Chord Formulary

It's been a busy week and I haven't managed to scrape up any material for a real post, but I didn't want to break my goal of a post a week, so here's a list of various chord formulas from the basic to the obscure.  Enjoy!

          THE CHORD FORMULARY
NAME              |FORMULA           |NOTES
------------------+------------------+-----{
     ~basic~      |                  |
major             | 1-3-5            |
minor             | 1-b3-5           |
major 7th         | 1-3-5-7          |
dominant 7th      | 1-3-5-b7         |
minor 7th         | 1-b3-5-b7        |
------------------+------------------+
    ~advanced~    |                  |
diminished        | 1-b3-b5          |
augmented         | 1-3-#5           |
------------------+------------------+
     ~no 3rd~     |                  |
suspended 2nd     | 1-2-5            |
suspended 4th     | 1-4-5            |
5th (power chord) | 1-5              |
------------------+------------------+
     ~added~      |                  |
add6              | 1-3-5-6          | The 5th can be dropped
add9              | 1-3-5-9          | (ie: 1-3-6; 1-3-9)
------------------+------------------+
   ~quandaries~   |                  |
minor 6th         | 1-b3-5-6         |
diminished 7th    | 1-b3-b5-bb7      | One whole step down
augmented 7th     | 1-3-#5-b7        |
minor/major 7     | 1-b3-5-7         |
------------------+------------------+
  ~extended 7th~  |                  |
nine              | 1-3-5-b7-9       |
eleven            | 1-3-5-b7-9-11    |
thirteen          | 1-3-5-b7-9-11-13 |
major nine        | 1-3-5-7-9        |
major eleven      | 1-3-5-7-9-11     |
major thirteen    | 1-3-5-7-9-11-13  |
------------------+------------------+
~first inversion~ |                  |
major             | 3-5-1            |
minor             | b3-5-1           |
dominant 7th      | 3-5-b7-1         |
------------------+------------------+
 ~2nd inversion~  |                  |
major             | 5-1-3            |
minor             | 5-1-b3           |
dominant 7th      | 5-b7-1-3         |
------------------+------------------+
 ~3rd inversion~  |                  |
dominant 7th      | b7-1-3-5         |
------------------+------------------+

That's it for now, I'll try and add more as they come up, but that's a fairly complementary list to start!

Long days and pleasant nights!

Creating Chords in Alternate Tunings

I see a ton of posts on various guitar forums about chord shapes and charts for this tuning or that tuning.  And inevitably the most prolific responses are: figure them out yourself.  Truth be told, there really aren't a lot of resources out there for alternate tunings, especially the more obscure ones, and the best way to learn the chords is to, well, figure them out yourself.  But that may be easier said than done without the right tools in your box.

In my last post, I explained how chords are constructed and how that plays into open tunings.  Now I'll talk about how I come up with chords for those tunings.  Some people are blessed with pitch perfect ears, and I curse you if you are one of them because I am not!  So if you're like me and can't just fiddle with the guitar and find a C#m7 chord or whatever, then this is for you.

I'll use a tuning I saw on a forum earlier this week for the examples here, since I've never seen it tuned precisely this way and I get a little tired of writing and rewriting chords I already know.  The tuning is Dsus2:

D A D E A E

Notice it's close to Open D (DADF#AD), but the 3rd (F#) is dropped in lieu of the 2nd (E).  You could just leave it there and still have Dsus2 as DADEAD, but for this particular example the high D is also tuned up to E.  The original post said it was used in a song by Boyce Avenue, so we'll stay true to that.  It's also interesting because, as I mentioned in a previous post, generally tunings that make a chord have 1st and 5th with only one string tuned to the "accent" note.

When I first sit down to come up with some chords for a tuning, I usually write out the first 5 frets of the guitar with the appropriate notes, as follows:

   1fr       3fr       5fr
E|| F  | F# | G  | G# | A  |
A|| A# | B  | C  | C# | D  |
E|| F  | F# | G  | G# | A  |
D|| D# | E  | F  | F# | G  |
A|| A# | B  | C  | C# | D  |
D|| D# | E  | F  | F# | G  |

So now you have a visual representation of where all the notes lie across the fretboard in Dsus2 tuning (I'm a visual person, so this works well for me).  Next, I come up with the chords I want to work out.  Major and minor are obvious choices, and dominant 7th as well as minor 7th are also common.  I use a lot of suspended chords in my music as well, so I usually work those out and some oddballs like add6 and add9, maybe some diminished and augmented as well, but for this example we'll stick with major and minor.

