The present work proposes a multimedia tutorial (developed using the Java programming language and Adobe Flash), whose aim is to illustrate the main types of symmetry commonly noticeable in the Western musical paradigm. The multimedia tutorial enables the learner to explore different examples of the proposed symmetries, by various sensory points of view, integrating the traditional representation (staff), the representation by means of sound’s spectrogram and the direct perception of sequences of sounds used. Particular emphasis is given out in the tutorial to a scheme well-known to musicians: the circle of fifths. This argument makes it possible to highlight a direct relationship between musical symmetry and mathematical properties, as the group underlying the circle of fifths is the cyclic group Z12. This correlation is interactively illustrated in the tutorial either by using the metaphor of the analog clock with twelve hours on the face or by projecting the points of a constant pitch helix on a plane perpendicular to its axis.
MUSIC’S MATHEMATICAL GROUPS: A MULTIMEDIA TUTORIAL ON THE CIRCLE OF FIFTHS AND OTHER MUSICAL SYMMETRIES
BONANNO, Assunta Carmela;Sapia P.
2010-01-01
Abstract
The present work proposes a multimedia tutorial (developed using the Java programming language and Adobe Flash), whose aim is to illustrate the main types of symmetry commonly noticeable in the Western musical paradigm. The multimedia tutorial enables the learner to explore different examples of the proposed symmetries, by various sensory points of view, integrating the traditional representation (staff), the representation by means of sound’s spectrogram and the direct perception of sequences of sounds used. Particular emphasis is given out in the tutorial to a scheme well-known to musicians: the circle of fifths. This argument makes it possible to highlight a direct relationship between musical symmetry and mathematical properties, as the group underlying the circle of fifths is the cyclic group Z12. This correlation is interactively illustrated in the tutorial either by using the metaphor of the analog clock with twelve hours on the face or by projecting the points of a constant pitch helix on a plane perpendicular to its axis.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
