25 OCT 2017 by ideonexus

 Canons and Fugues

The idea of a canon is that one single theme is played against itself. This is done by having "copies" of the theme played by the various participating voices. But there are means' ways to do this. The most straightforward of all canons is the round, such as "Three Blind Mice", "Row, Row, Row Your Boat", or " Frere Jacques". Here, the theme enters in the first voice and, after a fixed time-delay, a "copy" of it enters, in precisely the same key. After the same fixed time-delay in the second v...
Folksonomies: puzzles math music mathematics
Folksonomies: puzzles math music mathematics
  1  notes

Bach left his Musical Offering unfinished as puzzles for King Frederick to figure out.

21 JAN 2014 by ideonexus

 Knowing the World Requires Mathematics

For the things of this world cannot be made known without a knowledge of mathematics. For this is an assured fact in regard to celestial things, siDce two important sciences of mathematics treat of them, namely theoretical astrology and practical astrology. The first. . . gives us definite information as to the number of the heavens and of the stars, whose size can be comprehended by means of instruments, and the shapes of all and their magnitudes and distances from the earth, and thicknesses...
Folksonomies: mathematics knowledge
Folksonomies: mathematics knowledge
  1  notes

Everything can be reduced to mathematics.