If you need a refresher on what notes in the scale make up each chord, check my previous post on chord theory.  Since the alphabet is arbitrary anyway, let's start with A major.  The notes that make up the A major triad are A, C# and E.  Now just look at your fretboard layout and find the best way to play those three notes.

   1fr       3fr       5fr
E|| F  | F# | G  | G# | A  |
A|| A# | B  | C  | C# | D  |
E|| F  | F# | G  | G# | A  |
D|| D# | E  | F  | F# | G  |
A|| A# | B  | C  | C# | D  |
D|| D# | E  | F  | F# | G  |

Or in a more aesthetically pleasing form:

You'll notice there are quite a few E notes in there, as there happen to be a lot of open E notes in this tuning, so you could even drop the first string and mute the third string if you wanted.

Now let's make an A minor.  We know that a minor chord has the same formula as a major chord except the 3rd is minor, or dropped half a step.  So you can reexamine the fretboard if you want, or just realize that you can drop the C# to a C and get this:

Also feasible to play.  You'll notice I dropped the high E like I'd suggested before.  No reason, just all those Es have a droning effect, which may be what you're looking for, so do what sounds right to you!  With that, I should also mention it's a good idea to have your guitar close at hand and appropriately tuned since what looks good on paper might not sound so good to the ear!  And might be a stretch when it comes to actually fingering it.

Next let's move on to D to make some points about open tunings and multiple voicings.  Since this is Dsus2 tuning, then playing all the strings open gives you, surprise surprise, a Dsus2 chord.  Now think about that a minute.  With one or two frets, almost anywhere on the fretboard, you can achieve really any variation of the D chord.  The second fret on the first and third string would give you a D major; moving that down to the first fret gives you a Dm.  Up to the third fret and it becomes a Dsus4.

All you're really doing is moving that middle note around and leaving the 1st and 5th as is.  So say you want something really crazy, something that you're maybe transcribing from a piano to a guitar, like Dm7add13.  Unsightly on paper, unplayable in standard, but let's break it down.  The formula for a minor 7 chord is:

1 - b3 - 5 - b7

Then the added 13:

1 - b3 - 5 - b7 - 13

In D, those notes would be:

1 - b3 - 5 - b7 - 13
D   F    A   C    B 

So taking a look at the fretboard layout (and adding a few frets) we could come up with:

   Dm7add13
E|-7-------|
A|-8-------|
E|-7-------|
D|-0-------|
A|-0-------|
D|-0-------|

You could split hairs here and say the F played on the 8th fret is too high and makes it not technically correct, but this example suffices to make the point. 

One final note here: going back to D major.  You could play it as mentioned before, but you'll notice a few other ways you could play it:

E|-2--------------2--|-------------------||
A|-0--------------0--|------0------------||
E|-2----2---------2--|-5----2---------14-||
D|-0----0----4----0--|-4----4----7----12-||
A|-0----0----0-------|-5----5----9----12-||
D|-0----0----0-------|-----------0----12-||

As you can see, these are all D major chords, but just like standard tuning they can be played in different positions.  The take-home message here, however, is that the first measure chords are all in first position, so there in more than one way to play the right chord!

So have at it!  Use what you learned from the last post and apply it to whatever tuning floats your boat.  If you want some practice, work out some chords in Dsus2 tuning and I'll post at least a partial list below.  

Dsus2 Chord Chart

As promised, here is my chord chart for the most common chords in Dsus2 tuning.  I went for variety here, choosing different shapes in place of repetitious movable chords, especially with the sus2 chords, though as I said before, there are multiple ways to be right!  

 The chords at the bottom can be moved anywhere on the fretboard, the two "power chord" fifths, then a couple ways to play octaves (which can give a really full sound to riffs).  I also included moveable shapes for suspended 2nd and 4th, because as I was working out the shapes I realized that the 2nd is the 5th of the 5th, and the root is the 4th of the 5th...  all that means is that playing all the strings at a given fret makes a sus2, playing all of them but the 6th string makes a sus4.

