Chords

SIMPLE TRIADS

A Triad denotes a three note chord stack.

ToDo:

Construct and practice simple triads on the scale steps in the keys indicated.

Triads are chords structures composed of three notes; typically, the root, third and fifth notes in the primary key center...as C-E-G, for example.

These triads can be major, minor or diminished-according to the key signature. The defining criteria 'is that the notes are stacked in THIRDS.

As you construct these triads notice the enharmonic equivalences of many triads . that is, for ex., a triad on the root in the key signature of one flat (F Major) is F-A-C. This is the same (enharmonic) as a triad built on the fourth scale step in the key of C Major.
By paying attention to the sonic equivalences and pattern structures as you practice playing these triads, you will build-out your knowledge base and ‘finger memory’ of associated structural elements (chords).

INVERTED TRIADS

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ToDo:

Construct inversions of simple triads on the scale steps in the keys indicated.
As in the previous exercise, you will notice enharmonic equivalences in the patterns of notes among the various key centers. The relative complexity of notation acquires an additional dimension as the inversions of the triadic chords spell out the intervals in new ways; thirds become 6ths, 5ths become 4ths, etc.

We will limit the inversion complexity to the first and second inversions for now. Later we can investigate the 3rd inversions that deal with 7th chords.
Later in the course work you will note that the use of inverted triads is a method to enable smooth voice leading and coherent modulations.

TRIADS ON CIRCLE OF FIFTHS

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Building simple triads on the "Circle of Fifths" sequence of tonics is a valuable exercise that will build confidence and understanding of the fundamental relations embedded in the 12-tone music system.

ToDo:

Play the simple triads you developed in the previous exercise on each key center-starting on C minor and traversing the cyclic ring in a counter-clockwise direction.
It is not necessary at this juncture to be concerned about meter; just try to move from one key center to the next in the series using the most economical finger placements.
You can experiment in moving to an inverted chord structure as well as to one in root position, if the intervals cohere to a smooth transition.

**Note that as you move around the cycle of fifths the upper tetrachord of the current key center becomes the lower tetrachord of the following key center. Ex. In D (A-B-C#-D ) the upper tetrachord is the same as the lower tetrachord of A; in F (C-D-E-F) is the lower tetrachord of C major .

In the examples above complete the sequence around the circle of fifths. Start on the tonic of B minor and complete as in the example.

You may use inversions of triads as well as major or minor versions of the key centers; for ex., in the second staff (bar 20) the E minor triad could be followed by a tonal center of A Major or A minor.

Always look for small note intervallic movements when transitioning to the next cyclic center. This practice will aid you in developing smooth melodic lines in your later compositions and voicings.

NEAPOLITAN SIXTH CHORDS

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The Neapolitan Sixth chords comprise an important but perhaps not well-known structure that was developed during the "Common Practice Period" in European music and is still utilized today. The following information discusses this form and the common resolutions it addresses.

In music theory, a Neapolitan chord (or simply a "Neapolitan") is a major chord built on the lowered second (supertonic) scale degree.
It most commonly occurs in first inversion so that it is notated either as NII6 or N6 and normally referred to as a Neapolitan sixth chord. In C, a Neapolitan sixth chord in first inversion contains an interval of a sixth between F and Db.

Origin of the name

The Neapolitan chord is so named because it is associated with the so-called "Neapolitan school", which included Alessandro Scarlatti, Pergolesi, Paisiello, Cimarosa and other important 18th-century composers of Italian opera.

It was also a favourite idiom among composers in the Classical period, especially Beethoven, who extended its use to root-position and second-inversion chords.

The chord is known as the "neapolitan sixth" due to the interval of a sixth between the root and third notes of the chord.

In the graphic above notice the V/iii resolving to Eminor; it is structured as a Neapolitan sixth.

In the second red outlined box the chord is the DOMINANT in first inversion of a Neapolitan sixth chord which then resolves to the V, then the tonic.
Notice the smooth voice leading in this example.

NEAPOLITAN FUNCTIONS

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Neapolitan Harmonic Function

In tonal harmony, the function of the Neapolitan chord is to prepare the dominant, substituting for the IV or ii (particularly ii6) chord.
For example, it often precedes an authentic cadence, where it functions as a subdominant (IV).
In such circumstances, the Neapolitan sixth may be considered to be a type of chromatic alteration of the subdominant. The Neapolitan sixth chord is particularly common in minor keys. As a simple alteration of the subdominant triad (iv) of the minor mode, it provides contrast as a major chord compared to the minor subdominant or the diminished supertonic triad.

