18. ADVANCED CHORDS IN THE WESTERN MUSIC

 18.      ADVANCED CHORDS IN THE WESTERN MUSIC

The Seven notes of the different scales could be called by a Roman numeral and a degree according to its position as follows 

Roman numeral	Scale degree
I	Tonic
II	Supertonic
III	Mediant
IV	Subdominant
V	Dominant
VI	Submediant
VII	Leading tone / Subtonic

        

• Tertian chords can be decomposed into a series of (major or minor) thirds. For example, the C major triad (C-E-G) is defined by a sequence of two intervals, the first (C-E) being a major third and the second (E-G) being a minor third. The most common chords are tertian. Other tertian chords other than majors and minors include augmented, diminished, flat5, major7, minor7, dominant7, diminished7, half-diminished7 chords. For instance:-

Ø  Diminished chord, which has many Minor thirds and no Major thirds, many Tritones but no Perfect fifths.  From a minor triad, we can easily make it diminished by lowering the 5th scale degree a half step. This means from a major triad, we’ve to lower the 3rd and 5th scale degree both a half step.

Ø  Augmented chord, which has many Major thirds and no Minor thirds or Perfect fifths. An augmented chord is a major chord with the 5th degree raised a half step. This means from a minor triad, we’ve to raise the 3rd and 5th scale degree both a half step.

Again, chords that are not built that way is called non-tertian chords.

Ø  Dominant seventh flat five chord, which has many Major thirds and Tritones and no Perfect fifths (For example, the dominant seventh flat five built upon C (C7♭5) would be C-E-G♭-B ♭)

• Secundal chords can be decomposed into a series of (major or minor) seconds. For example, the chord C-D-E♭ is a series of seconds, containing a major second (C-D) and a minor second (D-E♭).
• Quartal chords can be decomposed into a series of fourths. Quartal harmony normally works with a combination of perfect and augmented fourths. Diminished fourths are enharmonically equivalent to minor thirds, so they are uncommon. For example, the chord C-F-B is a series of fourths, containing a perfect fourth (C-F) and an augmented fourth/tritone (F-B).

Quintal chords is harmonic structure preferring the perfect fifth, the augmented fifth, and the diminished fifth. Quintal chords (the harmonic layering of fifths specifically) is a lesser-used term, and since the fifth is the inversion or complement of the fourth, it is usually considered indistinct from quartal chords.

INTERVALS

All chords are made up of interlocking or overlapping intervals. An interval maybe defined as the distance between two notes. The names of the chords are derived from the intervals that they are built from. In order of smallest to largest ascending intervals (and distance in semitones) within the octave from a middle C would be as follows:

Interval	Note	Semitones
Minor 2nd	D♭	1
Major 2nd	D	2
Minor 3rd	E♭	3
Major 3rd	E	4
Perfect 4th	F	5
Augmented 4th Diminished 5th	F# G♭	6¹²
Perfect 5th	G	7
Augmented 5th Minor 6th	G# A♭	8¹
Major 6th	A	9
Minor 7th	B♭	10
Major 7th	B	11
Octave (8th)	C	12
Note: Some interval pairs are enharmonic; one interval with two names.

TRIADS

Triads, also called triadic chords, are tertian chords with three notes. The four basic triads are described below. The triad is a class of chords, specifically three-note chords formed by the formula: 1-3-5 or root, third, fifth. 

TRIAD	Root	3rd	5th
Minor	1	3	5
Minor	1	♭3	5
Augmented	1	3	#5
Diminished	1	♭3	♭5
♭=flat/lowered; #=sharp/raised

 

TRIAD	Component intervals		Chord symbol	Notes
	Third	Fifth
Major triad	major	Perfect	C, CM, Cmaj, CΔ, Cma	C E G
Minor triad	minor	Perfect	Cm, Cmin, C-, Cmi	C E♭ G
Augmented triad	major	Augmented	Caug, C+, C+	C E G♯
Diminished triad	minor	Diminished	Cdim, Co, Cm(♭5)	C E♭ G♭

INVERSIONS

If the root (C) is on the bottom, this voicing is called root position. If the third (E) is on the bottom, it is called the first inversion. If the fifth (G) is on the bottom this voicing of the triad is called second inversion. Since there are only three possible voicings of a triad it is relatively easy to hear them in that they are a common feature of the past two centuries of traditional harmonic structures in Western music.

