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Modulation library

This page contains a collection of modulation procedures, that is, harmonic progressions that can be used to effect a change of key in tonal harmony. They are stripped down to their barest essentials (more or less), and would rarely be used in the form shown. For ease of reference, the modulations are arranged in order of interval, largest first. In all cases, the starting key is shown as C. Unless noted otherwise, these procedures are all found with major and minor modes in both the old and new keys, but only major-to-major is (usually) shown.

Notes:

  • Roman numerals in capital letters indicate major chords, lower-case minor chords. However, in some cases these can be interchanged to interesting effect
  • A roman number followed by a 7 indicates the minor seventh rather than major seventh
  • A roman number followed by #6 indicates an augmented sixth on that degree of the scale — the number does not indicate on the imaginary, missing root that some authors propose these chords should be thought to be based on
  • A roman number preceded by a b (flat) sign indicates a root on that degree of the scale, but flattened
  • A note on diminished sevenths: these chords are so tonally ambiguous that they can be used, either singly or in succession, to stand between almost any pair of keys, major or minor. There doesn't seem to be much reason to document the eleven (or 22, if enharmonic equivalences are included) distinct possibilities here

Up a fifth / down a fourth

For example, modulation from tonic to dominant; modulation from subdominant to tonic
Via supertonic (seventh) of old key (= dominant (seventh) of new key)
Via tonic minor of old key and dominant of new key. If the old key is minor, then this procedure just reduces to the previous one
Via subdominant and supertonic (seventh) of old key (= dominant (seventh) of new key)
Via 'Neapolitan sixth' (first inversion of triad on flattened supertonic) of new key and dominant (seventh) of new key. Note that this procedure is technically applicable to modulation only from the minor mode only (see below). Widely used from the Baroque onwards
Via 'Neapolitan sixth' (first inversion of triad on flattened supertonic) of new key and dominant (seventh) of new key. Note that this procedure is technically applicable to modulation only from the major mode only. If the old key is minor, then the second chord is on the flattened submediant, even though the same notes are played. Widely used from the Baroque onwards
Via ambiguous augmented sixth. Other flavours of augmented six are also possible. It is conventional to interpret this progression as an ambiguous augmented sixth: the augmented sixth on bVI in the tonic is the same as that on bII in the dominant. Alternatively, we could just take the 'pair' of augmented sixths as a single augmented sixth on bII in the dominant, with no great loss of rigour. The pivot chord would then be the initial tonic in the old key

Down a fifth / up a fourth

For example, modulation from dominant to dominant, modulation from tonic to subdominant.
Directly via supertonic (seventh) of new key. This is probably the most widely used modulation in all periods of Western music
Via supertonic (seventh) and dominant seventh of new key
Via 'Neapolitan sixth' (first inversion of triad on flattened supertonic) of old key and dominant seventh of new key. Note that this procedure is usually described as suitable for modulation only to the subdominant minor
Via ambiguous augmented sixth. This procedure seems to be less used than the complementary one that raises a fifth — it's hard to make it sound smooth
Via the subdominant minor of the old key, which is the tonic of the new key. This procedure seems to be used largely for major-to-minor modulations

Up/down a diminished fifth

Via supertonic seventh of old key (= augmented sixth on flattened sixth of new key). Note that the augmented sixth has to be enharmonically respelled to fit the key convention of the new key
Via 'Neapolitan sixth' (first inversion of triad on flattened supertonic) of old key and dominant seventh of new key
Via augmented sixth on the flattened supertonic in the first key reinterpreted as the dominant seventh of the new key

Up a major third

Via dominant 7th of new key
Via dominant diminished 7th and dominant 7th of new key
Via 'Neapolitan sixth' (first inversion of flattened supertonic) and dominant 7th of new key
Via a direct jump into the new key. Very crude, but surprisingly widely used
Via tonic seventh, interpreted as a German sixth on the flattened submediant. A very common enharmonic modulation, which relies on the flattened seventh sounding the same as the augmented sixth (in equal temperament, at least)
Directly via the dominant of the new key. The tonic of the old key is equivalent to the flattened submediant of the new key, which resolves onto the dominant of the new key. Can be harsh and chromatic sounding, but widely used nonetheless, particularly by Schubert

