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%I #2 Feb 27 2009 03:00:00
%S 1,2,3,4,5,6,7,8,10,12,19,22,31,34,41,53,118,171,289,323,376,441,494,
%T 559,612,1171,1783,2513,3684,4296,12888,16572,20868,25164,44249,48545,
%U 52841,57137,69413,73709,78005,151714,229719,307724,537443,714321
%N A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the 7 pairs of complementary target ratios needed to express the 12 unsymmetrical steps of the untempered (Just Intonation) scale known as the Duodene: 3/2 and 4/3, 5/4 and 8/5, 6/5 and 5/3, 9/8 and 16/9, 10/9 and 9/5, 16/15 and 15/8 and 45/32 and 64/45.
%C The sequence was found by a computer search of all the equal divisions of the octave from 1 to 714321. The numerical value of each term represents a musical scale based on an equal division of the octave. The term 12, for example, signifies the scale which is formed by dividing the octave into 12 equal parts.
%F Recurrence Rule: The next term equals the current term plus one or more previous terms: a(n+1) = a(n) + a(n-x)... + a(n-y)... + a(n-z), etc.
%e 118 = 53 + [34 + 31]; Again, 69413 = 57137 + [4296 + 3684 + 2513 + 1783].
%Y A054540, A060525, A060526, A060527, A060528, A060529, A060233, A061918, A061919.
%K nonn
%O 1,2
%A Mark William Rankin (MarkRankin95511(AT)yahoo.com), May 15 2001
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