Jazz Harmony
Chord Substitution
In music theory, chord substitution is the technique of using a chord in place of another in a progression of chords, or a chord progression. A chord substitution occurs when a chord is replaced by another that is made to function like the original. Usually substituted chords possess two pitches in common with the triad that they are replacing.
Secondary Chords
Secondary chords are a type of altered or borrowed chord, chords that are not part of the music piece's key. They are the most common sort of altered chord in tonal music. Secondary chords are referred to by the function they have and the key or chord in which they function. Conventionally, they are written with the notation "function / key". Thus, the most common secondary chord, the dominant of the dominant, is written "V/V" and read as "five of five" or "the dominant of the dominant". The major or minor triad on any diatonic scale degree may have any secondary function applied to it; secondary functions may even be applied to diminished triads in some special circumstances.
Function / Key
The function is applied to the key. For example with V/V in the key of C. The function is V or the Dominant chord. This is not applied to the key of C, but to the key in the function which is the V (Dominant) of the key of C. So the resulting chord is the dominant of the key of G, which is D.
Secondary Dominant
A secondary dominant resolves down to the primary dominant, or the dominant in the current key. For example in the key of C, the secondary dominant is D. If we make it a D7, it will resolve to G, G7 will resolve to C. So the chord progression can be D7 - G7 - C. This follows a Circle of Fifths resolution. This sequence can be extended beyond one level which are known as Extended Dominants. An extended dominant chord is a secondary dominant seventh chord that resolves down by a fifth to another dominant seventh chord. A series of extended dominant chords continues to resolve downwards by the circle of fifths until it reaches the tonic chord. V/V/V is known as a Tertiary Dominant. V/V/V/V is known as a Quaternary Dominant.
Many of the following function examples are theoretical.
| Function/Key | Defined | Chord |
|---|---|---|
| V/ii | Dominant of D | A |
| V/iii | Dominant of E | B |
| V/IV | Dominant of F | C |
| V/V | Dominant of G | D |
| V/vi | Dominant of A | E |
| V/VII | Dominant of B | F# |
| Function/Key | Defined | Chord | Extended Progression |
|---|---|---|---|
| V/V/ii | Dominant of the Dominant of D | E | E7 - A7 - Dm7 |
| V/V/iii | Dominant of the Dominant of E | F# | F#7 - B7 - Em7 |
| V/V/IV | Dominant of the Dominant of F | G | G7 - C7 - F7 |
| V/V/V | Dominant of the Dominant of G | A | A7 - D7 - G7 |
| V/V/vi | Dominant of the Dominant of A | B | B7 - E7 - Am7 |
| V/V/vii° | Dominant of the Dominant of B | C# | C#7 - F#7 - B°7 |
Secondary Leading Tone
In music theory, a secondary leading-tone chord is a secondary chord that is rooted on a tone that is a leading-tone of (in short, has a strong affinity to resolve to) a tone just 1 semitone from that root (typically 1 semitone above, though can be below). Like the secondary dominant it can be used as tonicization of only one subsequent chord (which will be rooted in the resolution tone), or the music can continue with other chords/notes in the key of that chord's root for a phrase, or even longer to be considered a modulation to that key. This one-semitone-apart resolution of the secondary leading-tone is in contrast to the secondary dominant which resolves through a wider distance of perfect fifth below or perfect fourth above the chord's root (as per the two distances between dominant and tonic).
Because of their symmetry, secondary leading-tone diminished seventh chords are also useful for modulation; all four notes may be considered the root of any diminished seventh chord.
| Function/Key | Defined | Chord |
|---|---|---|
| vii°/ii | Leading Tone of D | C#° |
| vii°/iii | Leading Tone of E | D#° |
| vii°/IV | Leading Tone of F | E#° (F) |
| vii°/V | Leading Tone of G | F#° |
| vii°/vi | Leading Tone of A | G#° |
| vii°/VII | Leading Tone of B | A#° |
Secondary Supertonic
The secondary supertonic chord, or secondary second, is a secondary chord that is on the supertonic scale degree. Rather than tonicizing a degree other than the tonic, as does a secondary dominant, it creates a temporary dominant.