The most common variation on the Neapolitan chord is the Neapolitan major seventh, which adds a major seventh to the chord (this also happens to be the tonic).

A common use of the Neapolitan chord is in tonicizations and modulations to different keys.
It is the most common means of modulating down a semitone, which is usually done by using the I chord in a major key as a Neapolitan chord (or a flattened major supertonic chord in the new key, a semitone below the original).

Occasionally, a minor 7th or augmented 6th is added to the Neapolitan chord, which turns it into potential secondary dominant that can allow tonicization or modulation to the V/IV key area relative to the primary tonic.
Whether the added note were notated as a minor 7th or augmented 6th would largely depend how the chord was going to resolve. For example, in C major or C minor, the Neapolitan chord with an augmented 6th (B-natural added to Db major chord) would very likely resolve in C major or minor, or possibly into some other closely-related key

Voice leading

Because of its close relationship to the subdominant, the Neapolitan sixth resolves to the dominant using similar voice-leading.
In the present example of a C major/minor tonic, the Db generally moves down by step to the leading tone B-natural (creating the expressive melodic interval of a diminished third, one of the few places this interval is accepted in traditional voice-leading), while the F in the bass moves up by step to the dominant root G.

The fifth of the chord (Ab) usually resolves down a semitone to G as well. In four-part harmony, the bass note F is generally doubled, and this doubled F either resolves down to D or remains as the seventh F of the G-major dominant seventh chord.

In summary, the conventional resolution is for all upper voices to move down against a rising bass.

Care must be taken to avoid consecutive fifths when moving from the Neapolitan to the cadential 6/4. The simplest solution is to avoid placing the fifth of the chord in the top part. If the root or (doubled) third is in the top part, all upper parts simply resolve down by step while the bass rises.

PASSING CHORDS

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Definition:
In music, a passing chord is a nondiatonic chord that connects, or passes between, the notes of two diatonic chords.

Any chord that moves between one diatonic chord and another one nearby may be loosely termed a passing chord.
A diatonic passing chord may be inserted into a pre-existing progression that moves by a third in order to create more movement. In between chords that help you get from one chord to another are called passing chords.

For example in the chord progression:
|Cmaj7 |Em7 |Dm7 |G7 |
the diatonic passing chord (Dm7) may be inserted:
|Cmaj7 Dm7 |Em7 |Dm7 |G7 |
or the chromatic passing chord (Ebm7) may be inserted:
|Cmaj7 |Em7 Ebm7 |Dm7 |G7 |

A chromatic passing chord is a chord that is not in the harmonized scale

Suspended Chord (Sus chord)

A suspended chord (sus chord) is a chord in which the third is omitted, replaced usually with either a perfect fourth or a major second added, although the fourth is far more common. The lack of a minor or a major third in the chord creates an open sound.

The term is borrowed from the contrapuntal technique of suspension, where a note from a previous chord is carried over to the next chord, and then resolved down to the third or tonic, suspending a note from the previous chord.
However, in modern usage, the term concerns only the notes played at a given time; in a suspended chord the added tone does not necessarily resolve, and is not necessarily "prepared" (i.e., held over) from the prior chord.

Suspended second chords are merely inversions of suspended fourth chords, where the root of the sus2 is the fourth of the sus4. For example, Gsus2 (G-A-D) is an inversion of Dsus4 (D-G-A). Suspended fourth and second chords can be represented, in integer notation, as {0, 5, 7} and {0, 2, 7} respectively.

Suspended chords are commonly found in folk music and popular music. An example can be found in rock tunes, the verse of The Who song "Pinball Wizard" is a sequence of suspended fourth chords resolving to their major counterparts (Bsus4-B Asus4-A etc). In , Erasure's "A Little Respect" employs major to suspended changes in much of the song's harmonization.

A jazz sus chord is a dominant seventh chord with an added fourth (Gsus, for example), and may be written as a slash chord (F/G, or even Dm7/G) so as to show its function. Jazz from the 1940s on may retain the 3rd along with the 4th, though this makes the chord more dissonant, especially depending on whether the voicing is closed or open and whether the fourth is below or above the third.

