Music and the Making of Modern Science
72 Chapter 4 (1577), “ The arithmetician sees numbers in themselves, the musician and the algebraist indeed know numbers, but in ...
For Johannes Kepler, music was crucial to the emergence of a new astronomy. Kepler ’ s Harmonices mundi libri V ( Harmony of the ...
74 Chapter 5 musical traditions of W ü rttemberg Protestantism, in school and in church.^5 From age five, he practiced German ps ...
Kepler and the Song of the Earth 75 Kepler did not record his precise reaction to these developments but in a private letter wro ...
76 Chapter 5 musical experience of an amateur can be no less deep than that of a professional and, in Kepler ’ s time, amateurs ...
Kepler and the Song of the Earth 77 Boethius had assigned complex (hence less consonant) ratios to those intervals, according to ...
78 Chapter 5 on the Gregorian chant, Kepler notes that its underlying melodic structure outlines a triad as “ the skeleton of th ...
Kepler and the Song of the Earth 79 and manifold, and very nearly infinite. Since it is too much for my muscles, it would be mor ...
80 Chapter 5 centuries, Nature, always prodigal of herself, has at last brought forth, after an incubation of twice a thousand y ...
Kepler and the Song of the Earth 81 is a central feature of the planetary music itself. Since the planets move continuously in t ...
82 Chapter 5 me. Forsake me not, O Lord; O my God, be not far from me. ” As a devout Lutheran, he viewed the semitone of human s ...
Kepler and the Song of the Earth 83 pentagon, the hard third of 4:5 and the soft 5:6, moves minds, which are the images of God, ...
84 Chapter 5 Yet though geometry is archetypal, it depends on a sexual response that is mutual between partners. Thus, describin ...
Kepler and the Song of the Earth 85 and prescribed resolutions, individual to the six terms (as with vocal parts) and marking an ...
86 Chapter 5 emphasis, while maintaining harmonic continuity. ”^74 Though Kepler did not use this precise term, he clearly under ...
Kepler and the Song of the Earth 87 of the orbit of one planet can coincide at the same moment of time with all the states of th ...
88 Chapter 5 power of the bodies, ” which sway their souls away from uniformity and circularity to the elliptical orbits he disc ...
Ren é Descartes pioneered the “ new philosophy ” through his achievements in mathematics, natural science, and metaphysics, yet ...
90 Chapter 6 According to Beeckman, Descartes told him, “ Really you are the only one who has reawakened me from idleness. ”^4 B ...
Descartes’s Musical Apprenticeship 91 he finds the simpler lines of the rete more “ satisfying to the sense ” than the complex d ...
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