   Gsus2  Dsus4
E|-5------5----|
A|-5------5----|
E|-5------5----|
D|-5------5----|
A|-5------5----|
D|-5-----------|

Long days and pleasant nights!

Chord Theory

The Major Scale

Before talking too much about alternate tunings, we need to talk a little about theory, and how the major scale applies to chord structure.  I'm sure this is a bit of review and you can blow through the major scale up and down the neck in every key and position easy as kicking puppies, but it's not the scale so much that's important here, but the intervals. 
 

Interval: the distance between notes in a scale, usually referred to in steps and half-steps or tones and semitones.

 
A note on terminology here: A whole step is the same as a tone, meaning the distance between C and D on the musical scale is one tone, or one whole step.  The distance between C and C# would be one semitone, or one half step.  It's important you understand this now, or else as we start to build chord structures you're going to find yourself lost in the woods with no pants. 

The intervals of the major scale are as follows, in steps and semitones, respectively:

W - W - H - W - W - W - H

2 - 2 - 1 - 2 - 2 - 2 - 1

To avoid confusion between semitones and notes within a scale, from here on I will only refer to scales in steps.

The major scale is unbearably easy to remember, as long as you bear in mind that E and B have no sharps (I will also, for simplicity's sake, use sharp(#) notes rater than flat(b) notes, unless convention dictates otherwise, but know that C# is the same as Db), and that the C major scale has no sharped notes.

C - D - E - F - G - A - B

If you write out an entire chromatic scale starting on C and then apply the major scale steps as noted above, you'll see what I mean.

C - C# - D - D# - E - F - F# - G - G# - A - A# - B - C

'---W----'---W----'-H-'---W----'---W----'---W----'-H-'
|        |        |   |        |        |        |   |

C        D        E   F        G        A        B   C

 

Now here's where it gets a little tricky.  Lets move up to D.  We now apply to major scale intervals in the same manner, but start on D.

D - D# - E - F - F# - G - G# - A - A# - B - C - C# - D
'---W----'---W---'--H-'---W----'---W----'---W---'--H-'

|        |       |    |        |        |       |    |

D        E       F#   G        A        B       C#   D

 

So as you can see, in the D major scale we now have a couple of sharps: F# and C#, though the intervals remained the same.  If you're not comfortable with this concept, try writing out major scales in various keys.  I'll include a list of major scales in each key so you can check your work.

Building Chords

Now that we've gotten through all that garbage, we can start to look at the theory behind chord structure.  As everyone knows, different chords can be altered to have a different feel to them, such as major, minor, and all those pesky numbered chords.  Forgive me if I'm beating a dead horse or undermining anyone, but I'm just trying to be sure everyone reading this is on the same page.  What you may or may not know -- I didn't for a long time -- is that there is a predictable formula for each type of chord, regardless of the root note. 

Here is a list of the most common chord formulas (though as you'll soon realize there are so many possibilities it would be nigh impossible to list them all).  I considered explaining the formulas first, but I thought that presenting the list first might be more beneficial so you have some point of reference. 

Name          Formula
Major         1-3-5
Minor         1-b3-5
Dom. 7th      1-3-5-b7
Maj. 7th      1-3-5-7
Min. 7th      1-b3-5-b7
Sus2          1-2-5
Sus4          1-4-5
add6          1-3-5-6
Dim(°)        1-b3-b5
Aug(+)        1-3-#5
add9          1-3-5-9

Triad: The minimal chord requirements; three notes.

A lot of chord theory out there uses the obvious easy example of C when explaining chord formulas, but that always confounded me more (probably because I wasn't grasping the major scale as explained above) because there were no sharp or flat notes.  So for my examples I'll use D, or maybe switch it up some just for a sampler platter approach.

I'm sure you've heard people refer to a "major triad" before when discussing chord voicings.  That just refers to the major chord, and the fact that a major chord is made up of three notes.

