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Chords

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Note Intervals

Before we get into chord building it's important to understand the quality of note intervals. In the following table we are looking at the intervals from Middle C (C4) to the notes above.

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Chords

A chord, in music, is any harmonic set of pitches consisting of multiple notes,also called "tones", that are sounded simultaneously, or nearly so. For many practical and theoretical purposes, arpeggios and other types of broken chords (in which the chord tones are not sounded simultaneously) may also be considered as chords in the right musical context.

In tonal Western classical music, music with a tonic key or "home key", the most frequently encountered chords are triads, so called because they consist of three distinct notes: the root note, and intervals of a third and a fifth above the root note. Chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in contemporary classical music, jazz and almost any other genre.

A series of chords is called a chord progression. One example of a widely used chord progression in Western traditional music and blues is the 12 bar blues progression. Although any chord may in principle be followed by any other chord, certain patterns of chords are more common in Western music, and some patterns have been accepted as establishing the key (tonic note) in common-practice harmony—notably the resolution of a dominant chord to a tonic chord. To describe this, Western music theory has developed the practice of numbering chords using Roman numerals to represent the number of diatonic steps up from the tonic note of the scale.

Common ways of notating or representing chords in Western music, other than conventional staff notation, include Roman numerals, the Nashville Number System, figured bass, chord letters, and chord charts.

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Defining Chord Types & Chord Symbols

Position	Description	Half-Steps	In C Major Scale
1	The root of the chord	0	C
2	A major second above the root	2	D
b3	A minor third above the root	3	Eb
3	A major third above the root	4	E
4	A perfect fourth above the root	5	F
b5	A diminished fifth above the root	6	Gb
5	A perfect fifth above the root	7	G
#5	An augmented fifth above the root	8	G#
6	A major sixth above the root	9	A
°7	A diminished seventh above the root	9	A
b7	A minor seventh above the root	10	Bb
7	A major seventh above the root	11	B

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Triad Chords

Triads are chords built with three notes. They are the primary basis for chord building. The base of the chord is known as the root or root note. Triad chords are built by the stacking of two notes above the root. The flavor of the chord is determined by the quality of the notes above the root.

Triad Types

There are four basic types of triads and two commonly accepted variations. We're using C as an example of how the chord could be displayed.

C	The letter name defines the root of the chord.
C	A letter name by itself indicates a major triad in root position, C: 1-3-5
Csus4, Csus2, Csus	A letter name followed by a sus4 or sus2 indicates a major triad with a perfect fourth (substituting for the major third), Csus4: 1-4-5; a major triad with a major second (substituting for the major third), Csus2: 1-2-5. Typically suspensions resolve to a major third. If the chord quality is listed as only sus, assume it is a sus4.
C-, Cm	A letter name followed by a - (minus sign) or a lower case m indicates a minor triad, C- or Cm: 1-b3-5
C°, Cdim	A letter name followed by a ° (degree sign) or dim indicates a diminished triad, C° or Cdim: 1-b3-b5
C+, Caug	A letter name followed by a + (plus sign) or aug indicates an augmented triad, C+ or Caug: 1-3-#5

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Triad types with C as the root

Written	Triad Name	Root Note	2nd Note	3rd Note
C	C Major	C	E (Major 3rd)	G (Perfect 5th)
Cm	C Minor	C	Eb (Minor 3rd)	G (Perfect 5th)
C°	C Diminished	C	Eb (Minor 3rd)	Gb (Diminished 5th)
C+	C Augmented	C	E (Major 3rd)	G# (Augmented 5th)
Csus2	C Suspended 2nd	C	D (Major 2nd)	G (Perfect 5th)
Csus4	C Suspended 4th	C	F (Perfect 4th)	G (Perfect 5th)

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Triad Chords in the Key of C Major

The following illustration shows all of the naturally occuring triads chords in the key of C major and its relative minor, A natural minor.
Notice that there are naturally occuring major, minor and a single diminished chord amongst these chords.
All major and natural minor keys contain:

• 3 Major Triads: C, F, G
• 3 Minor Triads: Dm, Em, Am
• 1 Diminished Triad: B°

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Seventh & Sixth Chords

Seventh and sixth chords are three note triads with an added fourth note a sixth or seventh from the chord's root note. The following illustration shows all of the seventh and sixth chords in the key of C major.

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Sixth & Seventh Types

There are eleven types of seventh and sixth chords. We're using C as an example of how the chord could be displayed.

