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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 circular pitch class space is an example of a pitch space. The circle of fifths is another example of pitch space. In music theory, pitch spaces model relationships between pitches. These models typically use distance to model the degree of relatedness, with closely related pitches placed near one another, and less closely related pitches ...
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.
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.
Many models of communication include the idea that a sender encodes a message and uses a channel to transmit it to a receiver. Noise may distort the message along the way. The receiver then decodes the message and gives some form of feedback. [1] Models of communication simplify or represent the process of communication.
An example of a random vector that is Gaussian white noise in the weak but not in the strong sense is = [,] where is a normal random variable with zero mean, and is equal to + or to , with equal probability. These two variables are uncorrelated and individually normally distributed, but they are not jointly normally distributed and are not ...
The four-sides model (also known as communication square or four-ears model) is a communication model postulated in 1981 by German psychologist Friedemann Schulz von Thun. According to this model every message has four facets though not the same emphasis might be put on each.
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 ...