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The more precise mathematical definition is that there is never translational symmetry in more than n – 1 linearly independent directions, where n is the dimension of the space filled, e.g., the three-dimensional tiling displayed in a quasicrystal may have translational symmetry in two directions.
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 ...
A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic . [ 3 ] The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings , though strictly speaking it is the tiles themselves that are ...
The second definition of period in the New Harvard Dictionary of Music states: "A musical element that is in some way repeated," applying "to the units of any parameter of music that embody repetitions at any level." [15] In some sub-Saharan music and music of the African diaspora, the bell pattern embodies this definition of period. [16]
An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic regions or patches. A set of tile-types (or prototiles) is aperiodic if copies of these tiles can form only non-periodic tilings. The Penrose tilings are a well-known example of aperiodic tilings. [1] [2]
Some definitions refer to music as a score, or a composition: [18] [7] [19] music can be read as well as heard, and a piece of music written but never played is a piece of music notwithstanding. According to Edward E. Gordon the process of reading music , at least for trained musicians, involves a process, called "inner hearing" or "audiation ...
Twinkle Twinkle Little Star, lullaby from the European Union government funded, education project Lullabies of Europe: Languages from the Cradle [1]. Educational music, is a genre of music in which songs, lyrics, or other musical elements are used as a method of teaching and/or learning.
Music based on a single theme is called monothematic, while music based on several themes is called polythematic. Most fugues are monothematic and most pieces in sonata form are polythematic. [8] In the exposition of a fugue, the principal theme (usually called the subject) is announced successively in each voice – sometimes in a transposed form.