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copyright 2001, D. Glenn Arthur Jr.
Last updated 1995-04-27. |
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(This is a short introduction to chord formation I wrote for a friend. Caveat lector: most of what I know about chord theory I learned by "reverse-engineering" guitar chords, not from a music theory class or textbook.)
In this text I use capital letters to denote the names of keys and chords, and lowercase letters to indicate individual notes. Unfortunately this gets a little confusing in the case of "a", but I think it is possible to figure out when "a" is the indefinite article and when "a" refers to the note named "a".
It may be even more confusing where "b" is used in place of the "flat" sign. When more than one note is listed, the notes will be separated by punctuation or spaces (e.g. "a-c-e" or "g, b, d"), so if the letter "b" appears as the second letter of a pair (e.g. "eb", or, awkwardly, "bb") it indicates a flat sign rather than a b.
A "#" will represent a sharp sign, and if I need it, an "=" will represent a natural sign. Fortunately half-sharps and half-flats will not be needed in this text.
Arabic numerals, when not being used in an obviously conventional manner, will refer to notes of a scale, starting with "1" being the tonic (fundamental note) of the scale and "8" being the octave. Roman numerals will refer to chords based on the numbered note of a scale, as will be described below.
If I convert this to a format other than plain old ASCII, I may use underlining or boldface or italics to more clearly distinguish "a" from "a", "b" from "flat", and key names from chord names.
If you print the figures referenced from this document, use a mono-spaced font so that the "cursor art" musical staves line up correctly.
2. CHORD BASICS -- MAJOR CHORDS:
A major chord consists of a 'root' (the note on which the chord is based, usually also the lowest note of the chord), the note a 'major third' (four half-steps) higher than the root, and the note a 'minor third' (three half- steps) higher than the second note. This means the top note is a fifth higher than the root.
If we take a major scale, C for example, and look at the major chords in it, we have C-major (c-e-g), F-major (f-a-c), and G-major (g-b-d).
[Please click here to view
Figure 2.1]
Let's make a few observations about these chords...
The major chords have as their root notes the 1st, 4th, and 5th notes of
the scale. These are called the 'tonic', 'subdominant', and 'dominant'of
the scale, respectively.
For each of these chords, if we call the root '1' and count up the scale
we're using (C in this example) from there, the notes of the chord are
1-3-5.
For each of these chords, if we call the root '1' and count up from
there in the major scale that starts on that note
they're still all
1-3-5. For example, g, b, and d are the 1st, 3rd, and 5th notes of
the G-major scale.
So if you want to build a major chord in general, take the 1, 3, and 5
notes of the major scale that starts on the root of the chord. And if
you're already in the context of a particular key and don't want to
have to remember a different key signature to figure out a chord, start
at the root of the chord and go 1, 3, 5 in the key you're in (assuming
the chord in question is really in that key) starting from the root
of the chord.
For example:
If we're looking at a tune in G major (one sharp in the key signature)
and we see a D major chord named, we can start on D and go "1 = d,
skip 2 (e), 3 = f#, skip 4 (g), 5 = a", so the notes in a D major
chord are d, f#, and a.
OR we could say "A D major chord uses 1, 3, and 5 of a D major scale
(two sharps), so 1 = d, skip 2 (e), 3 = f#, skip 4 (g), 5 = a" and
we get the same answer, d, f#, and a.
This is enough information to figure out all twelve major chords and to
figure out what the major chords are in all twelve keys.
Sometimes major chords are indicated by Roman numerals, "I", "IV", and
"V". This lets us talk about the chords (or notate a chord progression)
without having to refer to oneparticular key. This is used most often
when talking about theory, but it does come up once in a while in
notation someone's actually going to read and play from. Some musicians
who have songs that they play in several different keys (to accomodate
different vocalists, for example) notate their chords this way. So they
might notate "Leavin' Liverpool" thus, if '/' represents a bar line:
[Or, with the words:
Playing this in the key of A, they'd strum
A minor chord consists of the root, the note a minor third (three half-
steps) above the root, and the note a major third (four half-steps)
above the second note. Again, the top note is a fifth above the root.
Let's look back at our major scale again and see how the minor chords fit
it. If we take a C-major as our key again, and look at the minor chords in
it, we have D-minor, E-minor, and A-minor. So let's make the same kinds of
observations about these as we did about the major chords -- there are plenty
of parallels.
The minor chords have as their root notes the 2nd, 3rd, and 6th notes of
the scale. Note that the 6th note of the major scale is the tonic of the
relative minor.
For each of these chords, if we call the root '1' and count up the scale
we're using (C in this example) from there, the notes of the chord are
1-3-5.
For each of these chords, if we call the root '1' and count up from
there in the minor scale that starts on that note
they're still all
1-3-5. For example, a, c, and e are the 1st, 3rd, and 5th notes of
the A-minor scale.
