![]() Finally, his knowledge-making practices are a conflation of his predominant careers as an experimentalist and geometer. Further, Hooke’s work is a cohesive whole centred on his studies of the similitudes between vibrating phenomena. ![]() By investigating Hooke’s studies within the context of his matter theory, I show that, in an epistemological inversion, Hooke used optical instruments to shift frames of reference from the microscopic to the celestial and vice versa for his knowledge production. Specifically, I focus on Hooke’s studies of vibrating bodies and vibrations, and his practical geometry. ![]() I attempt to show how Hooke addressed these challenges by reassessing and reconfiguring the role of traditional Euclidean geometry, and reformulating practical-geometrical definitions to create a geometry that could demonstrate the spring law. I argue that artificial instruments and apparatuses capable of magnifying and measuring never-before-seen minute bodies and motions also made the creation of a novel geometry necessary. This thesis reconstructs Hooke’s production of congruity and incongruity, and the spring law, analysing the inversions, reversals and paradoxes moulding his knowledge-making practices. Namely, that harmonious and discordant forces unify, shape and separate vibrating matter. Lectures de Potentia Restitutiva or Of Spring contains not only experimental and geometrical demonstrations of the spring law (which mutated into Hooke’s law after his time), but also a principle at the heart of his dynamic matter theory – Congruity and Incongruity. In 1678, Robert Hooke published a treatise on his metaphysics of vibration. The principal subject of the present work, originally begun as my personal notes, is an analysis and commentary on the specific contents of the manuscript pages of Newton’s discourse of strings sounding along with the ideas he later applied to colors compounding, and including a brief look at the topic of ‘rational symmetries’ in ancient tuning systems. Little of Newton’s early ‘musical’ interests were pursued in later years, although, significantly, he incorporated canonical concepts into his new theories of light, colors and visual perception, observing that in the refracted spectrum of sunlight the intervals (distances, spaces) occupied by the principal … “… prismatick Colours, red, orange, yellow, green, blue, indigo, violet,” … “in proportion as the Differences of the Lengths of a Monochord which sound the Tones in an Eight, sol, la, fa, sol, la, mi, fa, sol,” “proportional to … the Numbers, 1, 8/9, 5/6, 3/4, 2/3, 3/5, 9/16, 1/2, which express the Lengths of a Monochord sounding the Notes in an Eighth … and so to represent the Chords of the Key, and of a Tone, a third Minor, a fourth, a fifth, a sixth Major, a seventh and an eighth above that Key” (Newton, Opticks, 1704). Newton’s understanding of musical tuning was grounded in the ancient discipline of canonics (after Euclid, Sectio canonis), a ‘metrical geometry’ of a single tensioned string (monochord), whose techniques were widely known to and practiced by the natural scientists of the 17th century. ![]() His study notes and exercises toward that goal covered some nineteen pages of manuscripts, displaying a guileless curiosity, idiosyncratic constructions and a facility with diverse mathematical tools. He proposed to append to that essay a more mathematically oriented “discourse of ye motion of strings sounding … & of ye Logarithmes of those strings, or distances of yr notes” pertaining to a particular system of musical tuning. 1665) in which he addressed mostly musicological topics: rules of tonal composition, modes, voice, affects, consonance/dissonance. While a student at Cambridge University young Isaac Newton penned, but did not publish, a brief essay “Of Musick” (c.
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