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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.
Removing two notes for every one kept creates a new truncated mode of limited transposition. C F ♯ Keeping two notes for every one removed creates another truncated mode of limited transposition. C E F ♯ A ♯ Only Messiaen's mode 7 and mode 3 are not truncated modes: the other modes may be constructed from them or from one or more of their ...
In instrumental music, a style of playing that imitates the way the human voice might express the music, with a measured tempo and flexible legato. cantilena a vocal melody or instrumental passage in a smooth, lyrical style canto Chorus; choral; chant cantus mensuratus or cantus figuratus (Lat.) Meaning respectively "measured song" or "figured ...
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Another cause for disturbance of the spherical wavefront is the truncation effect. Because the resulting wavefront is a composite of elementary waves, a sudden change of pressure can occur if no further speakers deliver elementary waves where the speaker row ends. This causes a 'shadow-wave' effect.
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In music, form refers to the structure of a musical composition or performance.In his book, Worlds of Music, Jeff Todd Titon suggests that a number of organizational elements may determine the formal structure of a piece of music, such as "the arrangement of musical units of rhythm, melody, and/or harmony that show repetition or variation, the arrangement of the instruments (as in the order of ...
In both the global and local cases, the concept of a strict extremum can be defined. For example, x ∗ is a strict global maximum point if for all x in X with x ≠ x ∗, we have f(x ∗) > f(x), and x ∗ is a strict local maximum point if there exists some ε > 0 such that, for all x in X within distance ε of x ∗ with x ≠ x ∗, we ...