## Musical plane

*Designed and produced by the Spanish CoI*

The c-book unit «Musical Plane» was designed by five members of the Spanish CoI, from Math Secondary school teachers, researchers in Maths Education, to a musician.

The main aim of this c-book unit is to promote an inter-disciplinary study between Music and Mathematics. The main mathematical content addressed is the study of the line and piecewise-defined linear functions, its mathematical characteristics and their variety of representations. Points, lines (and other forms) will be drawn in a musical plane and then analysed their musical meaning.

This c-book unit is structured in three parts: (1) The main objective of part 1 is to get used to the musical plane and to find out its structure. The mathematical challenge is to define an appropriate way to identify points in the plane. There is an analogy between the Cartesian plane and the musical plane. (2) The second part focuses on the understanding of a line with multiple representations such as the ones offered by the musical plane, the Cartesian plane or its algebraic representation. This part also links each of the elements of a line in the Cartesian plane (slope and y-intercept) with its musical interpretation. (3) The third part introduces different patterns one can find in a melody and its mathematical representation. Different piecewise-defined functions are studied and listened.

Available at: http://mc2dme.appspot.com/dwo/dwo.jsp?profile=78&language=en&courseViewNr=5656156181626880