Down a major third

Directly via dominant (seventh) of new key (= flattened mediant of old key). When the old key is major, the chromatic step from I to bIII can sound rather harsh
Via dominant and supertonic minor of new key. Essentially the same procedure as above, but the iv somewhat softens the harshness of the chromatic step of a minor third in the major key
Via 'Neapolitan sixth' (first inversion of triad on flattened supertonic) of old key and dominant seventh of new key
Via subdominant minor and dominant of new key. Mostly used for major-to-major modulation

Up a minor third

For example, modulation from relative minor to tonic
Via supertonic and dominant seventh of new key
Via subdominant and dominant seventh of new key
Via subdominant minor and dominant of new key. This procedure seems to be used mostly for modulation to the major mode

Down a minor third

For example, modulation to the relative minor
Via dominant seventh of new key
Via supertonic (seventh) of old key and dominant seventh of new key. Very widely used, e.g., by Bach. The bracketed seventh is not diatonic in the new key if the new key is major
Via subdominant of old key, treated as the flattened submediant of the new key, resolving onto the dominant of the new key

Up a major second

Directly via dominant of new key (= submediant major of old key). Although strictly a chromatic modulation, this procedure is widely used from the Baroque onwards
Via subdominant and dominant 7th of new key
Via tonic, supertonic minor, and dominant 7th of new key
Via major supertonic seventh and dominant seventh of new key. Widely used in some genres of music, and sniffily dismissed as 'sentimental' by some authors

Down a major second

Via dominant 7th of new key. Note that the tonic of the old key can be seen as a chromatically-modified supertonic of the new key, so the progression in the new key is, in a sense, II-V7-I
Via tonic seventh of old key and dominant 7th of new key. Note that the tonic of the old key can be seen as a chromatically-modified supertonic of the new key, so the progression in the new key is, in a sense, II7-V7-I
Via the submediant major of the new key. This rather odd modulation is frequently used in sequence to span larger modulation intervals

Up a semitone

Via flattened supertonic of new key (supertonic of old key)
Via 'Neapolitan sixth' (first inversion of triad on flattened supertonic) of old key and dominant seventh of new key. The Neapolitan sixth of the old key is, in fact, the tonic on the new key, whether inverted or not. So the progression in the new key is just I-V-I
Directly via the dominant (seventh) of the new key. The dominant of the new key amounts to the flattened submediant of the old, but in reality all that's really happening here is sounding the dominant of the new key and jumping into it. Some writers interpret this procedure as being an enharmonic modulation that relies on the equivalence of the dominant of the new key and the German augmented sixth on the flattened submediant (which is often treated as a kind of supertonic, even though the supertonic root itself is absent)

Down a semitone

Via supertonic of old key (flattened supertonic of old key)
Via flattened supertonic of new key. Although this procedure has been widely used since the classical period, it amounts to little more than sounding the tonic of the new key following by its dominant, which can effect a kind of modulation between any two keys. It works here, presumably, because by the time the dominant of the new key is heard, the ear is willing to reinterpret the tonic of the old key as if it had been the tonic of the new key, their being only a semitone apart
Via flattened submediant and dominant of the new key. This works because V of the old key is is bVI of the new one; and bVI resolves onto V in the new key. But that resolution sounds very chromatic and can be harsh.
Via German sixth on the flattened submediant, reinterpreted enharmonically as the dominant seventh in the new key. This example is only very subtly different from the previous one and, like it, amounts to very little more than just jumping straight into the new key via its dominant
Copyright © 1994-2013 Kevin Boone. Updated Jul 05 2010