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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.
An example of such a tiling is shown in the adjacent diagram (see the image description for more information). 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]
Basic Concepts in Music Education is a landmark work published in the USA 1958 as the Fifty-Seventh Yearbook of the National Society for the Study of Education. In 1954, the Music Educators National Conference ( MENC ) had formed its Commission on Basic Concepts in an attempt to seek a more soundly-based philosophical foundation.
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. It has been shown in research to promote learning. Additionally, music study in general has been shown to improve academic performance of students.
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.
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 ...
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 ...
Diagram of a typical period consisting of two phrases [5] [6] [7]. In Western art music or Classical music, a period is a group of phrases consisting usually of at least one antecedent phrase and one consequent phrase totaling about 8 bars in length (though this varies depending on meter and tempo).