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In plane geometry, the einstein problem asks about the existence of a single prototile that by itself forms an aperiodic set of prototiles; that is, a shape that can tessellate space but only in a nonperiodic way. Such a shape is called an einstein, a word play on ein Stein, German for "one stone". [2]
The term can also be used for non-periodic or aperiodic signals, like chirps and pulses. [3] In electronics, the term is usually applied to time-varying voltages, currents, or electromagnetic fields. In acoustics, it is usually applied to steady periodic sounds — variations of pressure in air or other media.
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 ...
Harmonic Materials of Modern Music is a book on musical set theory by American composer Howard Hanson that overlaps significantly with composer Elliott Carter's Harmony Book and theorist Allen Forte's subsequent Structure of Atonal Music. Published in 1960, Hanson's theory was one of the first to examine all sets of pitches in terms of their ...
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]
Time Unit Box System (TUBS) is a simple system for notating events that happen over a period. This system is mostly used for notating rhythms in music . The notation consists of one or more rows of boxes; each box represents a fixed unit of time.
The Orff Approach of music education uses very rudimentary forms of everyday activity for the purpose of music creation by music students. The Orff Approach is a "child-centered way of learning" music education that treats music as a basic system like language and believes that just as every child can learn language without formal instruction so can every child learn music by a gentle and ...
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.