MYSTIC CHORD

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Play "Prometheus" suite

In music the mystic chord or Prometheus chord is a complex six-note scale which loosely serves as the harmonic and melodic basis for some of the later pieces by Russian composer Alexander Scriabin.It consists of the pitch classes: C, F#, Bb, E, A, D. This is often interpreted as a quartal hexachord consisting of an augmented fourth, diminished fourth, augmented fourth, and two perfect fourths. However the chord may be spelled in a variety of ways and is related to other pitch collections.

Scriabin was a Russian composer and pianist who invented the first colour keyboard and notation for lights and colors based on his scale of Synesthetic colors. His symphony 'Prometheus: The Poem of Fire' (1910) was the first composition in history which included notation for lights and colors

Use
Some sources suggest that much of Scriabin's music is entirely based on the chord to the extent that whole passages are little more than long sequences of this chord, unaltered, at different pitches; but this is rarely the case.
More often than not, the notes are reordered in order to supply a variety of harmonic or melodic material. Certain of Scriabin's late pieces are based on other synthetic chords or scales that do not rely on the mystic chord.

Contrary to many textbook descriptions of the chord, which present the sonority as a series of superposed fourths, Scriabin most often manipulated the voicings to produce a variety of melodic and harmonic intervals (in the same manner that a dominant seventh, built on superposed thirds, will deploy intervals of a sixth, fourth, and/or second under inversion)

Fig.3 Image of Symphony Hall at Yale University showing a live performance of Scriabin's "Prometheus-Poem of Fire".
Scriabin's score was faithfully performed, including computer controlled lighting effects rendered according to Scriabin's instructions.

TRISTAN CHORD

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Fig.1 Tristan chord highlighted

The Tristan chord is a chord made up of the tones F, B, D# and G#.

The notes of the Tristan chord spell an inversion of a Locrian VII ; a conventional half-diminished seventh chord. What distinguishes the chord is its relationship to the harmonic structure of its development as well as the perceived ambiguity of its root.
At the time Tristan und Isolde was first heard (1865), the chord was considered innovative and bizarre. Musicologists of the twentieth century often claim the chord as the first instance of the disintegration of classical tonality structure.

What makes the Tristan motif unusual to the critic or musicologists is the suspension of tonal gravity; the Tristan chord is commonly touted to be of great significance in the move away from traditional harmonic resolution and toward atonal gestures; with this chord, Wagner actually provoked the sonic material to function as a delayed resolution of elements, a notion which was soon after to be explored by Claude Debussy and others.

AUGMENTED SIXTH CHORD

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The development and use of Augmented sixth chords represent a significant feature in the evolution of Western music.
These chord structures vary in their subtle differences based upon the locale in question. For ex., The French, Italian and German composers each contributed a feature of tonal structure that resulted in a lasting designation (naming convention) that remains unique to each musical oeuvre.

We will present the three types of augmented sixth chords and advise students to understand that these chord structures can best be regarded as transitional, and should be evaluated in the context of voice leading analysis.

In fact, the forms of the French Sixth, German Sixth and Italian Sixth have been subjected to common or generic labels that at times present confusion to musicologists. Further problems in nomenclature occur when attempting to categorize these chords in the context of modern usage, as the complexities of contemporary musical forms induce a variety of explanations for the most coherent root basis of chord identification.

For ex., many musicologists are still in disagreement as to the designation of Wagner's famous Tristan Chord; some even maintaining that the chord itself is rootless, or too ambiguous in its structure to be categorized at all.
The study of these augmented sixth chords is important as a prelude to understanding how the evolution of music into contemporary uses has been influenced by usage, rather than rigorous labeling.

French sixth Chords

The augmented sixth interval is typically between the sixth degree of the minor scale (henceforth b6) and the raised fourth degree (henceforth #4). With standard voice leading, the chord is followed directly or indirectly by some form of the dominant chord, in which both b6 and #4 have resolved to the fifth scale degree (henceforth 5). This tendency to resolve outwards to 5 is why the interval is spelled as an augmented sixth, rather than enharmonically as a minor seventh (b6 and b5). Although augmented sixth chords are more common in the minor mode they are also used in the major mode by borrowing b6 of the parallel minor scale.

Variants

There are several variants of the augmented sixth chord. Though each is named after a European nationality, theorists disagree on their precise origins and have struggled for centuries to define their roots, and fit them into conventional harmonic theory

Italian Sixth chords

The Italian sixth (It + 6 or It6) is derived from iv6 with an altered fourth scale degree, ab c f# in C major. This is the only augmented sixth chord comprising just three distinct notes; in four-part writing, the tonic pitch is doubled.
The French sixth is similar to the Italian, but with an additional tone, d; [ab c d f#] in C major.

