Mastering Musical Intervals - 144 Cyclic Symmetric Patterns and Scales

This book is, in a way, a continuation of my undergraduate Thesis of the Bachelor of Music course

at the Federal University of Rio Grande do Sul - UFRGS.

The genesis of this work is to study,

understand and master musical intervals in a broad and complete way.

Cyclic patterns have always been present in nature, as well as in the most diverse civilizations and

cultures and the human being has developed the ability to recognize, absorb, manipulate, organize and

express different types of patterns. They are regular, symmetrical or asymmetrical shapes that occur in

different contexts and can often be mathematically modeled, natural patterns include trees, circles, waves,

mosaics, meanders, spirals, stripes and more details and shapes.

The search for recognition and understanding of these patterns is a fundamental premise of human existence

and survival, so man has been trying to understand and use these patterns in multiple ways. It is up to us

students and artists to look for the construction - or deconstruction - of these patterns, colors and sensations to

express the most diverse feelings, shapes and images that life is capable of providing us.