So if you want to build a minor chord in general, take the 1, 3, and 5
notes of the minor scale that starts on the root of the chord. And if
you're already in the context of a particular key and don't want to
have to remember a different key signature to figure out a chord, start
at the root of the chord and go 1, 3, 5 in the key you're in (assuming
the chord in question is really in that key) starting from the root
of the chord.
So here are some examples:
If we're looking at a tune in E-major (four sharps) and we see a C#-minor
chord named and want to figure out the notes in it, we can start on c#
and go "1 = c#, skip 2 (d#), 3 = e, skip 4 (f#), 5 = g#", so C#-minor
consists of c#, e, and g#.
If we want to build an E-minor chord, we can take the key of E-minor (one
sharp) and count "1 = e, skip 2 (f#), 3 = g, skip 4 (a), 5 = b", so an
E-minor chord consists of e, g, and b.
[Please click here to view
Figure 3.1]
When using the Roman numeral notation, minor chords can be named by
putting a lowercase 'm' after the Roman numeral, or by writing the
Roman numeral in lowercase (which I've seen more often). So the basic
major and minor chords of a major scale would be I, ii, iii, IV, V, and
vi. In the key of F-major, that'd be F-major, G-minor, A-minor,
Bb-major, C-major, and D-minor. D being the sixth tone of the F-major
scale, F's relative minor will be D.
If we're referring to a minor scale, we can still use the Roman
numerals, but the chord whose root is the tonic of the key will be
minor, so we'll have i, III, iv, v, VI, VII. In the key of A-minor,
those would translate to A-minor, C-major, D-minor, E-minor, F-major,
and G-major.
Writing out "-major" and "-minor" gets tedious, so we don't usually
bother. Instead, we just write the name of the root note of a major
chord and let it stand for the whole chord (e.g. "E" == "E-major").
To show a minor chord, we append a lowercase 'm' (e.g. "Em" == "E-minor).
More complex chords are abbreviated as well. We'll get to some of these
more interesting chords below, but in the meantime here are some chord
names we'll be using:
In the following, "X" stands for any root note
Note that some people use a lowercase letter to denote a minor chord,
e.g. "e" instead of Em. (It's certainly faster to write.) I will not
use that
notation in this text, so that I can use lowercase letters to represent
notes and uppercase letters to represent chords.
In the explanations of different types of chords and things you can
add to chords I'll be using these chord names regularly, along with
the Roman numeral notation some of the time.
Probably the most common deviation from a straight major or minor chord
is the dominant-seventh chord, also called a "major-minor seventh" chord.
Often, in a tune in a major key, instead
of using the I, IV, and V chords, we will use I, IV, and V7. (In fact,
most of the V chords in the "Leavin' Liverpool" example really should have
been V7 chords. I simplified it for the example.) In the key of C, we'd
likely use the chords C, F, and G7. In general, an arabic numeral after
a chord name means "add the Nth", e.g. C9 means to take a C major chord
and add the ninth tone of the C-major scale to it, so C9 would be composed
of c, e, g, c, and d, in that order (though on guitar the d might be added
an octave lower (the second) instead).
[Please click here to view
Figure 5.1]
Seventh chords, by default, are constructed slightly differently and
therefore deserve their own discussion. Because the most common use of
a seventh chord is on the dominant of the scale, the "seventh" we add
is not the seventh tone in the scale that starts on the root of the
chord, but rather the seventh tone up from the root
in the scale of which the root of the chord is the dominant.
So in our C major example, the
G7 chord is constructed thus: 1 = g, skip 2 (a), 3 = b, skip 4 (c),
5 = d, skip 6 (e), 7 = f natural because we're in the key of C. So G7
contains g, b, d, and f. Remember that we're not counting up in the key
of G (of which G is the tonic), but the key of C (of which G is the dominant)
instead.
[Please click here to view
Figure 5.2]
This "seventh chord as the dominant of a scale" is known as a "dominant
seventh" or "major-minor seventh", and the term "seventh chord", if not
modified somehow, almost always refers to this chord.
On those (less common) occasions when we really do mean to include the
seventh tone of the scale that starts on the root of the chord, we call
it a "major seventh" chord in order to distinguish it from the more common
dominant-seventh.
So to build GM7 (also written Gmaj7), we'd count up in the key of G, and
it would work thus: 1 = g, skip 2 (a), 3 = b, skip 4 (c), 5 = d, skip 6 (e),
7 = f# because f is sharped in the key of G.
[Please click here to view
Figure 5.3]
Note that the difference between Gmaj7 and G7 is that the "seventh" we add
in G7 is a half-step lower than it is in Gmaj7. If you want to figure out
what notes are in a dominant-seventh chord without having to figure out
what scale the root is the dominant of, you can build the major-seventh
chord and then flat the seventh and you'll get the same answer.
