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Search: id:A060233
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| A060233 |
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A list of equal temperaments (equal divisions of the octave) whose nearest scale steps are closer and closer approximations to six complementary pairs of ratios which generate simple musical tones (scale steps): 8/7 and 7/4, 6/5 and 5/3, 16/13 and 13/8, 5/4 and 8/5, 4/3 and 3/2, and 11/8 and 16/11. |
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6
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| 1, 2, 3, 4, 6, 7, 9, 10, 15, 19, 22, 24, 26, 31, 37, 41, 46, 50, 53, 72, 84, 87, 130, 137, 140, 171, 183, 217, 224, 270, 494, 764, 851, 1038, 1282, 1308, 1578, 2190, 2684, 3395, 4843, 5004, 5585, 6079, 8269, 14124, 14618, 17302, 20203, 22887, 31737
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The sequence was found by a computer search of all the equal divisions of the octave from 1 to over 31737. The numerical value of each term represents a musical scale based on an equal division of the octave. 19, for example, signifies the scale which is formed by dividing the octave into 19 equal parts.
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FORMULA
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Recurrence: The next term equals the current term plus one or more of the 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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6 = 4 + the previous term 2. Again, 48545 = 46625 + the previous terms (1578 + 270 + 72).
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CROSSREFS
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A054540, A060525, A060526, A060527, A060528, A060529, A001149, A000045.
Sequence in context: A088572 A071689 A076679 this_sequence A026468 A056176 A087072
Adjacent sequences: A060230 A060231 A060232 this_sequence A060234 A060235 A060236
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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 14 2001
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