It has been suggested that this article be split into multiple articles accessible from a disambiguation page. (Discuss)

In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and (in counterpoint) inverted voices. The concept of inversion also plays a role in musical set theory. Image File history File links Derived from public domain images featured at: http://commons. ... Music theory is a field of study that involves an investigation of the many diverse elements of a music, including the development and methodology for analyzing, hearing, understanding, and composing music. ... Counterpoint is a broad organisational feature of much music, involving the simultaneous sounding of separate musical lines. ... Musical set theory is an atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ...

Inverted chords

An inverted chord is a chord which has a note other than its root note as the bass note. Fingering for a C-major trichord on a guitar in standard tuning (assuming all six strings are played). ... The root (basse fondamentale) of a chord is the note upon which that chord is perceived or labelled as built or centered, the root of a chord in root position or normal form. ... This page is a candidate to be copied to Wiktionary. ...

For example, the root position of a triad of C major has the C in the bass: The root (basse fondamentale) of a chord is the note upon which that chord is perceived or labelled as built or centered, the root of a chord in root position or normal form. ...

moving over from meta File links The following pages link to this file: Inversion (music) Chord (music) Categories: Public domain images ineligible for copyright ...

A triad in root position, therefore, consists of the root note and a third and a fifth above it. Triads in root position are also in normal form. The term normal form is used in a variety of contexts. ...

The first inversion of the same triad has the E, the third of the triad, in the bass:

Image File history File links moving over from meta: http://meta. ...

This means that a triad in first inversion consists of the root plus a third and a sixth above it.

The second inversion has the fifth, the G, in the bass:

Image File history File links moving over from meta: http://meta. ...

A triad in second inversion, therefore, consists of the root plus a fourth and a sixth above it.

The third inversion of a triad does not really make much sense to discuss, since inverting the second inversion just leads to the tonic again, an octave higher. Chords of four notes or more, however, can be in their third inversion: the third inversion of a dominant seventh in C major, for example (made up of the notes G, B, D and F) has the seventh, F, in the bass. This gives a chord made up of the root plus a second, fourth and sixth above it. A seventh chord is a chord or triad which has a note the seventh above the tonic in it. ...

The terms "root", "first inversion", and "second inversion" may also be applied to chords in which the notes are not closely spaced. For instance, C-G-E, where the E is a major sixth above G, is also considered to be in root position, and more generally, any C major chord in which C is the lowest note is considered to be in root position. Similarly, any C major chord with E on the bottom counts as a first inversion, any C major chord with G on the bottom counts as a second inversion; and analogously for all other chords.

Notations for inverted chords

There are at least four different notations for the inversions of chords.

Figured bass, and corresponding chords.

(i) Perhaps the most commonly used method is figured bass. In this system, inversions are indicated by a digit or digits written below a given bass note. The digits refer to intervals above this bass note. A written note C with no digits stands for C 5 3, which is a root position C major triad (given a key signature that does not alter E or G), as G and E are a fifth and third above this note. Its second inversion would be notated E 6, which stands for E 6 3, giving E G and C. Its third inversion is G 6 4. Similarly a G dominant seventh chord would have a root figure of G 7 (fully 7 5 3), first inversion of B 6 5 (6 5 3), second of D 4 3 (6 4 3), and third of F 4 2 (6 4 2). (Chord tones which fall outside the given key signature are specified with accidentals. See Figured bass for a full explanation.) Figured bass, or thoroughbass, is a kind of integer musical notation used to indicate intervals, chords, and nonchord tones, in relation to a bass note. ... Figured bass, or thoroughbass, is a kind of integer musical notation used to indicate intervals, chords, and nonchord tones, in relation to a bass note. ...

Analysis of a common cadential progression, using figures to specify inversion.

In addition to this, the numbered figures used in figured bass are often used in music theory to simply denote a chord's inversion. Thus a 6/4 chord refers to a chord in second inversion, and is often seen with roman numeral analyses of harmonic function. For instance, a common cadential progression might be written: I 6/4, V, I. (In classical music, this type of progression is by far the most common place for a second inversion triad to appear.) A diatonic function, in tonal music theory, is the specific, recognized roles of notes or chords in relation to the key. ...

