User:Tony1/Inversions (music) draft resolution

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[edit] Root position

A root-position chord is often known as the parent chord of its inversions (see below). For example, C is the root of a C major triad and is in the bass when the triad is in root position; the third and the fifth of the triad are sounded above the bass. Thus, a root-position chord is known as a chord.

[edit] Inversions

In an inverted chord, the root is not in the bass (i.e., is not the lowest note). In the first inversion of a C major triad, the bass is E—the third of the triad—with the root and the fifth above it, forming the intervals of a sixth and a third above the bass, respectively. Thus, a first-inversion triad is known as a chord.

In the second inversion, the bass is G—the 5th of the triad—with the root and the 3rd above it, forming a 4th and a 6th above the bass, respectively. Thus, a second-inversion triad is known as a chord. This inversion can be either consonant or dissonant, and analytical notation sometimes treats it differently, depending on the harmonic and voice-leading context in which it occurs (see The cadential six-four chord: two contrasting views below).

Third inversions exist only for chords of four or more tones, such as 7th chords. In a third-inversion chord, the 7th of the chord is in the bass. For example, a C major 7th chord in third inversion consists of B in the bass, with C, E and G above it—a 2nd, 4th and 6th above the bass, respectively.

[edit] Notating chord position

Figure 1: the common chord positions and their corresponding figured-bass notation in abbreviated form

Figure 2: the closing phrase of the hymn-setting Rustington by the English composer Hubert Parry (1848–1918), showing all three positions of the C major chord

There are at least four systems of notation.

[edit] Figured bass

A commonly used method for indicating whether a chord is in root position or, if not, its inversion, is figured bass. In this system, arabic numerals (figures) are written below each bass note. These figures refer to intervals above the bass. The absence of figures under a bass-note C indicates a root-position chord; in Figure 1, the final chord is explicitly figured for clarity as a root-position chord—of C major chord, as G and E are a 5th and 3rd above this note, respectively. Its first inversion would be notated E 6, which stands for E , giving E, G and C (the first chord in Figure 2). Its second inversion is G (the third chord in Figure 2). Similarly a root-position G dominant-7th chord is figured as G 7 (fully 7 5 3), in first inversion as B (6 5 3), in second inversion D (6 4 3), and in third inversion F (6 4 2). (Chord tones outside the given key signature are marked with accidentals; see Figured bass for a full explanation.)

The numbered figures used in figured bass are often used in music theory to simply denote whether a chord is in root position or, if not, its inversion. Thus, a chord refers to a chord in first inversion.

[edit] Popular-music notation

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 bass note. For example, the C chord above, in first inversion (i.e., with E in the bass) may be notated as C/E. This notation works even when a note not present in a triad is the bass; for example, F/G is a way of notating a particular approach to voicing a G11th chord (G–B–D–F–A–C). (This is quite different from notations of function of function; e.g., the use of IV/V or S/D to represent the subdominant of the dominant).

[edit] Lower-case letters

Lower-case letters may be placed after a chord symbol to indicate root position or inversion. Hence, in the key of C major, the C major chord below in first inversion may be notated as Ib, indicating chord I, first inversion. (Less commonly, the root of the chord is named, followed by a lower-case letter: Cb). If no letter is added, the chord is assumed to be in root inversion, as though a had been inserted.

[edit] Arabic numerals

A less common notation 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. The C chord above in root position is notated as C, and in first inversion as C1. (This notation is quite different from the arabic numerals placed after note names to indicate the octave of a tone, typically used in acoustical contexts; for example, C4 is often used to mean the single tone middle C, and C3 the tone an octave above it.)

[edit] The cadential six-four chord: two contrasting views

Figure 3: the cadential

The cadential (Figure 3) is a common harmonic phenomenon that is understood in two quite different ways. The first designates it as a tonic triad, since it has the same tones as that triad (here, C, E and G); most harmony textbooks label this progression as , a label "that may be helpful for identification"^[1]. Since G is in the bass, this view of the cadential chord often regarded it as a second inversion, an analysis that can be traced as far back as the 18th century.^[2]

A fundamentally different view of this harmonic phenomenon also arose in the 18th century: that—in this example—since a root of C would be a dissonant 4th above the bass, resolving to a consonant 3rd (B) over the same bass, such a dissonant chord cannot substitute for the root-position parent chord.^[3] This resonates in the analysis of the chord by some modern-day theorists not as tonic second-inversion harmony, but as dominant harmony,^[4] the chord entirely dependent for its harmonic identity on the resolution of the 6th and the 4th to the 5th and the 3rd (D and B), and notated as . In this view, the 6th and the dissonant 4th are no different in principle from the 5th and the dissonant 4th in a 4–3 suspension over chord V, and "does not act as an inversion".^[5]

[edit] Notes