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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.
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 ...
Music education is a field of practice in which educators are trained for careers as elementary or secondary music teachers, school or music conservatory ensemble directors. Music education is also a research area in which scholars do original research on ways of teaching and learning music.
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]
Throughout the history of music education, many music educators have adopted and implemented technology in the classroom. Alice Keith and D.C. Boyle were said to be the first music educators in the United States to use the radio for teaching music. Keith wrote Listening in on the Masters, which was a broadcast music appreciation course. [44]
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.
Musical literacy is the reading, writing, and playing of music, as well an understanding of cultural practice and historical and social contexts.. Music literacy and music education are frequently talked about relationally and causatively, however, they are not interchangeable terms, as complete musical literacy also concerns an understanding of the diverse practices involved in teaching music ...
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]