(ii) A notation for chord inversion often used in popular music is to write the name of a chord, followed by a forward slash, and then the name of the note that is to sound in the bass. For example, the C chord above, in first inversion (i.e. with E in the bass) may be notated as C/E. Interestingly, this notation works consistently even when a note not present in a triad or other chord is to sound in the bass, e.g. F/G is a way of notating a particular approach to voicing a G11th chord. This should not be confused with notations of the "function of function" style, for instance the subdominant of the dominant is IV/V or S/D. Popular music is music belonging to any of a number of musical styles that are accessible to the general public and mostly distributed commercially. ... See also: function and functional. ...

(iii) The letters a, b, c, etc., may be placed after any chord symbol to indicate the root, first and second inversion respectively. Hence the C chord below, in first inversion (i.e. with E in the bass) may be notated as Cb. (If no letter is added, the chord is assumed to be in root inversion, having the same meaning as if 'a' had been added explicitly.)

Image File history File links moving over from meta: http://meta. ...

(iv) A less common, but occasionally used, notation for chord inversion is to place the number 1, 2 or 3 etc. after a chord to indicate that it is in first, second, or third inversion respectively. Hence the C chord above, in first inversion (i.e. with E in the bass) may be notated as C1. No number is added in the case of a chord in root inversion. This notation should not be confused with a quite different meaning of the same notation, where a number is placed after a note name to indicate the octave in which a single note is to sound, e.g. C4 is often used simply to mean the single note middle C. In music, the term middle C refers to the note C located between the staves of the grand staff, quoted as C4 in note-octave form. ...

Inverted intervals

An interval is inverted by raising or lowering either of the notes the necessary number of octaves, so that both retain their names (pitch class) and the one which was higher is now lower and vice versa, changing the perspective or relation between the pitch classes. For example, the inversion of an interval consisting of a C with an E above it is an E with a C above it - to work this out, the C may be moved up, the E may be lowered, or both may be moved. In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... In music, an octave (sometimes abbreviated 8ve or 8va) is the interval between one musical note and another with half or double the frequency. ... In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ...

Under inversion, perfect intervals remain perfect, major intervals become minor and the reverse, augmented intervals become diminished and the reverse. (Double diminished intervals become double augmented intervals, and the reverse.) Traditional interval names sum to nine: seconds become sevenths and the reverse, thirds become sixes and the reverse, and fourths become fifths and the reverse. Thus a perfect fourth becomes a perfect fifth, an augmented fourth becomes a diminished fifth, and a simple interval (that is, one that is narrower than an octave) and its inversion, when added together, will equal an octave. See also complement (music). In traditional music theory a complement is the interval added to another, that is placed on top of another, so that their complete span is an octave. ...

Inversion in counterpoint

Contrapuntal inversion requires that two melodies, having accompanied each other once, do it again with the melody that had been in the high voice now in the low, and vice versa. Also called "double counterpoint" (if two voices are involved) or "triple counterpoint" (if three), themes that can be developed in this way are said to involve themselves in "invertible counterpoint." Look up melody in Wiktionary, the free dictionary. ...

Invertible counterpoint can occur at various intervals, usually the octave (8va), less often at the 10th or 12th. To calculate the interval of inversion, add the intervals by which each voice has moved and subtract one. For example: If motive A in the high voice moves down a 6th, and motive B in the low voice moves up a 5th, in such a way as to result in A and B having exchanged registers, then the two are in double counterpoint at the 10th (6+5)-1 = 10.

