%I A089911
%S A089911 0,1,1,2,3,5,8,1,9,10,7,5,0,5,5,10,3,1,4,5,9,2,11,1,0,1,1,2,3,5,8,1,9,
%T A089911 10,7,5,0,5,5,10,3,1,4,5,9,2,11,1,0,1,1,2,3,5,8,1,9,10,7,5,0,5,5,10,3,
               1,
%U A089911 4,5,9,2,11,1,0,1,1,2,3,5,8,1,9,10,7,5,0,5,5,10,3,1,4,5,9,2,11,1,0,1,1
%N A089911 Fibonacci(n) mod 12.
%C A089911 Sequence has been applied by several composers to pitch structure in 
               12 tone equal temperament. The complete Fibonacci mod 12 system (a 
               set of 10 periodic sequences) exhausts all possible ordered dyads; 
               that is, every possible combination of two pitches is found in these 
               sets.
%D A089911 A. P. Shah, Fibonacci Sequence Modulo m, Fibonacci Quarterly, Vol. 6 
               (1968), pp. 139-141.
%D A089911 D. D. Wall, Fibonacci Series Modulo m, American Mathematical Monthly, 
               Vol. 67 (1960), pp. 525-532.
%H A089911 R. Knott, <a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/
               fib.html">Fibonacci Numbers and the Golden Section</a>
%H A089911 M. Renault, <a href="http://www.math.temple.edu/~renault/fibonacci/fib.html">
               The Fibonacci Sequence Modulo M</a>
%F A089911 Has period of 24, restricted period 12 and multiplier 5.
%F A089911 F(n) mod 12 = F(n-1) + F(n-2), F(0) = 0, F(1) = 1
%p A089911 with(combinat,fibonacci); A89911 := proc(n) fibonacci(n) mod 12; end;
%Y A089911 Cf. A000045, A003893.
%Y A089911 Sequence in context: A093086 A093092 A031111 this_sequence A098978 A111301 
               A096320
%Y A089911 Adjacent sequences: A089908 A089909 A089910 this_sequence A089912 A089913 
               A089914
%K A089911 nonn
%O A089911 0,4
%A A089911 Casey Mongoven (cm(AT)caseymongoven.com), Nov 14 2003
%E A089911 More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 15 
               2003