Archive for November, 2013


When is Harmonics a Science?

November 22, 2013

Marina Baldissera Pacchetti

Abstract: Aristotle bases the principle of harmony on the diesis being the indivisible unit that can be represented by number. This, in a passages of De Anima and De Sensu, sets aesthetic standards for ratios of numbers representing melodious concords (`symphonia’), which are demonstrated by arithmetic. This allows him to define harmonics to be one of the `more physical of the mathematical sciences’ because it shares the principle of indivisible unit number with arithmetic, and the demonstrations that provide knowledge about concords are arithmetical.

Aristoxenus says that this is not an appropriate treatment of harmonics and a proper explanation of what justifies aesthetic perception of consonant sounds. The principles of this science cannot rely on mathematics, but on movement with respect to pitch space. Harmonious sound arises from intervallic movement (to be defined), which is recognized only in terms of its phenomenology. He does not discard the use of arithmetic, but he rather sees it as a useful tool to calculate modes – as Barker says (note 50 GMW II p.135), Aristoxenus does not have a problem in including intervals smaller than a quarter tone (the diesis) in his `science of harmonics’. The inclusion of tones smaller than a quarter tone was problematic in explanations of concords for his predecessors (esp. Pythagoreans) and those who will come afterwards (Ptolemy 2C AD, Boethius 6C AD, Gafurio 15C AD, Zarlino 16C AD). Aristoxenus does not deny that the use of mathematics is not useful in harmonics, but as his `first principles’ are not mathematical, he seems to be able to accommodate standard calculations within his framework without incurring in inconsistencies in his philosophical framework.


The Early History of the Observatory on Cerro San Cristóbal: 1900-1929

November 1, 2013

Nora Mills Boyd

Abstract:   History tends to forget the patient and diligent episodes of cooperative science, which are eclipsed by the biographies of great individuals and their most brilliant discoveries and novel explanations.  This is too bad, since it means forgetting the careful cumulative work of long term research programs.  Resisting this trend, I look closely at the early history of astrophysics in Chile, focusing on the first few decades of an observatory originally established by astronomers from the Lick Observatory near Santiago, which today is called the Manuel Foster Observatory.  The observatory was initially funded as a short term “expedition” to collect the spectra of the approximately 200 brightest stars in the Southern sky with the aim of measuring the motion of the solar system with respect to the galaxy.  I will present some details of the physical construction and installation of the observatory and emphasize the motivation for the expedition.  I conclude by suggesting that this observatory emerges as a pivot-point on the eve of observational cosmology.