Inversion (music)

In music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth (for example C to G) is 3:2 (Play), 1.5, and may be approximated by an equal tempered perfect fifth (Play) which is 2 (about 1.498). If the A above middle C is 440 Hz, the perfect fifth above it would be E, at (440*1.5=) 660 Hz, while the equal tempered E5 is 659.255 Hz.

Ratios, rather than direct frequency measurements, allow musicians to work with relative pitch measurements applicable to many instruments in an intuitive manner, whereas one rarely has the frequencies of fixed pitched instruments memorized and rarely has the capabilities to measure the changes of adjustable pitch instruments (electronic tuner). Ratios have an inverse relationship to string length, for example stopping a string at two-thirds (2:3) its length produces a pitch one and one-half (3:2) that of the open string (not to be confused with inversion).

Voice leading (or part writing) is the linear progression of individual melodic lines (voices or parts) and their interaction with one another to create harmonies, typically in accordance with the principles of common-practice harmony and counterpoint. These principles include voices sounding smooth and independent, generally minimising movement to common tones as well as steps to the closest chord tone possible, therefore minimising leaps where possible. As a result, different voicings and inversions of chords may provide smoother voice leading.

Rigorous concern for voice leading is of greatest importance in common-practice music, although jazz and pop music also demonstrate attention to voice leading to varying degrees.

In the music theory of harmony, the root is a specific note that names and typifies a given chord. Chords are often spoken about in terms of their root, their quality, and their extensions. When a chord is named without reference to quality, it is assumed to be major—for example, a "C chord" refers to a C major triad, containing the notes C, E, and G. In a given harmonic context, the root of a chord need not be in the bass position, as chords may be inverted while retaining the same name, and therefore the same root.

In tertian harmonic theory, wherein chords can be considered stacks of third intervals (e.g. in common practice tonality), the root of a chord is the note on which the subsequent thirds are stacked. For instance, the root of a triad such as E Minor is E, independently of the vertical order in which the three notes (E, G and B) are presented. A triad can be in three possible positions, a "root position" with the root in the bass (i.e., with the root as the lowest note, thus E, G, B or E, B, G from lowest to highest notes), a first inversion, e.g. G, B, E or G, E, B (i.e., with the note which is a third interval above the root, G, as the lowest note) and a second inversion, e.g. B, E, G or B, G, E, in which the note that is a fifth interval above the root (B) is the lowest note.

In music, a pedal point (also pedal note, organ point, pedal tone, or pedal) is a sustained tone, typically in the bass, during which at least one foreign (i.e. dissonant) harmony is sounded in the other parts. A pedal point sometimes functions as a "non-chord tone", placing it in the categories alongside suspensions, retardations, and passing tones. However, the pedal point is unique among non-chord tones, "in that it begins on a consonance, sustains (or repeats) through another chord as a dissonance until the harmony", not the non-chord tone, "resolves back to a consonance".

Pedal points "have a strong tonal effect, 'pulling' the harmony back to its root". Pedal points can also build drama or intensity and expectation. When a pedal point occurs in a voice other than the bass, it is usually referred to as an inverted pedal point (see inversion). Pedal points are usually on either the tonic or the dominant (fifth note of the scale) tones. The pedal tone is considered a chord tone in the original harmony, then a nonchord tone during the intervening dissonant harmonies, and then a chord tone again when the harmony resolves. A dissonant pedal point may go against all harmonies present during its duration, being almost more like an added tone than a nonchord tone, or pedal points may serve as atonal pitch centers.

In classical music from Western culture, an augmented third (Play) is an interval of five semitones. It may be produced by widening a major third by a chromatic semitone. For instance, the interval from C to E is a major third, four semitones wide, and both the intervals from C♭ to E, and from C to E♯ are augmented thirds, spanning five semitones. Being augmented, it is considered a dissonant interval.

Its inversion is the diminished sixth, and its enharmonic equivalent is the perfect fourth.