Inversion (music)

The concept of inversion also plays an important role in musical set theory.

Texts that follow this restriction may use the term position instead, to refer to all of the possibilities as a category.

The inversions are numbered in the order their lowest notes appear in a close root-position chord (from bottom to top).

The three inversions of a G dominant seventh chord are: Figured bass is a notation in which chord inversions are indicated by Arabic numerals (the figures) either above or below the bass notes, indicating a harmonic progression.

Each numeral expresses the interval that results from the voices above it (usually assuming octave equivalence).

For example, in root-position triad C–E–G, the intervals above bass note C are a third and a fifth, giving the figures 53.

Figured-bass numerals express distinct intervals in a chord only as they relate to the bass note.

They make no reference to the key of the progression (unlike Roman-numeral harmonic analysis), they do not express intervals between pairs of upper voices themselves – for example, in a C–E–G triad, the figured bass does not signify the interval relationship between E–G, and they do not express notes in upper voices that double, or are unison with, the bass note.

However, the figures are often used on their own (without the bass) in music theory simply to specify a chord's inversion.

Similarly, in harmonic analysis the term I6 refers to a tonic triad in first inversion.

Lower-case letters may be placed after a chord symbol to indicate root position or inversion.

(Less commonly, the root of the chord is named, followed by a lower-case letter: Cb).

In Jean-Philippe Rameau's Treatise on Harmony (1722), chords in different inversions are considered functionally equivalent and he has been credited as being the first person to recognise their underlying similarity.

[7][8] Earlier theorists spoke of different intervals using alternative descriptions, such as the regola delle terze e seste ("rule of sixths and thirds").

This required the resolution of imperfect consonances to perfect ones and would not propose, for example, a resemblance between 64 and 53 chords.

Other exemplars can be found in the fugues in G minor Archived 2010-03-27 at the Wayback Machine and B♭ major [external Shockwave movies] from J.S.

Bach's The Well-Tempered Clavier, Book 2, both of which contain invertible counterpoint at the octave, tenth, and twelfth.

Bach's Three-Part Invention in F minor, BWV 795 involves exploring the combination of three themes.

One of the most spectacular examples of invertible counterpoint occurs in the finale of Mozart's Jupiter Symphony.

Here, no less than five themes are heard together: The whole passage brings the symphony to a conclusion in a blaze of brilliant orchestral writing.

According to Tom Service: Mozart's composition of the finale of the Jupiter Symphony is a palimpsest on music history as well as his own.

If the story of that operatic tune first movement is to turn instinctive emotion into contrapuntal experience, the finale does exactly the reverse, transmuting the most complex arts of compositional craft into pure, exhilarating feeling.

Its models in Michael and Joseph Haydn are unquestionable, but Mozart simultaneously pays homage to them – and transcends them.

Inversional equivalency is used little in tonal theory, though it is assumed that sets that can be inverted into each other are remotely in common.

The notation of octave position may determine how many lines and spaces appear to share the axis.