And Yet It Is Heard: Musical, Multilingual and Multicultural - download pdf or read online
By Tito M. Tonietti
We deliver into complete gentle a few excerpts on musical matters that have been previously scattered through the most famed clinical texts. the most medical and musical cultures outdoor of Europe also are considered. the 1st and most crucial estate to underline within the medical texts tested this is the language they're written in. which means our multicultural background of the sciences unavoidably additionally turns into a evaluation of some of the dominant languages utilized in the several historic contexts. during this quantity, the historical past of the advance of the sciences is informed because it occurred in genuine contexts, no longer in an alienated perfect world.
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Extra resources for And Yet It Is Heard: Musical, Multilingual and Multicultural History of the Mathematical Sciences - Volume 1
15 For some, the field of reasoning was to be limited to Euclidean geometry, because the rest would not be germane to the desired solution. Subsequently, however, Euclid’s incomplete argument was concluded by the arrival of algebra and group theory. 16 In the Meno, Plato described Socrates teaching a boy-slave. He led him to recognize, by himself, that twice the area of the square constructed on a given line is obtained by constructing a new square on the diagonal of the first one. We can interpret the reasoning of Socrates-Plato as an argument equivalent to the theorem of Pythagoras in the case of isosceles right-angled triangles.
But this is not possible, because it would imply that all epimoric ratios and their ratios are consonant, and so, for example, even the tone 9:8 would become consonant. For Tannery, this error is sufficient to prove that the treatise on music was not by Euclid. 32 After all, errors are commonly found in the work of other famous scientists. 33 In reality, they are often lapsus not noticed during the reasoning, which reveal aspects of their personality that would otherwise remain hidden. They are a precious help to better understand events that are significant for the evolution of the sciences, and not just useless details which become acts of lèse-majesté in the pages of hostile historians.
When he is mentioned, writers admit that they were forced to include him because in antiquity, the theory of music was a part of the quadrivium mentioned above. ”66 This judgement stems from a widespread prejudice. It should be underlined, however, that this Greek from Tarentum left us some important books on harmony and musical rhythm. They continue to be particularly interesting, also for historians of the mathematical 63 Euclid 1956, III, pp. 503–509. Euclid 1956, I, p. v. 65 Tonietti 1982b, pp.
And Yet It Is Heard: Musical, Multilingual and Multicultural History of the Mathematical Sciences - Volume 1 by Tito M. Tonietti