C7, C6	The letter name defines the root of the chord.
CMaj7, Cmaj7, CM7, CΔ7	A letter name followed by Maj or maj or M or Δ indicates a major seventh chord. CMaj7, Cmaj7, CM7, CΔ7: 1-3-5-7
C6	A letter name followed by a 6 indicates a major sixth chord. A major triad with an additional note a major sixth above the root. C6: 1-3-5-6
C7	A letter name followed by a 7 indicates a dominant seventh chord. A major triad with an additional note a minor seventh above the root. C7: 1-3-5-b7
C7sus4	A letter name followed by 7sus4 indicates a dominant 7sus4 chord. A major triad with a perfect fourth (substituting for the major third) and an additional note a minor seventh above the root. C7sus4: 1-4-5-b7
C-7, Cm7	A letter name followed by a -7 or m7 indicates a minor triad with an additional note a minor seventh above the root. C-7, Cm7: 1-b3-5-b7
C-7b5, Cm7b5, C⊘7	A letter name followed by a -7b5 or m7b5 or C⊘7 indicates a minor 7b5 chord. A diminished triad with a minor seventh above the root. Sometimes referred to as a half-diminished seventh chord. C-7b5, Cm7b5, C⊘7: 1-b3-b5-b7
C+7, Caug7	A letter name followed by a +7 or aug7 indicates an augmented seventh chord. An augmented triad with an additional note a minor seventh above the root. C+7, Caug7: 1-3-#5-b7
C7b5	A letter name followed by a 7b5 indicates dominant seventh flat fifth chord. A major triad with a lowered fifth and an additional note a minor seventh above the root. C7b5: 1-3-b5-b7
C-Maj7, CmM7	A letter name followed by a -Maj7 or mM7 indicates minor-major seventh chord. A minor triad with an additional note a major seventh above the root. C-Maj7, CmM7: 1-b3-5-7
C°7, Cdim7	A letter name followed by a °7 or dim7 indicates a fully diminished seventh chord. A diminished triad with an additional note a diminished seventh above the root. C°7, Cdim7: 1-b3-b5-°7
C-6, Cm6	A letter name followed by a -6 or m6 indicates a minor sixth chord. A minor triad with an additional note a major sixth above the root. C-6, Cm6: 1-b3-5-6

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Seventh Chord Varieties

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Seventh Chords in the Key of C Major

The following illustration shows all of the naturally occuring seventh chords in the key of C major and its relative minor, A natural minor.
Notice that there are naturally occuring major sevenths, a single dominant sevent, minor sevenths and a single half diminished seventh chord amongst these chords.
All major and natural minor keys contain:

• 2 Major 7th Chords - CM7, FM7
• 1 Dominant 7th Chord - G7
• 3 Minor 7th Chords - Dm7, Em7, Am7
• 1 Half Diminished 7th Chord - B^ø or Bm7^b5

Sevenths In The Key Of C Major

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Tension or Extended Chords

Tension or Extended Chords are tertian extensions, extensions by the interval of a third, of the basic seventh chord. Tensions are indicated in chord symbols by the numbers 9, 11, and 13, and their alterations. Tensions add color (i.e. a stylistically acceptable amount of dissonance) to the basic chord type.
Tensions are named for their distance from the root of the chord when the chord is in root position and closely spaced. The 13th is the farthest extension diatonically possible as, by that point, all seven tonal degrees are represented within the chord (the next extension, the 15th, is the same as the root of the chord). In practice however, extended chords do not typically use all the chord members; when it is not altered, the 5th is often omitted, as are notes between the 7th and the highest note (i.e., the 9th is often omitted in an 11th chord; the 9th and 11th are usually omitted in a 13th chord), unless they are altered to give a special texture.

The degrees do not include degrees that are already in the base chord. For example the degrees 10, 12, and 14 would just be doubling of the degrees 3, 5, and 7. Therefore the included degrees in the extended chords are 9, 11, and 13.

Any chord that does not include an underlying 7th chord, or extensions beyond the root triad are generally referred to as Add Chords, where the extended note is added to the triad. This includes Add 9, Add 11, and Add 13.

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Position	Description	Half-Steps	In C Major Scale
b9	A minor ninth above the root of the chord	13	Db
9	A major ninth above the root	14	D
#9	An augmented ninth above the root	15	D#
11	A perfect eleventh above the root	17	F
#11	An augmented eleventh above the root	18	F#
b13	A minor thirteenth above the root	20	Ab
13	A major thirteenth above the root	21	A

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Given that there are eleven variety of sixth and seventh chords and seven variety of extended chords, it would seem that there are seventy seven variations of extended chords. This is not the case exactly. If the chord is to be considered an extension, the note(s) in the extension cannot be repeats of notes in the base chord. For example if the base chord is a minor seventh as in Cm7, where the notes are C - E^b - G - B^b, then the chord Cm7#9 would just be a minor seventh chord with a repeating E^b.

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Ninth Chords

A ninth chord is a chord with a ninth degree added to it. The root chord may be a major 7th, a dominant 7th, a dominant minor 7th, or a minor 7th.

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Eleventh Chords

An eleventh chord is a chord that contains the tertian extension of the eleventh. Typically found in jazz, an eleventh chord also usually includes the seventh and ninth, and elements of the basic triad structure. Variants include the Dominant Eleventh (C11, C - E - G - B^b - D - F), Minor Eleventh (Cm11, C - E^b - G - B^b - D - F), and Major Eleventh chord (Cmaj11, C - E - G - B - D - F). Using an augmented eleventh produces the Dominant Sharp Eleventh (C9^#11, C - E - G - B^b - D - F^#) and Major Sharp Eleventh (Cmaj9^#11, C - E - G - B - D - F^#) chords.

