Editing Modulation (music) (section)

===Enharmonic modulation===
[[File:Schubert - op.9 D.365, mm.17-24 German sixth modulation.png|350px|thumb|Modulation from D major to D{{music|flat}} major in [[Schubert]]'s Op. 9, No. 14, D. 365, mm. 17–24, using the [[German sixth]], in the new key, that is enharmonic to the dominant seventh in the old key.<ref>Benward & Saker (2009), pp. 214–15.<!--ibid--></ref>{{audio|Schubert - op.9 D.365, mm.17-24 German sixth modulation.mid|Play}}]]
[[File:Schubert - op. 29, D.804, I, mm.144-49 enharmonic modulation.png|350px|thumb|Modulation from A minor to E{{music|flat}} minor in Schubert's Op.29, D. 804, I, mm.144-49, using vii{{music|dim}}<sup>7</sup>: G{{music|#}}{{music|dim}}<sup>7</sup> ≡ D{{music|dim}}<sup>7</sup> (≡ B{{music|dim}}<sup>7</sup> ≡ F{{music|dim}}<sup>7</sup>)<ref>Benward & Saker (2009), p.220.<!--ibid--></ref>{{audio|Schubert - op. 29, D.804, I, mm.144-49 enharmonic modulation.mid|Play}}]]

An enharmonic modulation takes place when a chord is treated as if it were spelled [[enharmonic]]ally as a functional chord in the destination key, and then proceeds in the destination key. There are two main types of enharmonic modulations: [[seventh chord|dominant seventh]]/[[augmented sixth chord|augmented sixth]], and (fully) [[seventh chord|diminished seventh]]. 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.<ref>{{Cite web |title=Enharmonic Reinterpretation |url=http://learnmusictheory.net/PDFs/pdffiles/03-09-EnharmonicReinterpretation.pdf |publisher=Feezell, M. |access-date=2016-04-05}}</ref> 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 chord]]s, such as the [[parallel major]], or other forms of the minor):

*C{{music|sharp}}–E–G–B{{music|flat}} (dim. 7th), C–E–G–B{{music|flat}} (lowering the root a semitone to a modulating dom. 7th), F–A–C (quasi-tonic) leads to F major—a [[relative key|relative]] major modulation (though not enharmonic); but exactly the same progression enharmonically C{{music|sharp}}–E–G–B{{music|flat}}, C–E–G–A{{music|sharp}} (Ger. aug. 6th), E–G–B–E (quasi-tonic) leads somewhat unexpectedly to E natural/harmonic minor—a half-step modulation (ascending).
*C{{music|sharp}}–E–G–B{{music|flat}} (dim. 7th), A–C{{music|sharp}}–E–G (lowering the 7th a semitone and respelling as a modulating dom. 7th), D–F{{music|sharp}}–A (quasi-tonic) leads to the key of D major—a parallel modulation (though not enharmonic). Enharmonically: C{{music|sharp}}–E–G–B{{music|flat}}, A–C{{music|sharp}}–E–F{{music|x}} (Ger. aug. 6th), C{{music|sharp}}–E–G{{music|sharp}} (quasi-tonic) modulates to C{{music|#}} minor—a major seventh modulation/half-step descending.
*C{{music|sharp}}–E–G–B{{music|flat}} (dim. 7th), C{{music|sharp}}–E{{music|flat}}–G–B{{music|flat}} ≡ E{{music|flat}}–G–B{{music|flat}}–D{{music|flat}} (lowering the major third a half tone and respelling as a modulating dom. 7th), A{{music|flat}}–C–E{{music|flat}} (quasi-tonic) leads to A{{music|flat}} 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 (see: [[augmented sixth 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+<sup>6</sup>). 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+<sup>6</sup>) 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.