Inmusic,modulation is the change from one tonality (tonic, ortonal center) to another. This may or may not be accompanied by a change inkey signature (akey change). Modulations articulate or create the structure orform of many pieces, as well as add interest. Treatment of achord as the tonic for less than aphrase is consideredtonicization.
Modulation is the essential part of the art. Without it there is little music, for a piece derives its true beauty not from the large number of fixed modes which it embraces but rather from the subtle fabric of its modulation.
— Charles-Henri Blainville (1767)[2]
The quasi-tonic is the tonic of the new key established by the modulation. The modulating dominant is the dominant of the quasi-tonic. The pivot chord is a predominant to the modulating dominant and a chord common to both the keys of the tonic and the quasi-tonic. For example, in a modulation to the dominant, ii/V–V/V–V could be a pivot chord, modulating dominant, and quasi-tonic.
Common-chord modulation (also known as diatonic-pivot-chord modulation) moves from the original key to the destination key (usually aclosely related key) by way of a chord both keys share: "Most modulations are made smoother by using one or more chords that are common to both keys."[7] For example, G major and D major have four triad chords in common: G major, B minor, D major and E minor. This can be easily determined by a chart similar to the one below, 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. Therefore, chords that are not generally found in the style of the piece (for example, major VII chords in aJ. S. Bach-style chorale) are also not likely to be chosen as the pivot chord. The most common pivot chords are thepredominant chords (ii and IV) in the new key. In analysis of a piece that uses this style of modulation, the common chord is labeled with its function in both the original and the destination keys, as it can be heard either way.
Where analtered 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 thechromaticism that would be introduced from the otherwise diatonic method.
An enharmonic modulation takes place when a chord is treated as if it were spelledenharmonically 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, and (fully)diminished seventh. Any dominant seventh orGerman 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 anItalian 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.[10] 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 analtered 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 asborrowed chords, such as theparallel major, or other forms of the minor):
(Ger. aug. 6th), C♯–E–G♯ (quasi-tonic) modulates to C♯ minor—a major seventh modulation/half-step descending.Note that in standardvoice leading practice, any type of augmented sixth chord favors a resolution to the dominant chord (see:augmented sixth chord), with the exception of the German sixth, where it is difficult to avoid incurringparallel fifths; to prevent this, acadential 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 inRomantic music, in whichchromaticism rose to prominence.
Other types of enharmonic modulation include the augmented triad (III+) andFrench 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.
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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 B♭ major could be used to transition to F major. This is used, for example, inSchubert'sUnfinished Symphony. "If all of the notes in the chord are common to both scales (major or minor), then we call it acommon chord modulation. If only one or two of the notes are common, then we call itcommon tone modulation."[13][self-published source?]
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, B♭ major, B major, B minor, C major, C minor, D minor, D major, E♭ major, E major, E minor.[14] Thus common-tone modulations are convenient for modulation by diatonic or chromatic third.
A chromatic modulation is so named because it occurs at the point of achromatic progression, one which involves thechromatic inflection of one or more notes whose letter name, thus, remains the same though altered through anaccidental.[15] Chromatic modulations are often between keys which arenot closely related.[15] Asecondary dominant or other chromaticallyaltered chord may be used to lead one voice chromatically up or down on the way to the new key. (In standard four-partchorale-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♭III,♭VI,♭II,♯iv, vii, and♭VII in major, and♮iii,♮vi,♭II,♯iv, ii, and♮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 lateRomantic music led to extremely complex progressions in the music of such composers asCésar 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 hisSymphony in D minor, of which he himself said (seeWikiquote) "I dared much, but the next time, you will see, I will dare even more..."; and hisTrois Chorals for organ, especially the first and third of these, indeed fulfill that promise.
Phrase (also called direct, static, or abrupt) modulation is a modulation in which one phrase ends with acadence 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 aclosely related key—particularly the dominant or the relative major/minor key.
An unprepared modulation is a modulation "without any harmonic bridge", characteristic ofimpressionism.[17]
For example:
| A | E | A | F | B♭ | 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 atruck driver's gear change, especially in popular music.
"A passage in a given key ending in a cadence might be followed by the same passagetransposed (up or down) to another key," this being known as sequential modulation.[19] Although asequence 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 eitherdiatonically 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 differenttonality than the home key, and the composition may continue naturally in that key.
Distant keys may be reached sequentially throughclosely related keys by chain modulation, for example C to G to D or C to C minor to E♭ major.[21] A common technique is the addition of the minor seventh after each tonic is reached, thus turning it into a dominant seventh chord:
| D | → | D7 | G | → | G7 | C | → | C7 | F |
| I | → | V7 | I | → | V7 | I | → | V7 | I |
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 inmode. Major tonic harmony that concludes music in minor contains what is known as aPicardy third. Any harmony associated with the minor mode in the context of major musical passages is often referred to as aborrowed chord, which createsmode mixture.
The most common modulations are toclosely related keys (I, V, IV, vi, iii, ii).[23] V (dominant) is the most frequent goal and, in minor, III (relative key) is also a common goal.[24] Modulation to thedominant or thesubdominant is relatively simple as they are adjacent steps on thecircle of fifths. Modulations to therelative major or minor are also simple, as these keys share all pitches in common. Modulation to distantly related keys is often done smoothly through using chords in successive related keys, such as through the circle of fifths, the entirety of which may be used in either direction:
If a given key were G major, the following chart could be used:
| C | — | G | — | D |
From G (which is the given key), a musician would go P5 (a perfect fifth) above G (which is D) and also P5 below G (which is C).
From this, the musician would go to G major's relative minor which is E minor, and potentially to C major and D major's related minor as well (a musician who does not know the related minor for C and D major may also go P5 below or above E minor).
| C | — | G | — | D |
| | | | | | | ||
| Am | Em | Bm |
By using the relative minor keys one can find the specific key that the key can modulate into.
Many musicians use the circle of fifths to find these keys and make similar charts to help with the modulation.
In certainclassical music forms, a modulation can have structural significance. Insonata form, for example, a modulation separates the first subject from the second subject. Frequent changes of key characterize thedevelopment section of sonatas. Moving to thesubdominant is a standard practice in thetrio section of amarch in a major key, while a minor march will typically move to the relative major.
Changes of key may also represent changes in mood. In many genres of music, moving from a lower key to a higher often indicates an increase in energy.
Change of key is not possible in thefull chromatic or thetwelve tone technique, as the modulatory space is completely filled; i.e., if every pitch is equal and ubiquitous there is nowhere else to go. Thus other differentiating methods are used, most importantly ordering andpermutation. However, certain pitch formations may be used as a "tonic" or home area.
The popularity of the key change varies with musical fashion over time. In Westernpopular music, from the 1960s to the 1990s, about one quarter of number-one hits on theBillboard Hot 100 featured a key change, but only one number-one hit in the 2010s had one.[25]
Though modulation generally refers to changes of key, any parameter may be modulated, particularly in music of the 20th and 21st century.Metric modulation (known also as tempo modulation) is the most common, while timbral modulation (gradual changes in tone color), and spatial modulation (changing the location from which sound occurs) are also used.
Modulation may also occur from a single tonality to apolytonality, often by beginning with a duplicated tonic chord and modulating the chords in contrary motion until the desired polytonality is reached.
