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An interval is inverted by raising or lowering either of the notes by one or more octaves so that the higher note becomes the lower note and vice versa. For example, the inversion of an interval consisting of a C with an E above it (the third measure below) 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.
A Wechsel inverted a triad according to the Riemann's theory of dualism, mapping a major triad to a minor triad. For example, Seitenwechsel ("die Seiten wechseln" translates as "to exchange sides") mapped a triad on to its parallel minor or major, transforming C major to C minor and conversely. [7]
Types of triads: I ⓘ, i ⓘ, i o ⓘ, I + ⓘ In music, a triad is a set of three notes (or "pitch classes") that can be stacked vertically in thirds. [1] Triads are the most common chords in Western music. When stacked in thirds, notes produce triads. The triad's members, from lowest-pitched tone to highest, are called: [1] the root
In music theory, retrograde inversion is a musical term that literally means "backwards and upside down": "The inverse of the series is sounded in reverse order." [1] Retrograde reverses the order of the motif's pitches: what was the first pitch becomes the last, and vice versa. [2]
For example, the minor triad in root position is made up of the 10th, 12th and 15th harmonics, and 10 / 10 , 12 / 10 and 15 / 10 meets the definition of otonal. A better, narrower definition requires that the harmonic (or subharmonic) series members be adjacent. Thus 4:5:6 is an otonality, but 10:12:15 is not.
In post-tonal music theory, identity is similar to identity in universal algebra. An identity function is a permutation or transformation which transforms a pitch or pitch class set into itself. Generally this requires symmetry. For instance, inverting an augmented triad or C4 interval cycle, 048, produces itself.
The second inversion of a chord is the voicing of a triad, seventh chord, or ninth chord in which the fifth of the chord is the bass note. In this inversion, the bass note and the root of the chord are a fourth apart which traditionally qualifies as a dissonance. There is therefore a tendency for movement and resolution.
In music theory, inversions higher than the third require extended chords; the fourth inversion requires a ninth chord, the fifth an eleventh chord, etc. Regarding these extensions, the writer Marcus Miller notes that: If you're working with extended chords, there are more than two possible inversions.