Music and the Making of Modern Science
52 Chapter 3 between the Julian calendar and the observed astronomical occurrences of solstices and equinoxes.^33 Zarlino thus e ...
Moving the Immovable 53 composed. But the reverse channel of influence is also possible: the teenaged Galileo may have learned f ...
54 Chapter 3 Copernican system all fixed stars, also intrinsically luminous bodies like the sun, are eternally at rest. ”^39 Gal ...
A century after the immovable center began to move, another seeming impossibility began to seem necessary: a new concept of numb ...
56 Chapter 4 both rational and irrational quantities.^2 Vi è te ’ s reading of Diophantus and Pappus, along with his own innovat ...
Hearing the Irrational 57 Figure 4.1 Jacques Lef è vre d ’ É taples ’ s diagram from Elementa musicalia (1496), demonstrating th ...
58 Chapter 4 It is properly debated whether irrational numbers are true numbers or fictions. For if we lack rational numbers in ...
Hearing the Irrational 59 rest of his vast output. Though Cardano ’ s De musica was published only in his Opera omnia (1663), am ...
60 Chapter 4 rule ” shows how to find what he calls the “ closest approximation ” to solving an equation through finding the int ...
Hearing the Irrational 61 extensive use of consecutive semitones, sometimes to evoke greater sensuality or expres- sivity ( ♪ so ...
62 Chapter 4 Figure 4.3 Portrait of Nicola Vicentino, aged forty-four, as the frontispiece of his book Ancient Music Adapted to ...
Hearing the Irrational 63 the true status of those ancient genera in contemporary music? The broader implications of this questi ...
64 Chapter 4 Figure 4.4 The sentence passed against Vicentino, as recorded in his book. ...
Hearing the Irrational 65 A B Figure 4.5 Vicentino ’ s archicembalo. (a) Detailed view of the split keys of an archicembalo reco ...
66 Chapter 4 What follows, then, is not a digression into antiquity but an account of how ancient prob- lems returned to life. B ...
Hearing the Irrational 67 with the sides of another square built on that diagonal).^38 If indeed Aristoxenus built tone and semi ...
68 Chapter 4 “ more sweet and smooth than the other two genera. ”^39 His emphasis on experience means that musical practice is t ...
Hearing the Irrational 69 chromatic genus, the latent problems hidden in the diatonic come forward sufficiently to cause “ disru ...
70 Chapter 4 private diversions of lords and princes. ”^47 Thus Vicentino brought his polemic on behalf of enharmonic music not ...
Hearing the Irrational 71 Figure 4.7 Zarlino ’ s geometric approach ( Sopplimenti musicali , 1588) to fretting a lute in equal t ...
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