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Betrachtung des Gegenstandes in Otto Dix' Radierzyklus quot;Der Kriegquot; (German Edition)

[audiobook] Betrachtung des Gegenstandes in Otto Dix' Radierzyklus quot;Der Kriegquot; (German Edition) by Cordula Gries in Arts-Photography

Description

Taking a "music first" approach; Gareth E. Robertsrsquo;s From Music to Mathematics will inspire students to learn important; interesting; and at times advanced mathematics. Ranging from a discussion of the geometric sequences and series found in the rhythmic structure of music to the phase-shifting techniques of composer Steve Reich; the musical concepts and examples in the book motivate a deeper study of mathematics.Comprehensive and clearly written; From Music to Mathematics is designed to appeal to readers without specialized knowledge of mathematics or music. Students are taught the relevant concepts from music theory (notation; scales; intervals; the circle of fifths; tonality; etc.); with the pertinent mathematics developed alongside the related musical topic. The mathematics advances in level of difficulty from calculating with fractions; to manipulating trigonometric formulas; to constructing group multiplication tables and proving a number is irrational. Topics discussed in the book include? Rhythm ? Introductory music theory ? The science of sound ? Tuning and temperament? Symmetry in music ? The Bartoacute;k controversy ? Change ringing ? Twelve-tone music? Mathematical modern music ? The Hemachandrandash;Fibonacci numbers and the golden ratio? Magic squares ? Phase shiftingFeaturing numerous musical excerpts; including several from jazz and popular music; each topic is presented in a clear and in-depth fashion. Sample problems are included as part of the exposition; with carefully written solutions provided to assist the reader. The book also contains more than 200 exercises designed to help develop studentsrsquo; analytical skills and reinforce the material in the text. From the first chapter through the last; readers eager to learn more about the connections between mathematics and music will find a comprehensive textbook designed to satisfy their natural curiosity.


2014-07-10 2014-07-10File Name: B01BPW9FN4


Review
0 of 0 people found the following review helpful. The unidentified ferry on the cover is our beloved VASHON ...By B. J. DensmoreThe unidentified ferry on the cover is our beloved VASHON which was launched in 1930; transferred to the San Juan Islands in 1941; and served county residents so well for many years.2 of 2 people found the following review helpful. The Definitive History of Orcas IslandBy LanceIve lived on Orcas Island for about 10 years and this is the first; and now the definitive; book about Orcas Island and its history. The collection of photos (historical in nature) is amazing ... thankfully folks have held onto those for the Historical Museum to use. I work at the Orcas Island Chamber of Commerce and I recommend this book to visitors (and locals) who are looking for a perfect gift about Orcas Island.2 of 2 people found the following review helpful. Its like a family albumBy Margaret CatherineThis book is a delight. In addition to enjoying the pictorial history; I also found a picture of my aunt (a member of the 1927 Girls Basketball Team) in her stylish bloomers (!) and two of my cousins as members of a volunteer fire department.

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