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Chord diagrams are conventionally visualized by arranging the objects in their order around a circle, and drawing the pairs of the matching as chords of the circle. The number of different chord diagrams that may be given for a set of cyclically ordered objects is the double factorial ()!!. [1] There is a Catalan number of chord diagrams on a ...
The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.
Bird changes: I vii ø –III7 vi–II7 v–I7, IV7 iv– ♭ VII7 iii–VI7 ♭ iii– ♭ VI7, ii V7 I–VI7 ii–V: 20: Major Chromatic descending 5–6 sequence: I–V– ♭ VII–IV: 4: Mix. Circle progression: vi–ii–V–I: 4: Major Coltrane changes: Coltrane changes in C: I–V/ ♭ VI ♭ VI–V/III III–V I. 6: Major Eight-bar ...
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.
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).
Musical symbols are marks and symbols in musical notation that indicate various aspects of how a piece of music is to be performed. There are symbols to communicate information about many musical elements, including pitch, duration, dynamics, or articulation of musical notes; tempo, metre, form (e.g., whether sections are repeated), and details about specific playing techniques (e.g., which ...
Rhythm changes is a common 32-bar jazz chord progression derived from George Gershwin's "I Got Rhythm". The progression is in AABA form , with each A section based on repetitions of the ubiquitous I–vi–ii–V sequence (or variants such as iii–vi–ii–V), and the B section using a circle of fifths sequence based on III 7 –VI 7 –II 7 ...
The I−vi−ii−V chord progression occurs as a two-bar pattern in the A section of the rhythm changes, [8] the progression based on George Gershwin's "I Got Rhythm". It can be varied as well: according to Mark Levine, "[t]oday's players usually play a dominant 7th chord rather than a minor 7th chord as the VI chord in a I-VI-II-V." [5]