**A little aside here: another pitfall of my musical naivety was not understanding how a major chord on the guitar can be a major triad when you almost never play only three string chords.  You might say the E major chord couldn't be a triad since you strum all 6 strings to play it (I'm using standard tuning here just for clarity's sake).  But let's dissect that:

e|-0------| >> E
B|-0------| >> B
G|-1------| >> G#
D|-2------| >> E
A|-2------| >> B
E|-0------| >> E

As you can see from the column on the right, though you're playing six notes, they are all repeats of the same three notes, which make up the E major triad.

So what do the three numbers in the formula for a major triad mean?  Well, taking our D major scale we can apply numbers to each of the notes:

D - E - F# - G - A - B - C#

1   2   3    4   5   6   7

(see now why I opted against using the semitone notation?)

Now take your major triad formula, 1-3-5, and plug in the notes labeled 1, 3, and 5 from our breakdown of the D major scale.  We get D, F#, and A.  Those three notes make a D major chord, no matter how many times you repeat them.  Digressing to a standard tuning example again, you can dissect the D major chord and see that it's true:

e|-2------| >> F#
B|-3------| >> D
G|-2------| >> A
D|-0------| >> D
A|--------|
E|--------|

So there you have it.  Not so difficult, right?  As long as you have a grasp on the major scale concepts, this should be a slice of pie.  Now to add another layer of whipped cream...

Let's look at the minor chord formula (another triad): 1-b3-5.  That flat(b) symbol on the three is usually spoken as "minor 3rd" when talking about chord formulas, but it means the same thing as flat 3rd.  Here's where things get a little tricky, and another reason I don't use C as an example.  Understand that a minor 3rd does not have to be a flat note, it only means that it is down one half step from the given 3rd note. 

Flat(b): a note one half step (or one semitone) lower than the stated note, not always a flat note.

Looking again at our D major scale, we can extrapolate our 1st, 3rd, and 5th notes again: D-F#-A.  But don't forget that a minor triad always has a minor 3rd, so simply move the 3rd down one half step from F# to F.  So a D minor chord has the notes D, F, and A.  Feel free to check this on your own if you want, I'm not going to provide any more standard tuning examples as it makes me feel like a sell out!

You should now have enough ammunition in your chord theory arsenal to work out the notes that build up other more complex chord, like the minor 7th or added 6th.  Another point worth noting is that some chord formulas have a sharped note rather than a flatted, such as the 5th in an augmented chord.  Keep in mind that just like a flat, a sharp doesn't exclusively mean a sharped note, only a note that is a half step higher than the given note.

Sharp(#): A note one half step higher than the stated note, not always a sharp note.

Also take a look at the last formula listed above, the add9.  I usually write out the scales with seven notes, but remember that the final half step bring you back to the root note, only one octave higher.  So the 9th in a D scale would be E, the same note as the 2nd but one octave higher.

Major scales

As promised, a list of notes for each major scale.  The first note listed, obviously, is the root note.

C  - D  - E  - F  - G  - A  - B
C# - D# - F  - F# - G# - A# - C
D  - E  - F# - G  - A  - B  - C#
D# - F  - G  - G# - A# - C  - D
E  - F# - G# - A  - B  - C# - D#
F  - G  - A  - A# - C  - D  - E
F# - G# - A# - B  - C# - D# - F
G  - A  - B  - C  - D  - E  - F#
G# - A# - C  - C# - D# - F  - G
A  - B  - C# - D  - E  - F# - G#
A# - C  - D  - D# - F  - G  - A
B  - C# - D# - E  - F# - G# - A#

Open Tunings

Without further ado, let's talk about some alternate tunings!  As a convention, a tuning is considered "open" when all the strings are tuned to a major chord.  Meaning when all the strings are strummed without fretting anywhere on the neck, you are playing a major chord.

Open Tuning: When the guitar is tuned in a fashion so that playing all the strings open produces a major chord.

Note I said a major chord.  It may seem dumb, but the rules (dispatched in the times of yore by the almighty guitar gods, I suppose) say that only a major chord may be produced to be called open.  That's not to say you can't tune your guitar to, say, a minor chord and still produce that chord when strumming open, you just can't call it an open tuning.  But really, who cares, right?

So now that you've suffered through all my chord theory geeking, you can understand the basis of open tunings that much better.  Let's take Open D as an example.  You would tune your guitar (from low to high) as follows:

D A D F# A D

Look somewhat familiar?  That's because they are the notes that make up the D major triad!  You may be asking, why tune them in that order?  As long as all three notes are present it's still a D, right?  That is right, but take a look at which notes are most prevalent:

D A D F# A D
1 5 1 3  5 1

A lot of 1sts and 5ths, right?  That's because (as you may have already noticed) it's the 3rd that tends to give the chord its feeling.  The root and 5th more or less stays the same.  So you could tune to a D major chord and throw in some more 3rds, but that would just make your chord shapes that much more difficult to finger.  As you'll see, there are really 3 main ways to make an open tuning, depending somewhat on what root note you're using, but I'll get to that later!

Sticking with Open D (one of my favorites and one of the more commonly used open tunings), if you play all the strings open you get a D major, so say you fret all the strings on the second fret.  Now you have an E major.  Just think of your barre chords but with only one finger, movable up and down the neck.  That's why open tunings are so popular with slide players.

Another thing about open tunings that I think is really cool is that you can change an entire chord often with moving one finger.  For example, we know that a suspended fourth (sus4) is a major triad with an added fourth and no third (hence "suspended;" it's neither major nor minor).  So in D:

1 - 4 - 5
D   G   A

So looking at our Open D tuning, it would only take a simple change to go from D major to Dsus4:

D |-0------|-0------|
A |-0------|-0------|
F#|-0------|-1------| >> F# changes to G
D |-0------|-0------|
A |-0------|-0------|
D |-0------|-0------|

By playing the first fret of the 3rd string you've now eliminated the third and made it a fourth.  Another reason for the order in which the strings get tuned.  You could really play through almost all the common chords in D without having to use more than one or two fingers; something that would not lend well to standard tuning.

    D    Dsus4  D5   Dadd6  D7   DMaj7  Dadd9
D |-0----0----|-0----0----|-0----0----|-2----
A |-0----0----|-0----2----|-3----4----|-0----
F#|-0----1----|-3----0----|-0----0----|-0----
D |-0----0----|-0----0----|-0----0----|-0----
A |-0----0----|-0----0----|-0----0----|-0----
D |-0----0----|-0----0----|-0----0----|-0----

I suppose the practical uses of this are arguable, but it can give you a fuller sound, especially if you're playing solo acoustic, and the above example are just basics.  Duncan Sheik uses a single chord shape moved down the neck, completely changing the chord root and voicing in his song Little Hands:

   Dm7      Ddim7    Gm/D
D|-0------|-0------|-0------|
A|-3------|-2------|-1------|
F|-4------|-3------|-2------|
D|-0------|-0------|-0------|
A|--------|--------|--------|
D|-0------|-0------|-0------|
  *Preformed in D minor tuning, note the minor 3rd...

But I digress.  Like I said before, there are 3 main ways to tune to open, and it often depends on the root note you're tuning to.  For example, tuning from low to high 1-5-1-3-5-1 works fine with D, but say you wanted to tune to Open A.  You'd end up with A-E-A-C#-E-A and probably a couple broken strings trying to get there!

So here are the three tuning formulas and the keys they are usually used in:

Formula       Root notes
1-5-1-3-5-1   D, E, F
5-1-5-1-3-5   G, A
1-5-1-5-1-3   B, C

The real take-home message here is that if you know your chords in Open D, then you also know them in Open E and Open F, they're just a step and half step higher, respectively!

A couple more points I'd like to make without rambling too much.  Notice that for the second formula the lowest string is the fifth, not the root.  You can still achieve your open chord by strumming all the strings (it would be in the second inversion, I believe, but that's a bit beyond the scope of this discussion), but the droning bass 5th can sometimes sound "messy," so it is common practice I think to play the five strings without the bass note.  That doesn't mean to disregard the 6th string all together, though.  The root note is actually the 4th in the key of the fifth... try to think that through when you've been drinking...  how about an example instead: Open A.

E-A-E-A-C#-E
5-1-5-1-3 -5

Playing the bottom five strings gets you an A, but take note that if you are looking at forming some E chords, you can get some cool ones from including that low E:

E-A-E-A-C#-E
1-4-1-4-6 -1 >> in the key of E the A is the 4th and the C# is the 6th

*this isn't a very practical way to work out chords, but suffices as an example

So by playing the top three strings, you'd get an Esus4(no5).  I throw in a second fret on the 3rd string to add the 5th (B) and make a really cool sounding movable sus4 chord shape!  You can also second fret both A strings and play all six strings to get an Eadd6.