SEVENTH CHORDS

Seventh chords are tertian chords, constructed by adding a fourth note to a triad, at the interval of a third above the fifth of the chord. This creates the interval of a seventh above the root of the chord, the next natural step in composing tertian chords. The seventh chord built on the fifth step of the scale (the dominant seventh) is the only one available in the major scale: it contains all three notes of the diminished triad of the seventh and is frequently used as a stronger substitute for it. There are various types of seventh chords depending on the quality of both the chord and the seventh added. In chord notation, the chord type is sometimes superscripted and sometimes not (e.g. Dm7, Dm⁷, and D^m7 are all identical).

SEVENTH CHORD	Component intervals			Chord symbol	Notes
	Third	Fifth	Seventh
TERTIAN CHORDS
Diminished seventh	Minor	diminished	diminished	Co7, Cdim7	C E♭ G♭ B
Half-diminished seventh	Minor	diminished	major	Cø7, Cm7♭5, C−7(♭5)	C E♭ G♭ B♭
Minor seventh	Minor	perfect	minor	Cm7, Cmin7, C−7, C−7	C E♭ G B♭
Minor major seventh	Minor	Perfect	major	Cm(M7), Cm maj7, C−(j7), C−Δ7, C−M7	C E♭ G B
Dominant seventh	Major	Perfect	minor	C7, C7, Cdom7	C E G B♭
Major seventh	Major	Perfect	major	CM7, Cmaj7, CΔ7, CΔ7, CΔ7, Cj7	C E G B
Augmented major seventh	Major	augmented	major	C+(M7), CM7+5, CM7♯5, C+j7, C+Δ7	C E G♯ B
NON- TERTIAN CHORDS
Augmented seventh	Major	augmented	minor	C+7, Caug7, C7+, C7+5, C7♯5	C E G♯ B♭
Diminished Major Seventh	Minor	Diminished	Major	Cm(M7)♭5, C−Δ7(♭5 )	C E♭ G♭ B
Dominant Seventh flat five	Major	Diminished	Minor	C7♭5	C E G♭ B♭

EXTENDED CHORDS

Extended chords are triads with further tertian notes added beyond the seventh: the ninth, eleventh, and thirteenth chords. After the thirteenth, any notes added in thirds duplicate notes elsewhere in the chord; all seven notes of the scale are present in the chord and adding more notes does not add new pitch classes. Such chords may be constructed only by using notes that lie outside the diatonic seven-note scale.

EXTENDED CHORDS	Components				Chord symbol	Notes
	Chord	Interval(s)
Dominant ninth	dominant seventh	major ninth	-	-	C9	C E G B♭ D
Dominant eleventh	dominant seventh (the third is usually omitted)	major ninth	eleventh	-	C11	C E G B♭ D F
Dominant thirteenth	dominant seventh	major ninth	perfect eleventh (usually omitted)	major thirteenth	C13	C E G B♭ D F A

Other extended chords follow similar rules, so that for example maj9, maj11, and maj13 contain dominant seventh chords, while min9, min11, and min13 contain minor seventh chords.