| Function/Key | Defined | Chord |
|---|---|---|
| ii/ii | Supertonic of D | Em |
| ii/iii | Supertonic of E | F#m |
| ii/IV | Supertonic of F | Gm |
| ii/V | Supertonic of G | Am |
| ii/vi | Supertonic of A | Bm |
| ii/vii | Supertonic of B | C#m |
Secondary Subdominant
The secondary subdominant is the subdominant (IV) of the tonicized chord.
| Function/Key | Defined | Chord |
|---|---|---|
| IV/ii | Subdominant of D | G |
| IV/iii | Subdominant of E | A |
| IV/IV | Subdominant of F | Bb |
| IV/V | Subdominant of G | C |
| IV/vi | Subdominant of A | D |
| IV/VII | Subdominant of B | E |
Secondary Mediant
| Function/Key | Defined | Chord |
|---|---|---|
| iii/ii | Mediant of D | F#m |
| iii/iii | Mediant of E | G#m |
| iii/IV | Mediant of F | Am |
| iii/V | Mediant of G | Bm |
| iii/vi | Mediant of A | C#m |
| iii/VII | Mediant of B | Ebm |
Secondary Submediant
| Function/Key | Defined | Chord |
|---|---|---|
| vi/ii | Submediant of D | Bm |
| vi/iii | Submediant of E | C#m |
| vi/IV | Submediant of F | Dm |
| vi/V | Submediant of G | Em |
| vi/vi | Submediant of A | F#m |
| vi/VII | Submediant of B | G#m |
Secondary Subtonic
| Function/Key | Defined | Chord |
|---|---|---|
| bVII/ii | Subtonic of D | C |
| bVII/iii | Subtonic of E | D |
| bVII/IV | Subtonic of F | E |
| bVII/V | Subtonic of G | F# |
| bVII/vi | Subtonic of A | G |
| bVII/vii | Subtonic of B | A# |
Tonicization
In music, tonicization is the treatment of a pitch other than the overall tonic (the "home note" of a piece) as a temporary tonic in a composition. In Western music that is tonal, the piece is heard by the listener as being in a certain key. A tonic chord has a dominant chord; in the key of C major, the tonic chord is C major and the dominant chord is G major or G dominant seventh. The dominant chord, especially if it is a dominant seventh, is heard by Western composers and listeners familiar with music as resolving (or "leading") to the tonic, due to the use of the leading note in the dominant chord. A tonicized chord is a chord other than the tonic chord to which a dominant or dominant seventh chord progresses. When a dominant chord or dominant seventh chord is used before a chord other than the tonic, this dominant or dominant seventh chord is called a secondary dominant. When a chord is tonicized, this makes this non-tonic chord sound temporarily like a tonic chord.
Modulation
In music, modulation is the change from one tonality (tonic, or tonal center) to another. This may or may not be accompanied by a change in key signature (a key change). Modulations articulate or create the structure or form of many pieces, as well as add interest. Treatment of a chord as the tonic for less than a phrase is considered tonicization.
Common Chord Modulation
Common Chord Modulation, also known as Diatonic Pivot Chord Modulation, is a technique in music that uses a chord shared by two keys to move from one key to another. The chord acts as a pivot, linking the two keys and making the transition smoother.
To compose a diatonic pivot chord modulation, you can:
- Identify the diatonic chords in each key
- Decide where in the progression to pivot to the new key
- Consider the harmonic function of the pivot chords
Composers often avoid using pivot chords that have a dominant function in the new key, as this can make the modulation sound abrupt.
