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The value of the two products in the chord theorem depends only on the distance of the intersection point S from the circle's center and is called the absolute value of the power of S; more precisely, it can be stated that: | | | | = | | | | = where r is the radius of the circle, and d is the distance between the center of the circle and the ...
In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle sharing an endpoint.
Equal chords are subtended by equal angles from the center of the circle. A chord that passes through the center of a circle is called a diameter and is the longest chord of that specific circle. If the line extensions (secant lines) of chords AB and CD intersect at a point P, then their lengths satisfy AP·PB = CP·PD (power of a point theorem).
Dominant 7th chords are generally used throughout a blues progression. The addition of dominant 7th chords as well as the inclusion of other types of 7th chords (i.e. minor and diminished 7ths) are often used just before a change, and more changes can be added. A more complicated example might look like this, where "7" indicates a seventh chord:
The circle progression is commonly a succession through all seven diatonic chords of a diatonic scale by fifths, including one progression by diminished fifth, (in C: between F and B) and one diminished chord (in C major, B o), returning to the tonic at the end. A full circle of fifths progression in C major is shown below.
The destination of a chord progression is known as a cadence, or two chords that signify the end or prolongation of a musical phrase. The most conclusive and resolving cadences return to the tonic or I chord; following the circle of fifths, the most suitable chord to precede the I chord is a V chord.
At its most basic, a single version of this blues scale is commonly used over all changes (or chords) in a twelve-bar blues progression. [7] Likewise, in contemporary jazz theory, its use is commonly based upon the key rather than the individual chord. [2] Greenblatt defines two blues scales, the major and the minor.
This is a plagal cadence featuring a dominant seventh tonic (I or V/IV) chord. However, Baker cites a turnaround containing "How Dry I Am" as the "absolutely most commonly used blues turnaround". [5] Fischer describes the turnaround as the last two measures of the blues form, or I 7 and V 7, with variations including I 7 –IV 7 –I 7 –V 7. [6]