In general, a number (or even a group of numbers) following a chord name
(e.g. G11, Am6) indicates a note (or notes) to add to the chord. So a
G11 chord is constructed by taking a G major chord and adding the eleventh
tone of a G major scale, c. Ideally the added note would be in the octave
indicated by the number, relative to the root of the chord -- that is to
say, the "11" in G11 should be the c an octave and a fourth above the lowest
g in the chord, as opposed to the one a mere fourth above the root, which
would be called for in a G4 chord. In practice, what fingerings are possible
or impossible on a given instrument, or even merely which are easy and which
are difficult, will lead to added notes appearing in an octave other than
the one specified in the chord name (or even left out entirely if the
resulting chord sounds awful when rearranged to fit the instrument).
In the case of a minor chord, a minor scale is used to count up to the
added note. So in an Am6 chord the sixth added is the sixth of the
A minor scale (f), not the sixth of the A major scale (f#).
Note that "7" chords are a special case! As described above, a seventh
chord is a "dominant seventh" chord unless explicitly marked as a major
seventh chord. See section 5 ("Seventh Chords").
Also note that a "5" does not mean "add the fifth" (since the fifth is
already in most chords), but indicates a "power chord" (no third).
See section 7 ("Power Chords").
The phrase "power chord" usually brings to mind rock 'n' roll, especially
low guitar sounds with distortion, but their use actually goes back a few
centuries. A power chord is a chord with no third; just the root and fifth.
It may be just two notes, or those notes can be repeated in different
octaves. Because there is no third, the chord is neither major nor minor
(which also means that it can be used in place of either a major or a minor
chord). So an F power chord contains only f and c, and a D power chord
contains only d and a.
In rock guitar transcriptions, power chords are abbreviated with a "5"
following the name of the root, e.g. G5 for a G power chord, C5 for a
C power chord, etc. They are also sometimes written out as "G no third"
(perhaps with parentheses around the "no third"). In this case, the "5"
doesn't meen to add the fifth; it means play only the root and fifth.
[Please click here to view
Figure 7.1]
A "suspended chord" also lacks the third, but differs from a power chord
in that there is usually some other note added to replace the missing
third. (Perhaps the name comes from usage in which the note that replaces
the third is a suspension from the previous chord? I don't know.) The
most common suspended chords are "sus4" (in which the fourth replaces
the third) and "sus2" (in which the second replaces the third).
So to make an Asus2 chord, we would start with an A chord (a, c#, e);
throw away the third (c#), leaving a and e; then add the second (b).
Thus, Asus2 contains a, b, and e.
Similarly, a Dsus4 would contain the 1, 4, and 5 of a D major scale:
d, g, and a.
[Please click here to view
Figure 7.2]
Sometimes "sus4" chords written are simply "sus".
So far major and minor chords have been described has having the root
of the chord as the lowest note in the chord, e.g. C being c, e, g in
that order (ascending). If a note other than the root is the lowest
note, then we say that we have a different "inversion" of the chord.
The 1-3-5 form of a chord is called the "first inversion" (and is often
played 1-3-5-1, the second "1" really being "8", an octave up from the
root). Putting the fifth on the bottom, (5)-1-3, is "second inversion",
and (3)-(5)-1 is "third inversion". A chord name that includes a slash
followed by a letter specifies an inversion other than first. The letter
after the slash indicates which note should be lowest.
For example, D/A means to play a D major chord with an a as the lowest
note (third inversion): a-d-f#. Similarly D/F# means to play a second
inversion D major chord, with the bottom being an f#: f#-a-d.
[Please click here to view
Figure 8.1]
A digression about inversions and guitar chords:
While guitar chords usually do have the root of the chord on the bottom,
they are not always built up in 1-3-5 order. Also, as noted previously,
when added notes are specified in the chord name, sometimes the added notes
wind up in a different octave than theory would dictate. Here are a few
examples of guitar chords in their customary "first position" fingerings:
As you can see from this table, when moved from the theoretical blackboard
(or from a real keyboard) to a real guitar neck, some chords retain the
order of their notes, while others are jumbled up somewhat, inverted,
stretched out over octaves, and so on. In the case of C7, one note is
simply discarded because it didn't fit on the fretboard when played by
a musician with only the usual number of fingers. (A six-fingered guitarist
could fret the missing g on the top string. The rest of us can't.)
This is an example of how chords get moved around to fit a particular
instrument.
An augmented chord is made up of the root, the note a major third above
the root, and the note another major third above the middle note. Compare
this to a major chord (a major third then a minor third) and a minor chord
(a minor third then a major third). The third note in an augmented chord
is a half step higher than the top note of either a major or a minor chord.
