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Greg's Music Theory Page
CHORDS
Intervals
To understand chords, we must first take a
close look at intervals.
- Interval
- The space between two notes.
A chord has to have a minimum of 3 notes,
called a chord triad. A chord triad consists of 2 intervals. The smallest
interval in western music is the half-step. On a piano keyboard, this would be
playing 2 notes without any other notes in between them. B - C, C - C#, E - F,
Gb - G, are all examples of half-step intervals.
The next largest interval is the whole
step. A whole step consists of 2 half steps. B - C#, C - D, E - F#, Gb - Ab are
all examples of whole step intervals.
The next largest interval is the minor
third. A minor third consists of 1 1/2 steps. The interval which is larger than
the minor third is the major third, which consists of 2 whole steps (or 4 half
steps).
The following chart shows the intervals
starting from G.
| Interval |
Name |
| G - Ab |
half-step |
| G - A |
whole-step |
| G - Bb |
minor third |
| G - B |
major third |
* There are more intervals than the ones listed, but for purposes of learning
chords, only the half-step, whole-step, minor third and major third intervals
will be covered.
There are only 4 types of chord triads;
major, minor, augmented and diminished. These chords are defined by their
intervals.
The following is a chart of the various G
chord triads, with the notes of the chord and interval names listed:
| G Chord |
Notes of Chord
|
Order of Intervals
|
| G Major |
G B D |
Maj-3rd Min-3rd |
| G Minor |
G Bb D |
Min-3rd Maj-3rd |
| G Augmented |
G B D# |
Maj-3rd Maj-3rd |
| G Diminished |
G Bb Db |
Min-3rd Min-3rd |
Knowing the intervals which make up
chords, will allow a person to find chords without any additional aids.
Seventh Chords
If we extend the chord triad by giving it
a fourth note, we get 7th chords. The following chart lists the most common 7th
chords for G along with the appropriate intervals:
| G 7th Chord |
Notes of Chord
|
Order of Intervals
|
| G Major 7 |
G B D F# |
Maj-3rd Min-3rd Maj-3rd
|
| G Dominant 7 |
G B D F |
Maj-3rd Min-3rd Min-3rd
|
| G Minor 7 |
G Bb D F |
Min-3rd Maj-3rd Min-3rd
|
| G Half-Diminished 7 |
G Bb Db F |
Min-3rd Min- 3rd Maj-3rd
|
| G Diminished 7 |
G Bb Db E |
Min-3rd Min-3rd Min-3rd
|
You may want to go further and chart out
the intervals for 5, 6 and 7 note chords as well. I will not go any farther than
charting 4 note chords.
Applying chords to music
To apply chords to music, first find out
the key of the song. Then by harmonizing the
corresponding scale, or simply using the number system,
one can find all of the chords which work for a given key.
An example would be if a song is in the
key of A major, it scale would be:
Any chord which contains notes derived
from this scale will work in this key. So, A major 9 (A C# E G# B) works since
all it's notes are derived from the A major scale. Db major (Db F Ab) won't work
within the key because this chord contains an F natural instead of an F sharp.
But try it anyhow, it may work in the song even though it doesn't fit the key.
Don't be afraid to place chords in a song which aren't derived from it's key(s).
In other words, don't limit yourself to the key of a song/progression. Keys are
to be thought of as guidelines.
Chord naming conventions
Let's use chords derived from the C major
scale as examples:
C D E F G A B
Chords are derived from numbering the
scale degrees of the corresponding root. (C=1, D=2, E=3, etc.). When the notes
of the scale go into another octave, the numbers continue.
C D E F G A B
C D E F G A
1 2 3 4 5 6 7 8 9 10
11 12 13
A chord triad will contain the 1, 3 and 5.
A Seventh chord will be numbered, 1, 3, 5, 7. Here is list of the basic chord
names and their corresponding numbers:
| Number of notes
|
Name |
| 1 3 5 |
Triad |
| 1 3 5 7 |
Seventh |
| 1 3 5 7 9 |
Ninth |
| 1 3 5 7 9 11 |
Eleventh |
| 1 3 5 7 9 11 13 |
Thirteenth |
Notice the pattern. The notes of all
chords (except suspended chords, 6th chords and some altered chords) are derived
from choosing a tonic, and building the rest of the notes from the corresponding
scale by skipping every other note of the scale.