This chord is called "French" because its notes are all contained within the same whole tone scale, lending a sonority common to French music in the 19th century (especially associated with Impressionist music).

GERMAN SIXTH CHORD

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The German sixth is also like the Italian, but with an added tone b3: F# in C major. In Classical music, however, it appears in much the same places as the other variants, though perhaps less used because of the contrapuntal difficulties

It is more difficult to avoid parallel fifths when resolving a German sixth chord to the dominant, V. These parallel fifths, referred to as Mozart fifths, were occasionally accepted by common practice composers. There are two ways they can be avoided:
The b3 can move to either 1 or 2, thereby generating an Italian or French sixth, respectively, and eliminating the perfect fifth between b6 and b3.

The chord can resolve to a "six-four" chord, functionally either as a cadential six-four intensification of V, or as the second inversion of I; the cadential six-four, in turn, resolves to a root-position V.

This progression ensures that, in its voice leading, each pair of voices moves either by oblique motion or contrary motion and avoids parallel motion altogether. In minor modes, both 1 and b3 do not move during the resolution of the German sixth to the cadential six-four. In major modes, b3 can be enharmonically respelled as #2 if it resolves upwards to b3, similar in voice leading to the resolution of French sixth to the cadential six-four.

This respelled chord is sometimes referred to as the English, Swiss or Alsatian sixth chord. (The respelled chord is sometimes erroneously labeled a "doubly augmented sixth chord".

AUGMENTED SIXTH INVERSIONS

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Noted international musicologists have explained the chord of the French Sixth Ab—C—D—F# in the key of C as being a chromatically altered version of a seventh chord on the second degree of the scale, and therefore gives the root as 'D'.

The German Sixth Ab—C—E- F# is explained as a chromatically altered ninth chord on the same root, but with the root omitted.)

The tendency of the interval of the augmented sixth to resolve outwards is therefore explained by the fact that the Ab, being a dissonant note, a diminished fifth above the root (D), and flatted, must fall, whilst the F# - being chromatically raised - must rise.

On the contrary, Tchaikovsky considers the augmented sixth chords, rather than being built on the minor sixth degree (Ab in C), as being altered dominant.

In his Guide to the practical study of harmony considers the augmented sixth chords to be inversions of the diminished triad and of dominant and diminished seventh chords with the second degree chromatically lowered, and accordingly resolving into the tonic.
He notes that, "some theorists insist upon [augmented sixth chord's] resolution not into the tonic but into the dominant triad, and regard them as being erected not on the altered 2-nd degree, but on the altered 6-th degree in major and on the natural 6-th degree in minor", yet calls this view, "fallacious", insisting that a, "chord of the augmented sixth on the 6-th degree is nothing else than a modulatory degression into the key of the dominant".

This would make the chord of the augmented sixth a member of a large group of chords with an altered second degree (which includes the Neapolitan chord.)

Enharmonic equivalency of the French sixth
The French sixth has two characteristics in common with the diminished seventh chord:
1. Both chords are constructed of two superimposed tritones; in the French sixth, between b6—2 (Ab—D) and 1—#4 (C—F#). Thus, both have inversional symmetry;

2. Both are enharmonically equivalent at the tritone; i.e., both chords transposed up or down a tritone will result in the same pitches as the original.

Irregular resolution through augmented sixth equivalence

All variants of augmented sixth chords are closely related to the applied dominant V7 of bII; both Italian and German variants are enharmonically identical to dominant seventh chords. For example, in the key of C (I), the German sixth chord, Ab—C—Eb—F#, could be reinterpreted as Ab—C—Eb—Gb, the applied dominant of Db (V/Db).

Classical harmonic theory would notate the "tritone substitute" as an augmented sixth chord on b2. (see image below) The Augmented sixth chord can either be the It+6 enharmonic to a dominant 7th chord without the 5th, Gr+6, enharmonically equivalent to a dominant 7th chord with the 5th, or enharmonically equivalent to the Lydian dominant without the 5th, all of which serve in a classical context as a substitute for the secondary dominant of V

AUGMENTED SIXTH FUNCTIONS

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Examples

The following excerpt shows an augmented sixth chord in inversion used by Bach. At the end of the second measure, the augmented sixth is inverted to create a diminished third or tenth between the bass and the soprano (C#/Eb); these two voices resolve inward to an octave:

Augmented sixth chords are occasionally used with a different chord member in the bass.
Since there is no consensus among theorists that they are in root position in their normal form, the word "inversion" isn't necessarily accurate, but is found in some textbooks, nonetheless.

