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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.
With; used in very many musical directions, for example con allegrezza (with liveliness), con calma (calmly lit. ' with calm '); (see also col and colla) con dolcezza See dolce con sordina or con sordine (plural) With a mute, or with mutes. Frequently seen in music as (incorrect Italian) con sordino, or con sordini (plural). concerto
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".
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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.