#1
Modulation

We have spent a lot of time trying to show how exotic chord changes, during which there is no real sense that the key centre has shifted, can be correctly numbered or named. Even so, there are times when the key centre does change and this we call modulation. Three types of modulation are given special names.

Parallel or Parallel Key Modulation change of key from one key to another where the key note remains the same
(e.g. A minor to A major, or E major to E minor)
Relative or Relative Key Modulation change of key from one key to another where the key signature remains the same
(e.g. A minor to C major, or G major to E minor)
Enharmonic Modulation where there is no audible change of key (at least not in equal temperament) but a chord is rewritten using enharmonic equivalents. There are two main types of enharmonic modulations: dominant seventh/augmented sixth, and diminished seventh. By respelling the notes, any dominant seventh can be reinterpreted as a German or Italian sixth (depending on whether or not the fifth is present), and any diminished seventh chord can be respelled in multiple other ways to form other diminished seventh chords

The chord naming convention expects that up to the point of modulation all chords will be numbered in relation to the original key centre, but that from the point of modulation, the chords will be numbered in relation to the new key centre. For the practical musician, the question is, when and where does modulation take place.

In some pieces the change can be from chord to chord, what is called direct modulation. In other cases, the music might pass through a chord that is common to both keys, the chord acting as a link or pivot. Unsurprisingly, this is called pivot chord modulation. There is no need to change the key signature when a piece modulates, although this can sometimes happen. However, it is not unusual in a piece where there has been a change of key, to find it modulate back to its original key so ending in the same key as it began. Walter Piston's analysis of what used to be called transient modulation demonstrates that modulation over a very short period might be better described in another way.

To summarise:

Phrase Modulation phrase modulation is a change of key centre at the juncture of two phrases, so that the first phrase ends in one key, and the next phrase begins in another
Static Modulation in static modulation the key centre can change anywhere, not just between two phrases.
Pivot Chord Modulation or
Common Chord Modulation when a chord functions diatonically in two different keys and this property is exploited so that before the chord the piece is in one key and after the chord the piece is in another, this is pivot chord or common chord modulation
Common Note Modulation a sustained or repeated pitch from the old key acts as a bridge between it and the new key. 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
Sequential Modulation or
Rosalia where during a sequence several keys might be visited for one or two beats at a time, such is an example of sequential modulation
Transient modulation the concept of the secondary dominant was not recognized in writings on music theory prior to 1939. Before this time, in music of Bach, Mozart, Beethoven, and Brahms, a secondary dominant, along with its chord of resolution, was considered to be a modulation. Because the effect of modulation was so short, and did not sound like a real arrival of a new key, the two chords had a special name--"transient modulation"--that is, a modulation in which the new key is not established. Since this was a rather self-contradictory description, theorists in the early 1900s, such as Frank Shepard, Benjamin Cutter, and George Wedge, searched for a better description of the phenomenon. In 1939, in a monograph entitled "Principles of Harmonic Analysis," Walter Piston first used the analysis "V7 of IV." (Notably, Piston's analytical symbol always used the word "of"--e.g. "V7 of IV" rather than the virgule "V7/IV.) In his 1941 "Harmony" Piston used the term "secondary dominant" for the first time. It has been generally accepted into music theory since then
[this entry directly quotes from Secondary dominant]
Abrupt or Shift Modulation a variant of phrase modulation, but applied at the end of a varse in a ballad. The reprise of earlier material is presented in an unrelated, usually at a high pitch, in order to inject some tension. It is not usual after a shift modulation in a ballad for there to be a return to the original key - usually the ballad ends in the higher key

One measure of the proximity of one key to another when considering modulation is the number of notes their scales have in common. For the scales of C major and the natural minor on a (which have the same notes are are therefore treated as being the same) the relationships may be summarised as follows.

Minor keys
on the flat side Major keys
on the flat side Number of notes in common
with C major or the natural minor on a Major keys
on the sharp side Minor keys
on the sharp side
d minor F major 6 G major e minor
g minor B flat major 5 D major b minor
c minor E flat major 4 A major f sharp minor
f minor A flat major 3 E major c sharp minor
b flat minor D flat major 2 B major g sharp minor
e flat minor G flat major 1 F sharp major d sharp minor

Chords use only a few notes from any scale. This allows composers to exploit the intrinsic ambiguity that chords have in that they can function diatonically in more than one key. This offers an effective way of modulating using the pivot chord principle where a single chord can be found in both the key from which one is modulating and in the key to which one wishes to modulate. Parallel major and minor keys (for example, C major and c minor) which have only four notes in common, happen to share a common tonic and dominant chord and seem harmonically more closely related than the measure based on the number of shared notes might lead one to expect. Modulation is easily achieved by using the common dominant chord as a pivot.

A further ambiguity arises from the way chords may be written in different keys. Chords can be rewritten enharmonically. For example, the dominant seventh (C-E-G-B flat) can be written as an augmented sixth (C-E-G-A sharp). This modulation is more effective if the fifth is unvoiced in the chord. Another example is the augmented triad (C-E-G sharp) which can be reinterpreted (A flat-C-E) or (E-G sharp-B sharp). A similar enharmonic reinterpretation is available with the diminished seventh chord (C-E flat-G flat-B double flat).

This topic is explained more fully in Andrew Milne's web page, part of The Tone Centre, entitled Modulation.

For those interested in reading further on this topic we recommend Arnold Schoenberg's Structural Functions of Harmony (first published in 1954).

Though modulation generally refers to changes of key, of course any parameter may be modulated. We describe some common non-harmonic modulations in the table below.

Metric Modulation tempo modulation, change in tempo
Timbral Modulation gradual changes in tone color
Spatial Modulation changing the location from which sound occurs
Last edited by TheEarlOfDublin at Aug 3, 2009,
#2
...what the hell?
Quote by TGautier13
Because e-cred on a sub-par 4Chan knockoff forum is what everyone strives to achieve.
We believe - so we're misled
We assume - so we're played
We confide - so we're deceived
We trust - so we're betrayed
#4
Quote by TheEarlOfDublin
disclaimer: article not nessecarly written by me. you are all ******s
We are all f aggots...alrighty then. Reported.
Quote by TGautier13
Because e-cred on a sub-par 4Chan knockoff forum is what everyone strives to achieve.
We believe - so we're misled
We assume - so we're played
We confide - so we're deceived
We trust - so we're betrayed
#5
Geez... I go upstairs to watch a movie for a while and I missed all the fun apparently.

*sigh*



CT
Could I get some more talent in the monitors, please?

I know it sounds crazy, but try to learn to inhale your voice. www.thebelcantotechnique.com

Chris is the king of relating music things to other objects in real life.