Search results
Results From The WOW.Com Content Network
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. [1] A graphical illustration of a zero-dimensional space is a point. [2]
For an n-dimensional lattice, identifying n linearly independent commas reduces the dimension of the lattice to zero, meaning that the number of pitches in the lattice is finite; mathematically, its quotient is a finite abelian group. This zero-dimensional set of pitches is a periodicity block.
An open cover of a topological space X is a family of open sets U α such that their union is the whole space, U α = X. The order or ply of an open cover A {\displaystyle {\mathfrak {A}}} = { U α } is the smallest number m (if it exists) for which each point of the space belongs to at most m open sets in the cover: in other words U α 1 ∩ ...
Examples of musical lattices include the Tonnetz of Euler (1739) and Hugo Riemann and the tuning systems of composer-theorists Ben Johnston and James Tenney. Musical intervals in just intonation are related to those in equal tuning by Adriaan Fokker's Fokker periodicity blocks. Many multi-dimensional higher-limit tunings have been mapped by Erv ...
The simplest pitch space model is the real line. A fundamental frequency f is mapped to a real number p according to the equation = + (/) This creates a linear space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and middle C is assigned the number 60, as it is in MIDI. 440 Hz is the standard frequency of 'concert A', which ...
Over a commutative ring, a trivial algebra is simultaneously a zero module. The trivial ring is an example of a rng of square zero. A trivial algebra is an example of a zero algebra. The zero-dimensional vector space is an especially ubiquitous example of a zero object, a vector space over a field with an empty basis. It therefore has dimension ...
The music, film and art business spearheaded by Veazey will join Three Six Zero to help propel and expand its global management and entertainment efforts. Veazy’s official post as a partner at ...
Spatial music is composed music that intentionally exploits sound localization. Though present in Western music from biblical times in the form of the antiphon , as a component specific to new musical techniques the concept of spatial music ( Raummusik , usually translated as " space music ") was introduced as early as 1928 in Germany.