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Zero-dimensional Polish spaces are a particularly convenient setting for descriptive set theory. Examples of such spaces include the Cantor space and Baire space. Hausdorff zero-dimensional spaces are precisely the subspaces of topological powers where = {,} is given the discrete topology.
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 ...
In music theory, pitch-class space is the circular space representing all the notes (pitch classes) in a musical octave. In this space, there is no distinction between tones separated by an integral number of octaves. For example, C4, C5, and C6, though different pitches, are represented by the same point in pitch class space.
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 ∩ ...
The main difference with a sound sculpture is that a sound installation has a three-dimensional space and the axes with which the different sound objects are being organized are not exclusively internal to the work, but also external. [12] A work of art is an installation only if it makes a dialog with the surrounding space. [13]
Thus Pythagorean tuning, which uses only the perfect fifth (3/2) and octave (2/1) and their multiples (powers of 2 and 3), is represented through a two-dimensional lattice (or, given octave equivalence, a single dimension), while standard (5-limit) just intonation, which adds the use of the just major third (5/4), may be represented through a ...
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.
Space music appears in many film soundtracks and is commonly played in planetariums. [21] According to Hill space music is an eclectic music produced almost exclusively by independent labels and it occupies a small niche in the marketplace, supported and enjoyed by a relatively small audience of loyal enthusiastic listeners. [22]