Sometimes, "inverted" augmented sixth chords occur as a product of voice leading.

SEVENTH CHORDS

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Seventh chords are composed of four tonal elements; root, third, fifth and seventh scale degrees
In those cases whire the chordal scale elements are restricted to three voices the fifth is usally omitted.
The important interval is the 3rd-7th; notably where the seventh is lowered a half-step to produce the tritone interval with the 3rd, which provides a dominant feel to the chord and when used in toniczations and cadential modulations results in an increased tension due to the tritone.
Fig. 1 Diminished 7th on B vs.G7b9 comparison.

Fig. 2 12 instances of 7th chords on G, major, minor and diminished (augmented fifth)

NINTH CHORDS

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Generic ninth chords contain the root, third, fifth, seventh and ninth scale steps as stacked tertial harmonic elements (3rds) .
There is a difference between a major ninth chord and a dominant ninth chord. A dominant ninth is a dominant chord (and minor seventh) with a ninth. A major ninth chord (e.g., Cmaj9), as an extended chord, adds the major seventh along with the ninth to the major triad. Thus, a Cmaj9 consists of C E G B and D.

When the symbol "9" is not preceded by the word "major" or "maj" (e.g., C9), the chord is a dominant ninth. That is, the implied seventh chord is a dominant seventh, i.e. a major triad plus the minor seventh, to which the ninth is added: e.g., a C9 consists of C, E, G, Bb and D. A C dominant ninth (C9) would usually be expected to resolve to an F major chord (the implied key, C being the dominant of F). The ninth is commonly chromatically altered by half-step either up or down to create more tension and dissonance. Fétis tuned the chord 4:5:6:7:9. In the common practice period, "the root, 3rd, 7th, and 9th are the most common factors present in the V9 chord," with the 5th, "typically omitted".
The ninth and seventh usually resolve downward to the fifth and third of I.

Example of tonic dominant ninth chords include Bobby Gentry's "Ode to Billie Joe" and Wild Cherry's "Play That Funky Music". James Brown's "I Got You (I Feel Good)" features a striking dominant 9th arpeggio played staccato at the end of the opening 12-bar sequence. The opening phrase of Chopin’s well-known "Minute Waltz" climaxes on a dominant 9th chord:

Fig. 1 Three versions of diminished 7th chords.

fig 2. An inventory of commom ninth chords.

NINTH CHORDS UPPER FUNCTIONS

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The first point to make is that extensions of the tenth and twelve are just thirds and fifths plus an octave. The extensions of real interest are the ninth, eleventh and thirteenth. The chords are named for the extension; so, ninth chords, eleventh chords and thirteenth chords. The extensions are added to seventh chords, the quality and function of which is preserved. Thus, a dominant chord with an added ninth remains a dominant chord.

It is assumed that ninths are added to seventh chords to produce ninth chords, that eleventh and ninths are both added to seventh chords to produce eleventh chords and that thirteenths, elevenths and ninths are all added to seventh chords to give thirteenth chords. So if one calls a chord an eleventh it is assumed that the ninth and eleventh are present and that there is a seventh chord present too. The quality of the chord is determined by the seventh and the greatest extension names the chord. Thus, a major thirteenth chord will be a major seventh chord plus a ninth, an eleventh and a thirteenth, while a dominant ninth is a dominant seventh chord plus a ninth.

THIRTEENTH CHORDS

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A thirteenth chord is the stacking of six thirds. Thus a thirteenth chord is a tertian (built from thirds) chord containing the interval of a thirteenth, and is an extended thirteenth if it includes the ninth and/or the eleventh.

Dominant thirteenth chord in four-part writing. 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 13th.

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.

Dominant thirteenth chord Debussy's Prelude to the Afternoon of a Faun. (1894)
In modern pop/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 Bb and A.
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, a major seventh.

