A MATHEMATICA NOTEBOOK ABOUT ANCIENT GREEK MUSIC AND MATHEMATICS

Luigi Borzacchini and Domenico Minunni (Dept. of Mathematics, University of Bari, Italy)
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Abstract

It is known that Information and Communication Technology are becoming increasingly useful in teaching mathematics, but so far it has not been considered as well that this technology, and symbolic calculus languages as Mathematica or Maple in particular, can pave the road to new connections between mathematics, computer and humanities.
Music and Mathematics have always been deeply connected. At the beginning of our mathematics there is Pythagorean mathematics that was first and foremost music-driven, and the end of ancient music was connected to the equal-temperament, linked to the idea of real number.
We give an outline of a Mathematica notebook about ancient Greek Music, that includes a short introduction to mathematical music theory, a part about Greek mathematical music theory and the difference between Pythagorean and equal-tempered tuning, a system to play ancient music, in which we can choose the system (enharmonic, chromatic, diatonic) and the mode (Doric, Lydian, Phrygian, etc.), and a short report about the different theories (geometric, arithmetic and music-theoretic) about the discovery of incommensurability. It is noteworthy that playing with this system the first stasimo of Euripides’ tragedy Orestes, both in well-tempered
and Pythagorean tuning, usually all participants recognize a difference.

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