Search results for "Pythagorean theorem"
showing 3 items of 3 documents
Fuzzy tuning systems: the mathematics of musicians
2005
We present some mathematical properties which determine tuning methods. We introduce the concept of fuzzy tuning systems and we analyze four of the systems coexisting within the current orchestras: Pythagorean, Just Intonation, Holder's and Equal Temperament systems. We show that the theoretical and practical tuning methods are the same. We introduce the idea of compatibility between tuning systems and we give some sufficient conditions to determine an appropriate number of notes into which the octave must be divided.
Hermann weyl, the reluctant revolutionary
2003
“Brouwer – that is the revolution!” – with these words from his manifesto “On the New Foundations Crisis in Mathematics” (Weyl 1921) Hermann Weyl jumped headlong into ongoing debates concerning the foundations of set theory and analysis. His decision to do so was not taken lightly, knowing that this dramatic gesture was bound to have immense repercussions not only for him, but for many others within the fragile and politically fragmented European mathematical community. Weyl felt sure that modern mathematics was going to undergo massive changes in the near future. By proclaiming a “new” foundations crisis, he implicitly acknowledged that revolutions had transformed mathematics in the past, …
Correcting ēthos and Purifying the Body. Musical Therapy in Iamblichus’ De vita pythagorica
2015
The tradition relating to the Pythagoreans and music therapy is most widely attested in two Neoplatonic works, Porphyry’s The Life of Pythagoras, and Iamblichus’ On the Pythagorean Way of Life. Although the chronological distance from the early Pythagoreans makes their accounts controversial, they offer interesting evidence on the beneficial effects of music. Iamblichus, whose work will be focused on in this paper, describes the effects of music on health through the notion of catharsis, which he often links with musical ēthos. The latter is not in fact attested before Plato, but Iamblichus, presenting Pythagoras in Platonic terms, emphasizes the importance he gives to the improvement of th…