Naming Chord Triads
Earlier, I demonstrated how to find the
name of chord triads using intervals. The chart below illustrates how a chord
name can be found by examining the numbers of the major scale in which it is
derived from.
| C Chord Triad |
Notes of Chord
|
Numbers of Chord
|
| C Major |
C E G |
1 3 5 |
| C Minor |
C Eb G |
1 b3 5 |
| C Augmented |
C E G# |
1 3 #5 |
| C Diminished |
C Eb Gb |
1 b3 b5 |
- Suspended Chords
- A chord which has its third either
raised to the 4th or lowered to the 2nd scale degree.
C F G = C sus 4 (sus 4 chords are usually
written without the "4", i.e., "C sus"
C D G = C sus 2
There has been some confusion about
suspended chords. I once saw a chord labeled as a Minor sus 4. This is an
erroneous name because by definition, a suspended chord has no third, but a
minor chord has to have a flatted third. The intended chord was a Minor add 11
chord.
The following is a list of most, if not
all, of the possible C chords and their corresponding names.
| Notes of Chord
|
Chord Name |
| C E G |
C Major |
| C Eb G |
C Minor |
| C E G# |
C Augmented |
| C Eb Gb |
C Diminished |
| C Eb Gb Bb |
C Half-diminished |
| C Eb Gb A |
C Diminished 7 |
| C F G |
C Suspended 4 |
| C D G |
C Suspended 2 |
| C F G Bb |
C Suspended 7 |
| C F G Bb D |
C Suspended 9 |
| C F G Bb D F |
C Suspended 11 |
| C F G Bb D F A |
C Suspended 13 |
| C E G B |
C Major 7 |
| C E G Bb |
C Dominant 7 |
| C Eb G Bb |
C Minor 7 |
| C E G A |
C Major 6 |
| C Eb G A |
C Minor 6 |
| C E G A D |
C 6/9 |
| C Eb G A D |
C Min 6/9 |
| C Eb G B |
C Minor/Major 7 |
| C E G# B |
C Maj 7 Sharp 5 |
| C E G# Bb |
C Dom 7 Sharp 5 |
| C E Gb B |
C Maj 7 Flat 5 |
| C E Gb Bb |
C Dom 7 Flat 5 |
| C Eb G# Bb |
C Min 7 Sharp 5 |
| C E G Bb D# |
C Dom 7 Sharp 9 |
| C E G Bb Db |
C Dom 7 Flat 9 |
| C E G B D |
C Maj 9 |
| C E G Bb D |
C Dom 9 |
| C Eb G Bb D |
C Minor 9 |
| C Eb G B D |
C Min/Maj 9 |
| C E G# B D |
C Maj 9 Sharp 5 |
| C E G# Bb D |
C Dom 9 Sharp 5 |
| C Eb G Bb Db |
C Min 7 Flat 9 |
| C E Gb B D |
C Maj 9 Flat 5 |
| C E Gb Bb D |
C Dom 9 Flat 5 |
| C Eb Gb Bb D |
C Min 9 Flat 5 |
| C E G B D# |
C Maj 7 Sharp 9 |
| C E G B Db |
C Maj 7 Flat 9 |
| C E G Bb Db |
C Dom 9 Flat 9 |
| C E G# B D# |
C Maj 7 Sharp 5 Sharp 9
|
| C E G# Bb D# |
C Dom 7 Sharp 5 Sharp 9
|
| C E G# B Db |
C Maj 7 Sharp 5 Flat 9
|
| C E G# Bb Db |
C Dom 7 Sharp 5 Flat 9
|
| C E Gb B D# |
C Maj 7 Flat 5 Sharp 9
|
| C E Gb Bb D# |
C Dom 7 Flat 5 Sharp 9
|
| C Eb G B D F |
C Min/Maj 11 |
| C Eb G Bb D F |
C Min 11 |
| C Eb Gb Bb D F |
C Min 11 flat 5 |
| C E G B D F |
C Maj 11 |
| C E G# B D F |
C Maj 11 Sharp 5 |
| C E G B D# F |
C Maj 11 Sharp 9 |
| C E G# B D# F |
C Maj 11 Sharp 5 Sharp 9
|
| C E Gb B D F |
C Maj 11 Flat 5 |
| C E G B Db F |
C Maj 11 Flat 9 |
| C E Gb B Db F |
C Maj 11 Flat 5 Flat 9
|
| C E G Bb D F |
C Dom 11 |
| C E G# Bb D F |
C Dom 11 Sharp 5 |
| C E G Bb D# F |
C Dom 11 Sharp 9 |
| C E G# Bb D# F |
C Dom 11 Sharp 5 Sharp 9
|
| C E Gb Bb D F |
C Dom 11 Flat 5 |
| C E G Bb Db F |
C Dom 11 Flat 9 |
| C E Gb Bb Db F |
C Dom 11 Flat 5 Flat 9
|
| C E G Bb D F A |
C Dom 13 |
| C E G B D F A |
C Maj 13 |
| C Eb Gb Bb D F A |
C Min 13 flat 5 |
| C E G Bb Db F A |
C 13 Flat 9 |
| C E G Bb D# F A |
C 13 Sharp 9 |
| C E G Bb D# F A |
C 13 Sharp 9 |
* "Dom" is an abbreviation for Dominant. All 7th chord names without the
"Dominant" or "Major" qualifier (C 7th) are implied to be Dominant seven chords.