For example, the Circle of Fifths is a great way to visually see keys that have a lof the same notes and consequently, same chords, in them. G major and D major are immediately adjacent to each other on the circle and have four triad chords in common: G, Bm, D and Em. This can be seen in the chart below, with common chords highlighted in green, which compares triad qualities. The I chord in G major, a G major chord is also the IV chord in D major, so I in G major and IV in D major are aligned on the chart.
| G Major | I G |
ii Am |
iii Bm |
IV C |
V D |
vi Em |
viio F#o |
|---|---|---|---|---|---|---|---|
| D Major | IV G |
V A |
vi Bm |
viio C#o |
I D |
ii Em |
iii F#m |
Any chord with the same root note and chord quality (major, minor, diminished) can be used as the pivot chord. The most common pivot chords are the predominant chords (ii and IV) in the new key.
The following example shows a pivot from C Major to G Major using the two common chords of Em and Am.
| C Major | I C |
ii Dm |
iii Em |
IV F |
V G |
vi Am |
viio Bo |
|---|---|---|---|---|---|---|---|
| G Major | IV C |
V D |
vi Em |
viio F#o |
I G |
ii Am |
iii Bm |
| Chord Progression: | C | F | G | Em | Am | D | G |
|---|---|---|---|---|---|---|---|
| Function C: | I | IV | V | iii | vi | ||
| Function G: | vi | ii | V | I |
Notice there are two pivot chords here: Em and Am. Because C Major and G Major are closely related keys (and thus, have several chords in common), we are at liberty to use more than one pivot chord. As a result, the modulation is seamless.
Altered Common Chord Modulation
Where an altered chord is used as a pivot chord in either the old or new key (or both), this would be referred to as altered common chord modulation, in order to distinguish the chromaticism that would be introduced from the otherwise diatonic method.
An altered chord is a chord that replaces one or more notes from the diatonic scale with a neighboring pitch from the chromatic scale. By the broadest definition, any chord with a non-diatonic chord tone is an altered chord. The simplest example of altered chords is the use of borrowed chords, chords borrowed from the parallel key, and the most common is the use of secondary dominants.
Enharmonic Modulation
An enharmonic modulation takes place when a chord is treated as if it were spelled enharmonically as a functional chord in the destination key, and then proceeds in the destination key. There are two main types of enharmonic modulations:
- dominant seventh/augmented sixth
- diminished seventh
Augmented Sixth Chord
In music theory, an augmented sixth chord contains the interval of an augmented sixth, usually above its bass tone. This chord has its origins in the Renaissance, was further developed in the Baroque, and became a distinctive part of the musical style of the Classical and Romantic periods.
Conventionally used with a predominant function (resolving to the dominant), the three most common types of augmented sixth chords are usually called the Italian Sixth, the French Sixth, and the German Sixth.
Augmented Sixth Interval
The augmented sixth interval is typically between the sixth degree of the minor scale, bscale degree 6, and the raised fourth degree, #scale degree 4. With standard voice leading, the chord is followed directly or indirectly by some form of the dominant chord, in which both bscale degree 6 and #scale degree 4 have resolved to the fifth scale degree, scale degree 5. This tendency to resolve outwards to scale degree 5 is why the interval is spelled as an augmented sixth, rather than enharmonically as a minor seventh (bscale degree 6 and #scale degree 5).
Although augmented sixth chords are more common in the minor mode, they are also used in the major mode by borrowing bscale degree 6 of the parallel minor scale.
| Italian 6th | French 6th | German 6th |
|---|---|---|
|
Bb E E C |
Bb Gb E C |
Bb G E C |
Any dominant seventh or German sixth can be reinterpreted as the other by respelling the m7 or A6 chord tone (respectively) in order to modulate to a key a half-step away (descending or ascending); if the fifth-from-root chord tone of a German sixth is omitted, the result is an Italian sixth. A diminished seventh chord meanwhile, can be respelled in multiple other ways to form a diminished seventh chord in a key a minor third (m3 as root), tritone (d5 as root) or major sixth (d7 as root) away. Where the dominant seventh is found in all diatonic scales, the diminished seventh is found only in the harmonic scale naturally; an augmented sixth is itself an altered chord, relying on the raised fourth scale degree.
