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A061920
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.
2
1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 19, 22, 31, 34, 41, 53, 118, 171, 289, 323, 376, 441, 494, 559, 612, 1171, 1783, 2513, 3684, 4296, 12888, 16572, 20868, 25164, 44249, 48545, 52841, 57137, 69413, 73709, 78005, 151714, 229719, 307724, 537443, 714321
OFFSET
1,2
COMMENTS
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.
FORMULA
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.
EXAMPLE
118 = 53 + [34 + 31]; Again, 69413 = 57137 + [4296 + 3684 + 2513 + 1783].
KEYWORD
nonn
AUTHOR
Mark William Rankin (MarkRankin95511(AT)yahoo.com), May 15 2001
STATUS
approved