Titlebook: Cool Math for Hot Music; A First Introduction Guerino Mazzola,Maria Mannone,Yan Pang Textbook 2016 Springer International Publishing Switze

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Contend

污秽

1868-0305 as harmony, counterpoint, tuning), composition (e.g., classical combinatorics, dodecaphonic composition), and gestural performance. The book includes many illustrations, and exercises with solutions..978-3-319-82698-1978-3-319-42937-3Series ISSN 1868-0305 Series E-ISSN 1868-0313

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Postulate

Universal Propertiesing arrows. We also introduce exponentials and subobject classifiers. These concepts are broadly used in modern mathematics, because they describe constructions that appear everywhere in mathematical creativity.

minaret

Recursionposed to be defined, and we use the concept for . to define the concept for .+1. Therefore, it is defined for all natural numbers .. This is the idea of recursion, namely the definition by induction. We will prove that this mathematical process is possible. We then apply recursion to create musical

minaret

外星人

Real Numbersor . = .. But there are many other equations, especially dealing with approximations in music theory, that cannot be solved with Z or Q. In this chapter we apply the above philosophy to find solutions of such problems, namely the real numbers.

富足女人

Guerino Mazzola,Maria Mannone,Yan PangBased on authors‘ experience teaching mathematics to music theorists.Presents ideas in a critical manner, highlighting problems with earlier teaching approaches.Includes many illustrations and exercis

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