By combining the diminished seventh with a dominant seventh and/or augmented sixth, altering only one pivot note (by a half tone), it is possible to modulate quite smoothly from any key to any other in at most three chords, no matter how distant the starting and ending keys (be aware that only when modulating between key signatures featuring double-sharps/flats may the need to respell natural notes enharmonically arise); however, this may or may not require the use of altered chords (operating in the harmonic minor without an augmented sixth would not) where the effect can be less subtle than other modulations. The following are examples used to describe this in chord progressions starting from the key of D minor (these chords may instead be used in other keys as borrowed chords, such as the parallel major, or other forms of the minor):
C# - E - G - Bb (dim. 7th), C - E - G - Bb (lowering the root a semitone to a modulating dom. 7th), F - A - C (quasi-tonic) leads to F major - a relative major modulation (though not enharmonic); but exactly the same progression enharmonically C# - E - G - Bb, C - E - G - A# (Ger. aug. 6th), E - G - B - E (quasi-tonic) leads somewhat unexpectedly to E natural/harmonic minor - a half-step modulation (ascending).
C# - E - G - Bb (dim. 7th), A - C# - E - G (lowering the 7th a semitone and respelling as a modulating dom. 7th), D - F# - A (quasi-tonic) leads to the key of D major - a parallel modulation (though not enharmonic). Enharmonically: C# - E - G - Bb, A - C# - E - F## (Ger. aug. 6th), C# - E - G# (quasi-tonic) modulates to C# minor - a major seventh modulation/half-step descending.
C# - E - G - Bb (dim. 7th), C# - Eb - G - Bb ≡ Eb - G - Bb - Db (lowering the major third a half tone and respelling as a modulating dom. 7th), Ab - C - Eb (quasi-tonic) leads to Ab major - a minor third and relative modulation (or tritone modulation if starting in D Major).
Note that in standard voice leading practice, any type of augmented sixth chord favors a resolution to the dominant chord, with the exception of the German sixth, where it is difficult to avoid incurring parallel fifths; to prevent this, a cadential six four is commonly introduced before the dominant chord (which would then typically resolve to the tonic to establish tonality in the new key), or an Italian/French sixth is used instead.
In short, lowering any note of a diminished seventh chord by a half tone leads to a dominant seventh chord (or German sixth enharmonically), the lowered note being the root of the new chord. Raising any note of a diminished seventh chord by a half tone leads to a half-diminished seventh chord, the root of which is a whole step above the raised note. This means that any diminished chord can be modulated to eight different chords by simply lowering or raising any of its notes. If also employing enharmonic respelling of the diminished seventh chord, such as that beginning the modulation in the above examples (allowing for three other possible diminished seventh chords in other keys), the versatility of this combination technique and the wide range of available options in key modulation become apparent.
This type of modulation is particularly common in Romantic music, in which chromaticism rose to prominence.
Other types of enharmonic modulation include the augmented triad (III+) and French sixth (Fr+6). Augmented triad modulation occurs in the same fashion as the diminished seventh, that is, to modulate to another augmented triad in a key: a major third (M3 as root) or minor sixth (A5 as root) away. French augmented sixth (Fr+6) modulation is achieved similarly but by respelling both notes of either the top or bottom major third (i.e. root and major third or diminished fifth and augmented sixth) enharmonically and inverting with the other major third (i.e. diminished fifth and augmented sixth becomes root and major third of the new Fr+6); either choice results in the same chord and key modulation (a tritone away), as the diminished fifth always becomes the new root.
Common Tone Modulation
Common-tone modulation uses a sustained or repeated pitch from the old key as a bridge between it and the new key (common tone). Usually, this pitch will be held alone before the music continues in the new key. For example, a held F from a section in Bb major could be used to transition to F major. This is used, for example, in Schubert's Unfinished Symphony. "If all of the notes in the chord are common to both scales (major or minor), then we call it a common chord modulation. If only one or two of the notes are common, then we call it common tone modulation."
Starting from a major chord, for example G major (G - B - D), there are twelve potential goals using a common-tone modulation: G minor, G# minor, Bb major, B major, B minor, C major, C minor, D minor, D major, Eb major, E major, E minor. Thus common-tone modulations are convenient for modulation by diatonic or chromatic third.
