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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.
Large images giving segments of music or depicting features of music should be displayed in thumbnails on the left or center of the page at 550px for visibility. For example, most melodies and scales should be displayed this way, while chords and simultaneities should be displayed to the right as small as reasonably visible.
A variety of musical terms is encountered in printed scores, music reviews, and program notes. Most of the terms are Italian, in accordance with the Italian origins of many European musical conventions. Sometimes, the special musical meanings of these phrases differ from the original or current Italian meanings.
Music examples are an obviously valuable and necessary addition to Wikipedia, often superior to text. These are both far more valuable and far more free than music samples being abstract categories applicable to multiple examples without any of the copyright or other law applicable to samples.
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".
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, or ...
For example, the C major scale, G major scale, and the major scale in all keys, are not identical but share transpositional equivalence in that the size of the intervals between scale steps is identical while pitches are not (C major has F ♮ while G major has F ♯). The major third and the minor sixth are not identical but share inversional ...
Music alignment and related synchronization tasks have been studied extensively within the field of music information retrieval. In the following, we give some pointers to related tasks. Depending upon the respective types of music representations, one can distinguish between various synchronization scenarios.