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The main objective of interval arithmetic is to provide a simple way of calculating upper and lower bounds of a function's range in one or more variables. These endpoints are not necessarily the true supremum or infimum of a range since the precise calculation of those values can be difficult or impossible; the bounds only need to contain the function's range as a subset.
The harmonic seventh chord is a dominant seventh chord formed by a major triad plus a harmonic seventh interval. The harmonic seventh interval is a minor seventh tuned in the 7:4 pitch ratio, one of the possible "just ratios" defined for this interval in just intonation (slightly below the width of a minor seventh as tuned in equal temperament ...
The harmonic seventh arises from the harmonic series as the interval between the fourth harmonic (second octave of the fundamental) and the seventh harmonic; in that octave, harmonics 4, 5, 6, and 7 constitute the four notes (in order) of a purely consonant major chord (root position) with an added minor seventh (or augmented sixth, depending ...
In music and in music theory, "seventh interval" refers to the following musical intervals: major seventh, minor seventh, augmented seventh, or; diminished seventh. It also refers to inverted second intervals.
The half-diminished seventh chord is frequently used in passages that convey heightened emotion. For example, the "mournful affect" [5] of the sombre opening Chorus of J. S. Bach's St Matthew Passion (1727) features the chord on the seventh beat of its first bar and on the first beat of its third bar:
The major seventh interval is considered one of the most dissonant intervals after its inversion the minor second. For this reason, its melodic use is infrequent in classical music. However, in the genial Gavotte from J.S. Bach’s Partita in E major for solo violin, a major seventh features both as a chord (bar 1) and as a melodic interval ...
For example, the interval from A 3 to G 4 is a minor seventh, as the note G 4 lies ten semitones above A 3, and there are seven staff positions from A 3 to G 4. Diminished and augmented sevenths span the same number of staff positions, but consist of a different number of semitones (nine and twelve, respectively).
The major seventh chord, sometimes also called a Delta chord, can be written as maj 7, M 7, Δ, ⑦, etc. The "7" does not have to be superscripted, but if it is, then any alterations, added tones, or omissions are usually also superscripted. For example, the major seventh chord built on C, commonly written as Cmaj 7, has pitches C–E–G–B: