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The relation between local and global truncation errors is slightly different from in the simpler setting of one-step methods. For linear multistep methods, an additional concept called zero-stability is needed to explain the relation between local and global truncation errors.
Some other music publishers also apply the term Real Book to their own publications. The Associated Board of the Royal Schools of Music publishes The AB Real Book. [7] Alfred Publishing Co. has several Real Books. [8] Sher Music Co. publishes The New Real Book, in 3 volumes. [9] The collection of tunes differs from that of the original Real Book.
It is used in tonal and atonal music, and is a common method of localized development and closure. Fragmentation is related to Arnold Schoenberg 's concept of liquidation , [ 1 ] a common compositional technique that describes the reduction of a large-scale musical idea to its essential form (such as a contour line, a specific harmonic motion ...
Modes of limited transposition are musical modes or scales that fulfill specific criteria relating to their symmetry and the repetition of their interval groups. These scales may be transposed to all twelve notes of the chromatic scale, but at least two of these transpositions must result in the same pitch classes, thus their transpositions are "limited".
This list is of songs that have been interpolated by other songs. Songs that are cover versions, parodies, or use samples of other songs are not "interpolations". The list is organized under the name of the artist whose song is interpolated followed by the title of the song, and then the interpolating artist and their song.
Schenkerian analysis is a method of analyzing tonal music based on the theories of Heinrich Schenker (1868–1935). The goal is to demonstrate the organic coherence of the work by showing how the "foreground" (all notes in the score) relates to an abstracted deep structure, the Ursatz.
The "transformations" of transformational theory are typically modeled as functions that act over some musical space S, meaning that they are entirely defined by their inputs and outputs: for instance, the "ascending major third" might be modeled as a function that takes a particular pitch class as input and outputs the pitch class a major third above it.
In vocal music, contrafactum (or contrafact, pl. contrafacta) is "the substitution of one text for another without substantial change to the music". [1] The earliest known examples of this procedure (sometimes referred to as ''adaptation'') date back to the 9th century used in connection with Gregorian chant.