Emblems of Mind: The Inner Life of Music and MathematicsFrom Kepler and the music of the spheres to Einstein and his violin, music and mathematics seem to share a strong relationship. This pathbreaking book seeks to unravel the mystery at the heart of that relationship. Illustrations. Index. |
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Page 162
... proportion became central , the rectangle and ratio became a reference point for painters and architects . Leonardo da Vinci's friend Luca Pacioli called the Divine Proportion . And later Johannes Kepler made it central even in his ...
... proportion became central , the rectangle and ratio became a reference point for painters and architects . Leonardo da Vinci's friend Luca Pacioli called the Divine Proportion . And later Johannes Kepler made it central even in his ...
Page 165
... Proportion is a power- ful example of eurythmy because of the clear relationship it displays between the whole and the parts . It may even have been a Pythago- rean belief that the proportion extended from the human body ( which , as ...
... Proportion is a power- ful example of eurythmy because of the clear relationship it displays between the whole and the parts . It may even have been a Pythago- rean belief that the proportion extended from the human body ( which , as ...
Page 167
... proportion found . Mathe- matics is always using analogy and proportion in its argument . In fact , when faced with a form - whether it is musical or mathematical or even in the physical world — we attempt to make analogies among the ...
... proportion found . Mathe- matics is always using analogy and proportion in its argument . In fact , when faced with a form - whether it is musical or mathematical or even in the physical world — we attempt to make analogies among the ...
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Common terms and phrases
Abraham Robinson abstract aesthetic analogy arpeggio asserted attempt Bach Bach's beauty become Beethoven's begin calculation Carl Friedrich Gauss century chord Classical close composition concepts connections constructed create define elements equivalent eurythmy example experience exploration feel fugue fundamental fundamental group G. H. Hardy geometry gesture harmony hear infinite number infinitesimal integers interpretation intervals irrational numbers listen loop mapping mathe mathematical proof mathematician mathematics and music matics mean measure melodic metaphor Milton Babbitt mind move movement music and mathematics musical space nature notes notion objects overtones pattern phrase physical pitches play precisely prelude proof proportion ratio realm relations relationship reveal rhythm seemingly seems sense similar simple Socrates sonata sonata form sort sound string structure surface Symphonie Fantastique tensions theme theory things thinking tion tonal music tones topology transformation truth understanding universe variation vibrating voice Well-Tempered Clavier wine