Instead of being a fifth above the root, it's an augmented fifth up.
Since the first interval is a major third, just as it is in a major chord,
and the top note is a half step higher than it is in a major chord, one
easy way to figure out what notes are in an augmented chord is to take the
major chord that has the same root, and simply augment the fifth.
Example: Caug contains c; the note a major third above c, which is e;
and the note a major third above e, which is g#. Starting with a C chord
(c-e-g) and raising the fifth (g) a half step to g# gets us the same
answer, c-e-g#.
[Please click here to view
Figure 9.1]
Just as an augmented chord is made of two major thirds, a diminished
chord is made up of two minor thirds. So a diminished chord consists of
the root, the note a minor third higher than the root, and the note a
minor third above that. So the top note of the chord, instead of being
a fifth above the root, is a diminished fifth up from the root.
And just as an augmented chord can be made by raising the 5 of a major
chord a half step, a diminished chord can be made by lowering the 5 of
a minor chord a half step.
Thus to create Ddim, we can start with Dm (d-f-a) and lower the 5 of
that (a) a half step (to ab). The result, d-f-ab, has a minor third
from d to f and another minor third from f to a-flat.
[Please click here to view
Figure 9.2]
The sections of this text have been arranged not only in an order that
allows later sections to build on earlier ones, but also in an order that
reflects approximately how often you will likely encounter each kind of
chord discussed. Simple major and minor chords are the most common, with
seventh chords being fairly common as well. Chords with extra notes added
to them and suspended chords / power chords, along with inversions of
simple chords, are less common but by no means rare. Augmented and diminished
chords generally show up much less often than any of the others.
This discussion has been geared toward reading chord names and figuring out
what notes to play. Doing the opposite, taking a pile of notes and trying
to figure out what to call the resulting chord, can get confusing, as quite
often there is more than one name for a given collection of notes.
Sometimes a chord name will include more than one additional note to add
to the basic chord. Such names can get downright funky-looking. [A good
one to mention would be the "Hendrix chord", but at the moment I've forgotten
it.]
When playing chords, you usually don't stop to figure out what notes
to play -- either the chord is a familiar one or an easy variation on a
familiar one, and your fingers know where to land from having played the
chord countless times, or you look up a diagram of the chord or figure out
the notes to play and jot down your own diagram before starting the piece.
On the other hand, when basing a harmony or countermelody on the chords being
played by others, you do start thinking of the notes that make up a chord.
This tutorial is intended to show you how to figure out a chord from scratch
on those occasions when you have to do so.
This tutorial is not exhaustive, but it should give you a good running start.
"I I I I / IV IV I I / I I IV I / V V V V /
I I I I / IV IV I I / I I V V / I I I I".
/ I I I I / IV IV I I /
Fare thee / we-ell to Princess / landing stage, Mersey /
I I IV I / V V V V /
River, fare thee / well. I am /
I I I I / IV IV I I /
bound for Cal-i-/-for-ni-a, A /
I I V V / I I I I //
place that I know right / well. //
if that makes things clearer.]
"A A A A / D D A A / A A D A / E E E E /
A A A A / D D A A / A A E E / A A A A".
3. CHORD BASICS -- MINOR CHORDS:
4. CHORD SYMBOLS <--> CHORD NAMES:
X X major
Xm X minor
X7 X dominant-seventh, major-minor seventh (usu. spoken simply "X seventh")
XM7 X major-seventh
Xmaj7 X major-seventh
Xdim X diminished
Xaug X augmented
X+ X augmented
X/Y X major with a Y underneath
X9 X major with a ninth added
Xm6 X minor with a sixth added
X5 X "power chord" (no third)
Xsus X suspended (no third, usually with some other note added)
Xsus2 X suspended second, spoken "X sus two" -- leave out third, add second
Xsus4 X suspended fourth, spoken "X sus four" -- leave out third, add fourth
So, for example, Em7 is read as "E minor seventh" and is an E-minor
chord with a seventh added to it, Ab11 is read as "A-flat eleven"
and is an A-flat major chord with an added eleventh, and F#dim is
read as "F sharp diminshed" and is a diminshed chord starting on
F-sharp.
7. POWER CHORDS AND SUSPENDED CHORDS:
Chord Theoretical Guitar
======================================================================
C c e g c e g c e
D d f# a d a d f#
E e g# b e b e g# b e
F f a c f c f a c f
G g b d g b d g b g
g b d b d b Another common fingering of G
A a c# e a e a c# e
Dsus2 d e a d a d e
D7 d f# a c d a c f#
A7 a c# e g a e g c# e
B7 b d# f# a b d# a b f#
C7 c e g bb c e bb c e Note that the fifth (g) is
missing entirely!
9. AUGMENTED AND DIMINISHED CHORDS:
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