"Half-diminished" is also called "Minor 7 flat 5" and is listed twice.
"Augmented" is an alternative name for any chord with a sharp 5. Ex; C Dom 7
Sharp 5 = C Augmented 7
The names of the chords are cumulative. In
other words, if a chord is called a ninth, it must contain all of the triad
numbers below nine. An eleventh chord must contain 1 3 5 7 9 11 in order to be
called a true "eleventh" chord. If a chord does not hold to the pattern, say the
alleged eleventh is missing the 9, containing 1 3 5 7 11, then it is said to be
a "seven add eleven". For instance, C E G B F is a C major 7 add eleven, while C
E G B D F is a legitimate C major eleven chord. Here are some more examples:
| Notes of Chord
|
Chord name |
| D F# A E |
D major add 9 |
| Eb G Bb Db A C |
Eb Dom 7 add 11 add 13
|
| G B D A C |
G major add 9 add 11 |
Inversions
The best way to define an inversion is to
illustrate a few:
The C major triad has three inversions:
- C E G - root inversion
- E G C - 1st inversion
- G C E - 2nd inversion
C Major 7 has four inversions
- C E G B - root inversion
- E G B C - 1st inversion
- G B C E - 2nd inversion
- B C E G - 3rd inversion
C G B E is not an inversion. All the notes
of the chord must be present and no note can be skipped, only the sequence of
the notes can be altered in a chord inversion.
Voicings
A chord voicing is different from a chord
inversion in that a note can be skipped or repeated in a chord voicing. Again,
the best way to teach about chord voicings is to illustrate them:
C G B E is a chord voicing of C major 7.
C B E G is a chord voicing of C major 7
G C E G is a chord voicing of C major 7.
C G C B E is a chord voicing of C major 7.
B G E C E is a chord voicing of C major 7.
As chords get bigger (elevenths and
thirteenths), most musicians will tend to drop one note of the chord. Usually,
(this is not a rule) the eleventh is the first note to go in a thirteenth chord,
thus technically making the chord a 9 add 13 (assuming no other note is
dropped).
One thing to keep in mind about voicings
and inversions is that with bigger chords, voicings/inversions become
increasingly important as to how the chord sounds. For instance, for the G major
7 chord, voiced G B D F#, this chord can sound "jazzy", while voiced B D F# G is
too disonant because of the F# and G being placed right next to each other. The
latter voicing is a rarely used one for this chord.
Alternate names for chords
In the notes above, I talked about some
alternate names for chords (Half-diminished/Minor 7 b5 is one example). But some
chords have alternate names which can be chosen based upon how the chord is
being used within the context of the song/progression. Some examples are:
| Notes of Chord
|
Chord Name |
Chord Name |
| A C E G |
A minor 7 |
C major 6 (3rd inversion)
|
| B D F A |
B half-diminished |
D minor 6 (3rd inversion)
|
| G C D |
G suspended 4 |
C suspended 2 (1st inversion)
|
Augmented chords have 3 possible names,
usually chosen based upon which inversion is being used:
| Notes of Augmented Chord
|
Chord Name |
| C E G# |
C Augmented |
| E G# C |
E Augmented |
| G# C E |
G# Augmented |
So, which name should be used in which situations? Whichever is easiest. The way
a chord is being used will help you in deciding upon its name. For instance, if
the G sus 4/C sus 2 chord is used (the notes are G C D) before or after a G
major chord, I'm more likely to call this a G sus 4 because I associate it with
the preceding G chord. This is especially
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