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A060527
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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 ratios of 8 musical tones: 8/7 16/11 5/4 4/3 3/2 8/5 11/8 7/4.
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11
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1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 15, 22, 26, 31, 41, 63, 72, 87, 109, 161, 202, 224, 270, 494, 612, 742, 764, 836, 1012, 1084, 1106, 1308, 1417, 1578, 3426, 4843, 6421, 6691, 10698, 12276, 18355, 19461, 21039, 22887, 25046, 26894, 31737, 33585, 35163
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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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 35163.
The numerical value of each term represents a musical scale based on an equal division of the octave. 12, for example, signifies the scale which is formed by dividing the octave into 12 equal parts.
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LINKS
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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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109 = 87 + the previous term 22. Again, 184417 = 121524 + the previous terms (54624 and 6691 and 1578).
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CROSSREFS
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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 01 2001
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STATUS
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approved
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