
 Modular arithmetic  LearnThis.Info Enclyclopedia (Site not responding. Last check: ) 
  Modular arithmetic, first systematically studied by Carl Friedrich Gauss at the end of the eighteenth century, is applied in number theory, abstract algebra, cryptography, and visual and musical art. 
  In music, because of octave and enharmonic equivalency (that is, pitches in a 1/2 or 2/1 ratio are equivalent, and C# is the same as Db), modular arithmetic is used in the consideration of the twelve tone equally tempered scale, especially in twelve tone music. 
  In abstract algebra, it is realized that modular arithmetic is a special case of forming the factor ring of a ring modulo an ideal. 
 encyclopedia.learnthis.info /m/mo/modular_arithmetic.html (1898 words) 
