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A060526
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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 six simple musical tones: 8/7 5/4 4/3 3/2 8/5 7/4.
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12
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1, 2, 3, 4, 5, 7, 9, 10, 12, 15, 19, 21, 22, 31, 53, 84, 87, 94, 99, 118, 130, 140, 171, 270, 410, 441, 612, 935, 966, 1053, 1106, 1277, 1547, 1578, 2954, 3125, 3566, 6691, 9816, 11664, 14789, 18355, 39835, 48545, 54624, 58190, 59768, 63334, 81689, 84814
(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 84814.
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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84 = 53 + the previous term 31. Again, 291152 = 103169 + the previous terms (84814 + 81689 + 11664 + 9816).
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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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