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Search: id:A054540
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| A054540 |
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A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to the six simple ratios of musical harmony: 6/5, 5/4, 4/3, 3/2, 8/5 and 5/3. |
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21
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| 1, 2, 3, 5, 7, 12, 19, 31, 34, 53, 118, 171, 289, 323, 441, 612, 730, 1171, 1783, 2513, 4296, 12276, 16572, 20868, 25164, 46032, 48545, 52841, 73709, 78005, 151714, 229719, 537443, 714321, 792326, 944040, 1022045, 1251764, 3755292, 3985011
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The sequence was found by a computer search of all of the equal divisions of the octave from 1 to over 3985011. There seems to be a hidden aspect or mystery here: what is it about the more and more harmonious equal temperaments that causes them to express themselves collectively as a perfect, self-accumulating recurrent sequence?
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FORMULA
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Stochastic 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.
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EXAMPLE
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34 = 31 + the earlier term 3. Again, 118 = 53 + the earlier terms 34 and 31.
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CROSSREFS
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Cf. A001149, A018065, A001856, A002858, A007335, A060525-A060527.
Sequence in context: A048808 A013983 A060986 this_sequence A117537 A137713 A018065
Adjacent sequences: A054537 A054538 A054539 this_sequence A054541 A054542 A054543
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KEYWORD
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nonn
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AUTHOR
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Mark William Rankin (MarkRankin95511(AT)Yahoo.com), Apr 09 2000; Dec 17 2000
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