I think there’s a great beauty to having problems. That’s one of the ways we learn
The activities in Making Music Count will provide opportunities for you and your students to develop and explore assumptions, intuitions and understandings regarding the mathematics inherent in music. In this way we hope that math class will be awakened by the sounds of music with a particular emphasis in this case on the rhythmic aspects of music.
What is a BEAT, how is it generated, and how do we measure it? This Unit or Module linking math to music is created for teachers to use in their classrooms. It is both sequential in scope, yet it can also exist as stand alone activities for teachers to employ with regard to Ratio, Proportion & Durational Relationships. While exploring how composers and musicians play with and against time to create a variety rhythmic permutations, we will also be uncovering the underlying math embedded within these rhythmic patterns.
Consider, for example, that the word, RHYTHM, as used in everyday language and also in science usually refers to a series of events that recur at regular time intervals. But rhythm as a musical term is created and is uniquely dependent on the means composers develop to regulate, articulate, group, constrain, and confound the passing of musical time. This temporal structuring of music is probably the aspect to which we respond most instinctively and most directly.
Impromptu was developed to make the link between intuition and thinking more explicit. Impromptu, is a project oriented, multi-sensory computer-based music environment. It tempts students to use everyday mathematics such as proportion, ratio, fractions, and common multiples to discover the structures that organize mathematics. Rather than being an abstract idea, Impromptu makes it possible for users actually to hear and see the math happening.
- On this website you start with listening activities for you and your students in finding and grouping beats → Listening Activities
- There are several interactive lessons/modules uncovering the embedded mathematics in music with regard to ratio, proportion, multiplication, fractions and common multiples. → Lessons & Materials
- Templates and lessons for having your students import their favorite tunes into Impromptu and mathematically figuring out a rhythmic accompaniment → More Activities for Students
- How-To guides and videos for working with Impromptu → About Impromptu
- Information about Jeanne Bamberger’s creation of this approach to finding the math in music → Jeanne Bamberger’s Work
- Videos of Jeanne and students thinking and listening in action → Resources