    Esus4    Eadd6    Dsus4
E |--------|-0------|--------|
C#|--------|-0------|--------|
A |-2------|-2------|-12-----|
E |-0------|-0------|-10-----|
A |-0------|-2------|-10-----|
E |-0------|-0------|-10-----|
                      ^I threw this one in to show that it can be moved

And my final point before I try and park this thing is that there are no hard-fast engraved-in-stone gospel rules for alternate tunings.  Do whatever you think will sound cool and bam! you'll have something that sounds like nothing anyone else has!  It's not uncommon to tune Open D using the formula for Open C (D-A-D-A-D-F#) to play some cool octave riffs or to capo Open D on the fifth fret to get an Open G without having that 5th bass note.  Some bands (Sonic Youth and Soundgarden come to mind) have even tuned all the strings to the same note just an octave apart!  Experiment!

D.s. al Coda

I think I've covered all the basics here to get you started with some alternate tunings.  I have some chord charts I made up for Open D and Open A (and working on Open C) that I'll post before too long, but what really grounded me in music theory was coming up with the chord shapes on my own.  Next time I'll talk about some non-open alternate tunings and maybe go over some chords and scales (without all the theory!).  Until then, long days and pleasant nights!

Beyond standard...

After playing guitar for more than a decade, I found myself in a creative slump.  And then I found altered tunings.  I know, I know, a lot of people say they are a "creative dead end" unless you're playing slide guitar, but I beg to differ.  Soundgarden guitarist Kim Thayil put it best in his interview with Guitar World earlier this year when he said, "we liked the fact that what we were playing [in alternate tunings] didn't sound like what our friends and peers were playing." (1/2/2013).  That being said, my new found aversion to standard EADGBe tuning came about when I realized that, 1.) I had done all I could do in standard (not meaning to say I'm a guitar virtuoso -- actually far from it -- but that I was playing the same old chords and scales I had for the last ten years), and 2.) that a lot of my favorite songs actually turned out to be written in tunings other than standard.

My favorite album growing up (and still on my top five today) was Lemon Parade by Tonic.  And even then, some years before picking up an instrument of any kind, I knew that some of those songs had a sound to them that wasn't like the other slew of alt rock and heavy metal I was listening to.  Turns out, it was Dadd9 (DADF#Ae) tuning I was hearing.

Without rambling too much about my musical preferences and pulling apart every cool song out there, I'd like to present an introduction to tunings "beyond standard."  The other relevant thing about learning these alternate tunings was the lack of information out there.  A quick internet search for chords and scales in standard tuning will give you more information then you'd ever need, but that isn't true for other tunings, especially the more obscure ones.  So this also forced me to learn chord theory, and subsequently, music theory, just to come up with reliable chords.  I'd like to impart as much of that wisdom as I can here, and hopefully not provide too much misinformation.

So without further ado, here is a short list of some of my favorite tunings and some examples of songs written in them.

Name        Tuning            Examples
Open D      D A D F# A D      Nothing as it Seems by Pearl Jam
                              London by 3rd Eye Blind
                              The Cave by Mumford and Sons
                              (capo II)
                              Almost anything from Bob Dylan's
                              Blood on the Tracks album

Open A      E A E A C# E      Seven Nation Army by The White 
                              Stripes
                              As Flat as the Earth by Chris
                              Whitley

Dadd9       D A D F# A E      Casual Affair, Soldier's Daughter, 
                              Mr. Golden Deal, all by Tonic

Dm          D A D F A D       Little Hands by Duncan Sheik

Open F      F C F A C F       Seasons by Chris Cornell

Obviously not a comprehensive list of tunings, but a few I've been favoring lately.   You can probably extrapolate some of my favorite bands from there too. Hopefully before too long I'll be able to put up a list of tunings along with the theory behind them and the relations to each other, since that was what helps me learn. I'm also working on transcribing some fairly accurate tabs of some of the above songs and more, so check back soon!

Until then, long days and pleasant nights!