SLASH CHORDS

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In popular music a slash chord or slashed chord, also compound chord, is a chord whose bass note or inversion is indicated by the addition of a slash and the letter of the bass after the root note letter

"So What" Chord

In jazz a So What chord is a particular 5-note chord voicing such as employed by Bill Evans in the "'amen' response to the head of the tune "So What".
For example, an 'Eminor' "So What" chord (see example) is an Em7sus4 voicing, or as a polychord:

Bill Evans was the first to record the use of this chord structure when a member of the Miles Davis group. Notice the form of the 'call' laid down by the bass, and subsequent 'response' in the following measure from the piano-later the ensemble.

From the top note downwards, it consists of a major third interval followed by three perfect fourth intervals. The So What chord is often used as an alternative to quartal voicings and may be used in diatonic and chromatic planing, and is identical to the standard tuning of a guitar's bottom five strings (minus the top E-string).
It is essentially a minor eleventh chord (-11, m11), arranged as it would be played on a guitar (root, 4th, b7th, b3rd, 5th).

It may also be thought of as a five-note quartal chord (built from fourths) with the top note lowered by a semitone.
More modern sounding than "tertial chords" (built from thirds), it is useful in comping; since the structure of quartal harmony is usually vague, many roots may be applied to the So What chord and it may work well in various contexts including a major scale context; a Mixolydian mode context; or a minor context.

For example, the E chord described above can also be C6b9, Asus4 7 9, G69, Dsus2 4 6 [no 7], F lydian (F#9 #11 13 [no 5]) or F# phrygian (F#m7b9 11 b13 [no 5]).

The circle of fifths- the dominant or secondary dominant will always be found immediately clockwise of the tonic or tonicized chord and functionally resolves counterclockwise to that chord. For example, in C: V is G and resolves to C, V/V is D and resolves to G.

SECONDARY DOMINANT

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Secondary dominant (also applied dominant) is an analytical label for a specific harmonic device, It refers to a dominant-like function of a chromatically-altered chord built on a scale degree other than the 5th of the prevailing key, with V7/V, the dominant of the dominant, "being the most frequently encountered.

The chord to which a secondary dominant progresses can be thought of as a briefly tonicized chord or pitch.
The secondary dominant terminology is still usually applied even if the chord resolution is non-functional (for example if V/ii is not followed by ii)

To further illustrate, here are the secondary dominants of C major, given as dominant seventh chords. They are shown leading into their respective tonics, as given in the second inversion. Secondary dominant (V/ii resolving to ii) vs. chromatic mediant (VI progressing to I) In C major: C-A-d vs. C-A-C. Generic Progressions
When used in music, a secondary dominant is very often (though not inevitably) directly followed by the chord of which it is the dominant.
Thus V/ii is normally followed by ii, V/vi by vi, and so on.

This is similar to the general pattern of music wherein the simple chord V is often followed by I. The tonic is said to "resolve" the slight dissonance created by the dominant. Indeed, the sequence V/X + X, where X is some basic chord, is thought of by some musicians as a tiny modulation acting as a miniature dominant-tonic sequence in the key of X.

SECONDARY DOMINANT (cont'd)

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On the 4th beat of measure #1 see an example of a German Sixth chord-the typical usage would be that of a preparatory chord for a dominant or in this case secondary dominant chord preceded by the chord in interval form.
The Bb in the bass makes an equivalent root-seventh enharmonic interval.

History

The concept of the secondary dominant was not widely recognized in writings on music theory prior to the 20th century. Before this time, a secondary dominant, along with its chord of resolution, was considered to be a modulation.

Mozart’s Usage

In the Fifth edition of "Harmony" by Walter Piston and Mark DeVoto, a passage from the last movement of Mozart’s Piano Sonata K. 283 in G major serves as one illustration of secondary dominants. Below, the harmony alone is first given, labeled both for the literal names of the chords and for their chord number in the key of G major.

Mozart used many modern harmonic and melodic devices in his compositions. The secondary dominants that he frequently inserted into his works predated the impressionist innovative excursions into altered musical forms.

Although highly innovative, Mozarts compositions fall within the rubric of conventional Common Practice Period elements and structures.

Study his works to gain a fuller understanding of the Circle of Fifths concept and tonicization of chord movements as well as modulations.

QUARTAL CHORDS

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In music, quartal harmony is the building of harmonic structures with a distinct preference for the intervals of the perfect fourth, the augmented fourth and the diminished fourth.

At left, Alexander Scriabin's "Mystic" chord ,which is a complex tonal structure composed of intervals that are open to characterization.

Quintal harmony is harmonic structure preferring the perfect fifth, the augmented fifth and the diminished fifth.
In modern tuning, the augmented fourth and the diminished fifth are identical and are often called the tritone because the interval between the two notes is three tones.

