By Seymour Fink
This holistic method of the keyboard, in line with a legitimate realizing of the connection among actual functionality and musical objective, is a useful source for pianists and lecturers. Professor Fink explains his principles and demonstrates his leading edge developmental routines that set the pianist loose to specific the main profound musical principles. HARDCOVER.
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Additional info for Mastering Piano Technique: A Guide for Students, Teachers and Performers
Example text
Xi+1 then s(xi , v) ≥ s(xi+1 , v). Proof. t. t. s(xi+1 , w) ≥ s(xi+1 , v) then s(xi , v) > s(xi+1 , v). Otherwise, s(xi , v) = s(xi+1 , v). Ordering on Values. The two following properties establish the links between the natural ordering of values in D(xi ) and the minimum and maximum number of stretches in the sub-sequence starting from xi . Property 4. Let X = [x0 , x1 , . . , xn−1 ] be a sequence of variables and let i ∈ [0, n−1] be an integer. ∀v, w ∈ D(xi ) two well-ordered values, v ≤ w ⇒ s(xi , v) ≤ s(xi , w) + 1.
Cip−1 is initial (resp. final) if ci = 0 whenever s is not the initial (resp. a final) state of A. The number of states of # AR is the number of ordered partitions of p, and thus exponential in p. However, it is possible to have a compact encoding via constraints. Toward this, we use K + 1 sequences of p decision variables Sik in the domain {0, 1, . . , R} to encode the states of an arbitrary path of length K (the number of k columns) in # AR . For k ∈ {1, . . , K}, the sequence S0k , S1k , .
Proof. t. Increasing Nvalue. Otherwise, p(xi , v) is the exact minimum number of stretches among well-ordered instantiations I[x0 , . . , xi ] such that I[xi ] = v and s(xi , v) is the exact minimum number of stretches among well-ordered instantiations I[xi , . . , xn−1 ] such that I[xi ] = v. Thus, by construction p(xi , v) + s(xi , v)−1 is the exact minimum number of stretches among well-ordered instantiations I[x0 , x1 , . . , xn−1 ] such that I[xi ] = v. Let Dv ⊆ D be the set of domains such that all domains in Dv are equal to domains in D except D(xi ) which is reduced to {v}.