ALTERED CHORDS

Although the third and seventh of the chord are always determined by the symbols, the fifth, ninth, eleventh and thirteenth may all be chromatically altered by accidentals (the root cannot be so altered without changing the name of the chord, while the third cannot be altered without altering the chord's quality). These are noted alongside the altered element. Accidentals are most often used with dominant seventh chords. Altered dominant seventh chords (C^7alt) may have a flat ninth, a sharp ninth, a diminished fifth, or an augmented fifth. Some write it as C⁷⁺⁹, which assumes also the flat ninth, diminished fifth and augmented fifth. The augmented ninth is often enharmonically equivalent to the flat third or tenth. When superscripted numerals are used the different numbers may be listed horizontally (as shown) or else vertically.

 

ALTERED CHORDS	Components		Chord symbol	Notes
	Chord	Interval(s)
Seventh augmented fifth	dominant seventh	augmented fifth	C7+5, C7♯5	C E G♯ B♭
Seventh flat ninth	dominant seventh	minor ninth	C7-9, C7♭9	C E G♭ B♭ D♭
Seventh sharp ninth	dominant seventh	augmented ninth	C7+9, C7♯9	C E G♯ B♭D♯
Seventh augmented eleventh	dominant seventh	augmented eleventh	C7+11, C7♯11	C E G♯ B♭ D♯ F♯
Seventh flat thirteenth	dominant seventh	minor thirteenth	C7-13, C7♭13	C E G♭ B♭ D♭ F♭ A♭
Half-diminished seventh	minor seventh	diminished fifth	Cø, Cm7♭5	C E♭ G♭ B♭

ADDED TONE CHORDS

Suspended chord (sus2) and added tone chord (add9) both with D   (ninth=second), distinguished by the absence or presence of the third (E♭).

An added tone chord is a triad chord with an added, non-tertian note, such as the commonly added sixth as well as chords with an added second (ninth) or fourth (eleventh) or a combination of the three. These chords do not include "intervening" thirds as in an extended chord. Added chords can also have variations. Thus madd9, m4 and m6 are minor triads with extended notes. Sixth chords can belong to either of two groups. One is first inversion chords and added sixth chords that contain a sixth from the root. The other group is inverted chords in which the interval of a sixth appears above a bass note that is not the root.

The major sixth chord (also called, sixth or added sixth with the chord notation 6, e.g., "C6") is by far the most common type of the sixth chord of the first group. It comprises a major triad with the added major sixth above the root, common in popular music. For example, the chord C6 contains the notes C-E-G-A. The minor sixth chord (min6 or m6, e.g., "Cm6") is a minor triad with the same added note. For example, the chord Cmin6 contains the notes C-E♭-G-A. In chord notation, the sixth of either chord is always assumed a major sixth rather than a minor sixth, however, a minor sixth interval may be indicated in the notation as, for example, "Cm (m6)", or Cm^m6.

The augmented sixth chord usually appears in chord notation as its enharmonic equivalent, the seventh chord. This chord contains two notes separated by the interval of an augmented sixth (or, by inversion, a diminished third, though this inversion is rare). The augmented sixth is generally used as a dissonant interval most commonly used in motion towards a dominant chord in root position (with the root doubled to create the octave the augmented sixth chord resolves to) or to a tonic chord in the second inversion (a tonic triad with the fifth doubled for the same purpose). In this case, the tonic note of the key is included in the chord, sometimes along with an optional fourth note, to create one of the following (illustrated here in the key of C minor):

• Italian augmented sixth: A♭, C, F♯
• French augmented sixth: A♭, C, D, F♯
• German augmented sixth: A♭, C, E♭, F♯

The augmented sixth family of chords exhibits certain peculiarities. Since they are not based on triads, as are seventh chords and other sixth chords, they are not generally regarded as having roots (nor, therefore, inversions), although one re-voicing of the notes is common (with the namesake interval inverted to create a diminished third).