Use of the terms quartal and quintal arises from a contrast, compositional or perceptual, with traditional tertian harmonic constructions. Listeners familiar with music during and after the Common practice period perceive tonal music as that which uses major and minor chords and scales, wherein both the major third and minor third constitute the basic structural elements of the harmony.

Quintal harmony (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 harmony. Indeed, a circle of fifths can be arranged in fourths (G -> C -> F -> Bb etc. are fifths when played a "circle of fourths".

Definition

The concept of quartal harmony outlines a formal harmonic structure based on the use of the interval of a perfect fourth to form chords. The fourth, thus, substitutes for the third as used in chords based on major and minor thirds. Although the fourth replaces the third in chords, quartal harmony rarely replaces tertian harmony in full works. Instead, the two types of harmony are found side by side.

USAGE HISTORY

parallel developments in both vocal and instrumental music, occurred in the traditional music of many non-western cultures. Some composers who have featured quartal or quintal harmonies in their work include Arnold Schoenberg, Béla Bartók, and Steve Reich.

In the Middle Ages, simultaneous notes a fourth apart were heard as a consonance. During the Common practice period (between about 1600 and 1900), this interval came to be heard either as a dissonance (when appearing as a suspension requiring resolution in the voice leading) or as a consonance (when the tonic of the chord appears in parts higher than the fifth of the chord).
In the later 19th century, during the breakdown of tonality in Classical music, all intervallic relationships were once again reassessed. Quartal harmony was developed in the early 20th century as a result of this breakdown and reevaluation of tonality. Jazz and rock of the 1960s frequently used quartal harmony.

Precursors

The Romantic composers Frédéric Chopin and Franz Liszt used the special "thinned out" sound of fourth-chords in late works for piano ( La lugubre gondola, shown below, and other works).

OTHER PRECURSORS

The Tristan chord is made up of the notes F, B, D# and G# and is the very first chord heard in Richard Wagner's opera Tristan und Isolde. The bottom two notes make up an augmented fourth the upper two make up a perfect fourth. This layering of fourths in this context has been seen as highly significant.

The chord had been found in earlier works (notably Beethoven's Piano Sonata No. 18) but Wagner's usage was significant, first because it is seen as moving away from traditional tonal harmony and even towards atonality, and second because with this chord Wagner actually provoked the sound or structure of musical harmony to become more predominant than its function, a notion which was soon after to be explored by Debussy and others.

Beethoven's usage of the chord is of short duration and it resolves in the accepted manner; whereas Wagner's usage lasts much longer and resolves in a highly unorthodox manner for the time. Despite the layering of fourths, it is rare to find musicologists identifying this chord as "quartal harmony" or even as "proto-quartal harmony", since Wagner's musical language is still essentially built on thirds, and even an ordinary dominant seventh chord can be laid out as augmented fourth plus perfect fourth (F-B-D-G).

Wagner's unusual chord is really a device to draw the listener in to the musical-dramatic argument that the composer in presenting us with. However, fourths become important later in the opera, especially in the melodic development.
From 1850 to 1900, the application of tonality began to dissolve as evidenced in the works of composers of the Late Romantic such as Wagner, Anton Bruckner, Gustav Mahler and Claude Debussy, and as the 20th century began with tonality no longer a strong binding force, quartal harmony became one of the new means of expression.

At the beginning of the 20th century, fourth-based chords finally became an important element of harmony. Alexander Scriabin used a self-developed system of transposition using fourth-chords, like his Mystic chord in his 6th Piano Sonata. This was best realized by his work Prometheus: The Poem of Fire. Earlier sketches left by Scriabin indicate that the composer apparently first intended that the work develop from a single non-transposed tonal centre.

Opening measures of Wagner's Tristan and Isolde

Fourth-based harmony became important in the work of Slavic and Scandinavian composers such as Modes Mussorgsky, Leoš Janácek, and Jean Sibelius. These composers used this harmony in a pungent , uncovered, almost archaic way, often incorporating the folk music of their particular homelands.

In the example from Mussorgsky's piano-cycle Pictures at an Exhibition, the fourth always makes an "rude" entrance. Rudiments of quartal harmony appear in Janácek's rhapsody Taras Bulba, and his operas The Makropulos Affair and From the House of the Dead. Descending fourths and sevenths can be found dominating the writing.

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