Chromatic Modulation
A chromatic modulation is so named because it occurs at the point of a chromatic progression, one which involves the chromatic inflection of one or more notes whose letter name, thus, remains the same though altered through an accidental.[15] Chromatic modulations are often between keys which are not closely related. A secondary dominant or other chromatically altered chord may be used to lead one voice chromatically up or down on the way to the new key. (In standard four-part chorale-style writing, this chromatic line will most often be in one voice.) For example, a chromatic modulation from C major to D minor:
| C Major | IV F |
V/ii A |
ii Dm |
|
|---|---|---|---|---|
| D Minor | i Dm |
(...) |
In this case, the IV chord in C major (F major) would be spelled F - A - C, the V/ii chord in C major (A major) spelled A - C# - E, and the ii chord in C major (D minor), D - F - A. Thus the chromaticism, C - C# - D, along the three chords; this could easily be part-written so those notes all occurred in one voice. Despite the common chord (ii in C major or i in D minor), this modulation is chromatic due to this inflection.
The consonant triads for chromatic modulation are bIII, bVI, bII, #iv, vii, and bVII in major, and (natural)iii, (natural)vi, bII, #iv, ii, and (natural)vii in minor.
In the example pictured, a chromatic modulation from F major to D minor:
| F Major | I F |
V C |
||||
|---|---|---|---|---|---|---|
| D Minor | V A |
i Dm |
iv Gm |
V A |
In this case, the V chord in F major (C major) would be spelled C - E - G, the V in D minor (A major) would be spelled A - C# - E. Thus the chromaticism, C - C# - D, which is here split between voices but may often easily be part-written so that all three notes occur in one voice.
The combination of chromatic modulation with enharmonic modulation in late Romantic music led to extremely complex progressions in the music of such composers as César Franck, in which two or three key shifts may occur in the space of a single bar, each phrase ends in a key harmonically remote from its beginning, and great dramatic tension is built while all sense of underlying tonality is temporarily in abeyance. Good examples are to be found in the opening of his Symphony in D minor, of which he himself said "I dared much, but the next time, you will see, I will dare even more..."; and his Trois Chorals for organ, especially the first and third of these, indeed fulfill that promise.
Phrase Modulation
Phrase (also called direct, static, or abrupt) modulation is a modulation in which one phrase ends with a cadence in the original key, and the next phrase begins in the destination key without any transition material linking the two keys. This type of modulation is frequently done to a closely related key - particularly the dominant or the relative major/minor key.
An unprepared modulation is a modulation "without any harmonic bridge", characteristic of impressionism.
For example:
| A | E | A | F | Bb | F | |
| A Major | I | V | I | |||
| F Major | I | IV | I |
When phrase modulation comes at or near the end of a musical piece, it is referred to as a truck driver's gear change, especially in popular music.
Sequential Modulation
A passage in a given key ending in a cadence might be followed by the same passage transposed (up or down) to another key, this being known as sequential modulation. Although a sequence does not have to modulate, it is also possible to modulate by way of a sequence. A sequential modulation is also called rosalia. The sequential passage will begin in the home key, and may move either diatonically or chromatically. Harmonic function is generally disregarded in a sequence, or, at least, it is far less important than the sequential motion. For this reason, a sequence may end at a point that suggests a different tonality than the home key, and the composition may continue naturally in that key.
Chain Modulation
Distant keys may be reached sequentially through closely related keys by chain modulation, for example C to G to D or C to C minor to Eb Major. A common technique is the addition of the minor seventh after each tonic is reached, thus turning it into a dominant seventh chord:
This might also be referred to as a Circle Progression as it moves through dominant sevenths of the Circle of Fifths counter-clockwise to a desination key
Changes Between Parallel Keys
Since modulation is defined as a change of tonic (tonality or tonal center), the change between minor and its parallel major or the reverse is technically not a modulation but a change in mode. Major tonic harmony that concludes music in minor contains what is known as a Picardy third. Any harmony associated with the minor mode in the context of major musical passages is often referred to as a borrowed chord, which creates mode mixture.