Search results
Results From The WOW.Com Content Network
Thus the major third is considered not a third but a ditone, literally "two tones", and is (9:8) 2 = 81:64, rather than the independent and harmonic just 5:4 = 80:64 directly below. A whole tone is a secondary interval, being derived from two perfect fifths minus an octave, (3:2) 2 /2 = 9:8.
Unit disks are special cases of disks and unit balls; as such, they contain the interior of the unit circle and, in the case of the closed unit disk, the unit circle itself. Without further specifications, the term unit disk is used for the open unit disk about the origin , D 1 ( 0 ) {\displaystyle D_{1}(0)} , with respect to the standard ...
In geometry, a disk (also spelled disc) [1] is the region in a plane bounded by a circle. A disk is said to be closed if it contains the circle that constitutes its boundary, and open if it does not. [2] For a radius, , an open disk is usually denoted as and a closed disk is ¯.
The disk covering problem asks for the smallest real number such that disks of radius () can be arranged in such a way as to cover the unit disk.Dually, for a given radius ε, one wishes to find the smallest integer n such that n disks of radius ε can cover the unit disk.
8 (six beats per bar, with each beat being an eighth note) and 12 8 (twelve beats per bar, with each beat being an eighth note; in practice, the eighth notes are typically put into four groups of three eighth notes. 12 8 is a compound time type of time signature). Many other time signatures exist, such as 2 2 or 3 8.
On the other hand, the octave series is a geometric progression (2f, 4f, 8f, 16f, ...), and people perceive these distances as "the same" in the sense of musical interval. In terms of what one hears, each successively higher octave in the harmonic series is divided into increasingly "smaller" and more numerous intervals.
A number of dots (n) lengthen the note value by 2 n − 1 / 2 n its value, so two dots add two lower note values, making a total of one and three quarters times its original duration. The rare three dots make it one and seven eighths the duration, and so on.
Music theorists sometimes use mathematics to understand music, and although music has no axiomatic foundation in modern mathematics, mathematics is "the basis of sound" and sound itself "in its musical aspects... exhibits a remarkable array of number properties", simply because nature itself "is amazingly mathematical". [87]