What is a transformation theory?
Transformation theory of music is a mathematical attempt to explain its nature, structure and effect on human experience. Students of music theory, even ancient Greeks, knew that music could be explained by science and mathematics, as well as aesthetic pleasure. The arrival of sophisticated electronics and powerful computers at the end of the 20th century finally made it possible to attempt to model music numeric. Transformation theory was first designed by a mathematician and musician at the University of Harvard. Professor David Lewin's book from 1987 was called "Generalized Music Intervals and Transformation".
The diatonic scale used in tonal music - for example, only the white piano keys - is a very small set of seven elements with the starting point {C, D, E, F, G, A, & B}. This is its conventional designation. There is no reason not to indefinitely numeric {1,2,3,4,5,6,7}. A complete chromatic scale of atonal music without startuint - including the black piano keys - is still a small set of only twelve elements. AlmostAll world music is contained in this small set.
The theory of music set borrows from mathematics of orchards and sequences for this limitation of twelve elements. Their infinitely variable sequences explain the almost endless song catalog in the world. The pianist instructed to play three ascending notes behind-to-Re-Mi, for example, using the Latin Convention-by, it was represented by the sequence {C, D, E}. Transformation theory is completely issued with a set and claims that individual music elements may not be determined if the rules and relationships of changing sounds can be defined.
In the example of the three notes of the above paragraph, the sequence may be represented {n, n+1, n+2}. The numbers represent a musical interval or space for a well -defined pitch, not only piano pitch, but also science of sound waves. Vocalists who demand accompanying music in a "different key" to better fit its extentnná "n" in the sequence. Transformation theory would describe that the element "N" is subject to sequential transformation equivalent to three ascending notes.
It also expanded into its essence, transformation theory defines the musical composition as "sound space" marked "S", which contains only one element "N". All many music notes in the composition can be mapped to this space according to their transformation operation "T" in relation to "n". For example, the dramatic piano technique that hit all the white keys from left to right in one rapid sweeping can be spatially represented as a spiral helix in the shape of a metal spring. Music is expressed as a network rather than a collection of symbols.
David Lewin Plášelpryry in 2003 without publishing most of his theoretical articles. Advanced mathematicians, computer programmers and music theorists have since proceeded and improved their original framework. One group of scientists fed several orchestral symphonies from the 18th century, includingOne of the composer Ludwig Beethoven, into a computer programmed by the mathematics of transformation theory. Each piece of music resulted in a geometric shape called torus, more often known as a donut with a hole.