Musical Scales and their Mathematics: 14 (Mathematics Study Resources, 14)

The Musical Scale - a Triviality or a Problem?This book examines this provocative question.It soon becomes clear that combining tones into “harmonious” tonal systems represents a challenge of unexpected complexity, encompassing a remarkably large number of interconnected problems. Why does a scale have precisely 12 tones? And could there be others?Aren't 12 perfect fifths always exactly the same as 7 octaves?What exactly is "consonance" or when are intervals "pure," when "impure"?What is meant by "temperament characteristic" in relation to whole and half tones?What does "old tuning" mean - and is there a "new" one that differs from it, and if so, what exactly are the differences?and many similar ones quickly show that their answers not only require well-considered justifications but are also closely interconnected.In this examination, "mathematics" plays a key role.Starting with "simple proportions and numerical relationships", a veritable network emerges, in which both the methods of