A perfect eleventh creates a highly dissonant minor ninth interval with the major third of major and dominant chords. To reduce this dissonance the third is often omitted (such as for example in the dominant eleventh chord that can be heard 52 seconds into the song "Sun King" on The Beatles' Abbey Road album), turning the chord into a suspended ninth chord (e.g. C9sus4, C - G - B^b - D - F), which can be also notated as Gm7/C.

Another solution to this dissonance is altering the third or eleventh factor of the chord to turn the problematic minor ninth interval within the chord into a major ninth. A dominant eleventh chord can be altered by lowering the third by a semitone for a minor eleventh chord, or by raising the eleventh by a semitone for a dominant sharp eleventh chord, implying the lydian dominant mode.

As its upper extensions (7th, 9th, 11th) constitute a triad, a dominant eleventh chord with the third and fifth omitted can be notated as a compound chord with a bass note. So C - B^b - D - F is written as B^b/C, emphasizing the ambiguous dominant/subdominant character of this voicing.

In the common practice period, the root, 7th, 9th, and 11th are the most common factors present in the V11 chord, with the 3rd and 5th typically omitted. The eleventh is usually retained as a common tone when the chord resolves to I or i.

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Thirteenth Chords

A thirteenth is the note thirteen scale degrees from the root of a chord and also the interval between the root and the thirteenth. The thirteenth is most commonly major or minor

A thirteenth chord is the stacking of six (major or minor) thirds, the last being above the 11th of an eleventh chord. Thus a thirteenth chord is a tertian (built from thirds) chord containing the interval of a thirteenth, and is an extended chord if it includes the ninth and/or the eleventh. "The jazzy thirteenth is a very versatile chord and is used in many genres." Since 13th chords tend to become unclear or confused with other chords when inverted, they are generally found in root position. For example, depending on voicing, a major triad with an added major sixth is usually called a sixth chord, because the sixth serves as a substitution for the major seventh, thus considered a chord tone in such context.

Most commonly, 13th chords serve a dominant function (V13), whether they have the exact intervals of a dominant thirteenth or not. Typically, a dominant chord anticipating a major resolution will feature a natural 13, while a dominant chord anticipating a minor resolution will feature a flat 13. Since thirteenth chords contain more than four notes, in four-voice writing the root, third, seventh, and thirteenth are most often included, excluding the fifth, ninth, and eleventh. The third indicates the quality of the chord as major or minor, the seventh is important for the quality as a dominant chord, while the thirteenth is necessary in a thirteenth chord.

In modern pop and jazz harmony, after the dominant thirteenth, a thirteenth chord (usually notated as X13, e.g. C13) contains an implied flatted seventh interval. Thus, a C13 consists of C, E, G, B^b, and A. The underlying harmony during a thirteenth chord is usually Mixolydian or Lydian dominant. A thirteenth chord does not imply the quality of the ninth or eleventh scale degrees. In general, what gives a thirteenth chord its characteristic sound is the dissonance between the flat seventh and the thirteenth, an interval of a major seventh.

In the common practice period the "most common" pitches present in V13 chord are the root, 3rd, 7th, and 13th; with the 5th, 9th, and 11th "typically omitted". The 13th is most often in the soprano, or highest voice, and usually resolves down by a 3rd to the tonic I or i. If the V13 is followed by a I9 the 13th may resolve to the 9th.

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Chords - Inversions

A chord inversion is a rearrangement of the top-to-bottom elements in a chord. In the root position a chord has its root note in the lowest (bass) position. Any variation, where all of the chords voices are represented, but the root is not the lowest note is an inversion. The number of possible inversions depends upon how many voices (tones) are in the chord. For example, a triad has three voices, so it has three possible configurations. Since one of the configurations is the root position, it can be said that a triad has two inversions.

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Triad Inversions

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Seventh Inversions

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Ninth Inversions

Note that when going from the 3rd inversion to the 4th inversion, it's not as simple as moving the bottom voice to the top because that would leave the bottom voice as the chord's root note, in this case the C note. To fix this, the C note must be moved up an octave.

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Roman Numerals

The method of using Roman Numerals allows a well versed musician to easily transpose the chords into any key, but has a disadvantage for beginner musicians who doesn't yet understand their meaning with regard to keys.

 

How the Roman Numeral System Works

Every major and minor key has a set of chords based upon the notes in the key scale. These chords are numbered by their respective root notes from 1 to 7 or I to VII. In the key of C the chord roots are C, D, E, F, G, A, B or their degrees from the root: 1, 2, 3, 4, 5, 6, 7. Using Arabic numerals alone cannot convey the flavor of the chord as being major or minor, but since Roman Numerals can be written as upper or lower case, the case can be used to denote what type of chord it is. In a major key, there are three major triads, three minor triads and one diminished triad. The diminished chord must have further embellishment since it is neither major or minor. Other than that, the Roman Numeral system works pretty well in most cases.

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• Major Chord: Upper case Roman Numeral: I, IV, V
• Minor Chord: Lower case Roman Numeral: ii, iii, vi
• Diminished Chord: Lower case Roman Numeral with a degree symbol: vii°

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Key of C Major

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