The second group of sixth chords includes Inverted major and minor chords, which may be called sixth chords in that the six-three (6/3) and six-four (6/4) chords contain intervals of a sixth with the bass note, though this is not the root. Nowadays this is mostly for academic study or analysis but the Neapolitan sixth chord is an important example; a minor triad with a flat supertonic scale degree as its root that is called a "sixth" because it is almost always found in the first inversion. Though a technically accurate Roman numeral analysis would be ♭II, it is generally labeled N⁶. In C# minor, the chord is notated (from root position) D♭, F, A♭. Because it uses chromatically altered tones and the chord is often grouped with the borrowed chords, but the chord is not borrowed from the relative major or minor and it may appear in both major and minor keys.

ADDED TONE CHORDS	Components			Chord symbol	Notes
	Chord	Interval(s)
Add nine	Major triad	major ninth	-	C2, Cadd9	C E G D
Add fourth	major triad	perfect fourth	-	C4, Cadd11	C E G F
Add sixth	major triad	Major sixth	-	C6	C E G A
Six-nine	major triad	major sixth	major ninth	C6/9	C E G A D
Mixed-third	minor triad	major third	-	-	C E♭ E G

 

SUSPENDED CHORDS

A suspended chord, or "sus chord" (sometimes wrongly taken as sustained chord), is a chord in which the third is replaced by either the second or the fourth. This produces two main chord types: the suspended second (sus2) and the suspended fourth (sus4). The chords, C^sus2 and C^sus4, for example, consist of the notes C D G and C F G, respectively. There is also a third type of suspended chord, in which both the second and fourth are present, for example the chord with the notes C D F G.

The name suspended derives from an early polyphonic technique developed during the common practice period, in which stepwise melodic progress to a harmonically stable note in any particular part was often momentarily delayed or suspended by extending the duration of the previous note. The resulting unexpected dissonance could then be all the more satisfyingly resolved by the eventual appearance of the displaced note. In traditional music theory the inclusion of the third in either chord would negate the suspension, so such chords would be called added ninth and added eleventh chords instead.

Extended versions are also possible, such as the seventh suspended fourth, which along with root C, contains the notes C F G B♭ and is notated as C7^sus4. C^sus4 is sometimes written C^sus since the sus4 is more common than the sus2.

	SUSPENDED CHORD	Interval(s)			Chord symbol	Notes
Sus2	open fifth	major second	-	-	Csus2	C D G
Sus4	open fifth	perfect fourth	-	-	Csus4	C F G
Jazz sus	open fifth	perfect fourth	minor seventh	major ninth	C9sus4	C F G B♭ D

Borrowed chords

A borrowed chord is one from a different key than the home key, the key of the piece it is used in. The most common occurrence of a borrowed chord is where a chord from the parallel major or minor key is used. For instance, in the C major key, a minor ♭III chord would be borrowed, which appears only in the C minor key. Although borrowed chords could theoretically include chords taken from any key other than the home key, this is not how the term is used when a chord is described in formal musical analysis. When a chord is analyzed as "borrowed" from another key it may be shown by the Roman numeral corresponding with that key, for example, V/V indicates the dominant chord of the dominant key of the home-key. The dominant key of Cmajor is Gmajor, the secondary dominant is the chord of the fifth degree of the Gmajor scale, which is Dmajor. If used, this chord causes a modulation.

Diminished supertonic triad (iio)             D– F –A♭

Half-diminished supertonic seventh (iiø7) D– F –A♭– C

"Flat three" (♭III)  E♭– G– B♭

Minor Subdominant (iv)          F –A♭– C

"Flat six" (♭VI) A♭–C– E♭

Fully diminished leading-tone seventh (viio7) B–D–F–A♭

Applying chords

The easiest way to apply a triad, or indeed any chord, is to pick the chord on a polyphonic instrument (such as a piano) and play its three or more notes simultaneously. This is how chords occur in actual music, which infers that an instrument plays all the notes in the chord at the same time. However, there are other possibilities for monophonic instruments. The simplest is to arpeggiate the chord, that is, to play its notes one at a time in any order, especially in an ascending or descending order. Often melody can be written around the chord, using notes in the chord as well as the diatonic and chromatic passing notes between the chord tones.