Invertible counterpoint achieves its highest expression in the four canons of J. S. Bach's Art of Fugue, with the first canon at the 8va, the second canon at the 10th, the third canon at the 12th, and the fourth canon in augmentation and contrary motion. Other exemplars can be found in the fugues in G minor and B-flat major [external Shockwave movies] from Book II of Bach's Well-Tempered Clavier, both of which contain invertible counterpoint at the 8va, 10th, and 12th. The Art of Fugue (Die Kunst der Fuge), BWV1080, is an unfinished work by Johann Sebastian Bach composed in 1748-1749 and published after his death in 1750. ... Title-page of Das wohtemperierte Clavier A flat major (As-dur) fugue from the second part of Das wohtemperierte Clavier (manuscript) The Well-Tempered Clavier (Das wohltemperierte Clavier, Clavier meaning keyboard instrument) is a collection of solo keyboard music composed by Johann Sebastian Bach. ...

Inverted melodies

When applied to melodies, the inversion of a given melody is the melody turned upside-down. For instance, if the original melody has a rising major third (see interval), the inverted melody has a falling major third (or perhaps more likely, in tonal music, a falling minor third, or even some other falling interval). Similarly, in twelve-tone technique, the inversion of the tone row is the so-called prime series turned upside-down. Look up melody in Wiktionary, the free dictionary. ... In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... Twelve-tone technique (also dodecaphony) is a method of musical composition devised by Arnold Schoenberg. ... In music, a tone row or note row is a permutation, an arrangement or ordering, of the twelve notes of the chromatic scale. ...

Inversional equivalency

Inversional equivalency or inversional symmetry is the concept that intervals, chords, and other sets of pitches are the same when inverted. It is similar to enharmonic equivalency and octave equivalency and even transpositional equivalency. Inversional equivalency is used little in tonal theory, though it is assumed a set which may be inverted onto another are remotely in common. However, taking them to be identical or near-identical is only assumed in musical set theory. In music theory, an interval is the relationship between two notes or pitches, the lower and higher members of the interval. ... Fingering for a C-major trichord on a guitar in standard tuning (assuming all six strings are played). ... In music, an enharmonic is a note which is the equivalent of some other note, but spelled differently. ... For the numerical computation software, see GNU Octave. ... In music transposition is moving a note or collection of notes (or pitches) up or down in pitch by a constant interval. ... The adjective tonal can refer to: tonality in music a tonal language the opposite of Nagual, in the specific context of Carlos Castaneda, the tonal is what makes the world. ...

All sets of pitches with inversional symmetry have a center or axis of inversion. For example, the set C-E-F-F♯-G-B has one center at the dyad F and F♯ and another at the tritone, B/C, if listed F♯-G-B-C-E-F. For C-E♭-E-F♯-G-B♭ the center is F and B if listed F♯-G-B♭-C-E♭-E. (Wilson 1992, p.10-11)

Inversion in musical set theory

In musical set theory inversion may be usefully thought of as the compound operation transpositional inversion, which is the same sense of inversion as in the Inverted melodies section above, with transposition carried out after inversion. Pitch inversion by an ordered pitch interval may be defined as: Musical set theory is an atonal or post-tonal method of musical analysis and composition which is based on explaining and proving musical phenomena, taken as sets and subsets, using mathematical rules and notation and using that information to gain insight to compositions or their creation. ... In music theory, the word inversion has several meanings. ...

which equals

First invert the pitch or pitches, x=-x, then transpose, -x+n.

Pitch class inversion by a pitch class interval may be defined as: In music and music theory a pitch class contains all notes that have the same name; for example, all Es, no matter which octave they are in, are in the same pitch class. ...

History

In the theories of Rameau (1722), chords in different positions were considered functionally equivalent. However, theories of counterpoint before Rameau spoke of different intervals in different ways, such as the regola delle terze e seste ("rule of sixths and thirds") which required the resolution of imperfect consonances to perfect ones, and would not propose a similarity between and sonorities, for instance. Jean-Philippe Rameau, by Jacques André Joseph Aved, 1728 Jean-Philippe Rameau (September 25, 1683 - September 12, 1764) was one of the most important French composers and music theorists of the Baroque era. ...

Source

• Wilson, Paul (1992). The Music of Béla Bartók. ISBN 0-300-05111-5.