway)! Of course, as with other 13th chords, we can omit the optional 9th (B), and maybe the 5th. These shapes are a little tricky on guitar - and rarely useful anyway! but try these:

Amaj13#11 = x-0-6-8-7-9 (A G# D# F# C#)
Amaj13#11 = 5-4-4-4-4-4! (A C# F# B D# G#)

I've not been able to find a shape for A13#11, even omitting the B and E. The issue is that the G needs (ideally) to be below the F#, and you need both C# and D#. (There is probably a really stretchy one, but who needs it?)
9#11 shapes are not too hard, and occasionally useful, for those occasional serious jazz moments... x-1-0-1-1-0 (Bb9#11) to x-3-2-4-3-x (Cmaj9). I'm sure you can work out moveable options for the 9#11 shape if you want.

Questions welcome...

[tomh]

Stupid question time:

Take a first position C chord. Why does low E string sound bad, when E is part of the chord?

[mr. beaumont]

It's the interval between the low E and low C note on the fifth string. Play just those two notes together.

If you want the fancy answer it's that the major third interval (E above C) is inverted, C above E is a minor sixth, and that is a dissonant sound. There are times that interval can sound great...but it's too much for the bottom of a plain old C chord.

[mr. beaumont]

Jon, you got complicated on me!

But the next step is being able to understand what a chord symbol means...so your post is a fine segue.

So while you CAN certainly memorize a ton of chord formulas (if I did it, you can, trust me) but more important is to be able to break down any chord symbol and figure out what it's asking for and what will be possible on guitar.

Need some coffee first, be back in a bit.

[hubcapsc]

Originally Posted by mr. beaumont

Great sounds...and the 6/9!

1 3 5 6 9

The Beatles chord I call it.

I just stretched my brain to imagine how to make a D 6/9
near the nut without having a guitar in my hands. Then
I went over and played it hitting all the notes with a
fingerpicking pattern that took me several trys
to arrive at.

Its like sitting here drinking coffee reading the guitar forum
and getting a surprise pop quiz...

-Mike

[hubcapsc]

waitaminute...

1 3 5 6 9

9 = 2

Every edge of the pentatonic scale must be
a 6/9 chord...

In G that's just strumming the open strings. That sounds like
A Hard Day's Night ...

-Mike

[mr. beaumont]

Originally Posted by hubcapsc

I just stretched my brain to imagine how to make a D 6/9
near the nut without having a guitar in my hands. Then
I went over and played it hitting all the notes with a
fingerpicking pattern that took me several trys
to arrive at.

Its like sitting here drinking coffee reading the guitar forum
and getting a surprise pop quiz...

-Mike

Easy D 6/9 shape-- x54455 (those are fret #'s)

that gives you Root, 3rd, 6th, 9th, 5th on top

[JonPR]

Originally Posted by hubcapsc

waitaminute...

1 3 5 6 9

9 = 2

Every edge of the pentatonic scale must be
a 6/9 chord...

Yes, if the "1" sounds like the chord root - which it will if it's in the bass: G B D E A.

Originally Posted by hubcapsc

In G that's just strumming the open strings. That sounds like
A Hard Day's Night ...

-Mike

Not far off!
I.e., the Hard Day's Night chord is an m11 chord, the same 5 notes as a 6/9, but with a different root.
And part of the legend about the chord is George Martin's tantalising (but unhelpful) quote years later: "John hit a chord which I still, to this day, don't know exactly what the notes were - but it was almost the open strings."

However, it seems that wasn't the chord they used in the end: firstly because, if they'd stuck with that chord, Martin would certainly have worked out what the notes were, because he was planning to add piano later; and secondly because in the one available live film where you see John's chord, he's playing the same Fadd9 that George Harrison said was the chord he (George) played.

So, George (12-string) and John both played a full 6-string Fadd9 (1-0-3-2-1-3, thumb on 6th). Paul played a D in the bass. And George Martin beefed it up in the mid-low register with nobody seems sure what. Definitely another D (maybe 2), and probably an extra C or G somewhere. But it's essentially Dm11. (D F A C G, which would be F69 if F was the bass note.)

Randy Bachman thought he'd worked it out from the original tapes, but he missed the piano, and had George H playing a ridiculous 3-3-3-2-1-3 chord. So that would suggest George M (mixed to the same track as George H) played those low G-C notes; except in an analysis of the frequency spectrum, those pitches are completely absent! So if they are audible - and they are to a lot of people - they must be virtual pitches caused by some kind of difference tone effect.
After all, the common 6-string "cheat" chord for a single player is G7sus4: 3-5-3-5-3-3: including a low G that nobody seems to have played on the original, while missing at least two A notes that clearly were played.