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Search: id:A098295
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| A098295 |
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((3/2)^n)/2^a(n) lies in the half-open interval [1,2). |
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2
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| 0, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 23, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 31, 31, 32, 32, 33, 33, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 42, 42, 43, 43
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Stacking perfect fifths (the frequency ratio of a fifth is 3/2), a division by 2^a(n) leads the equivalent tone belonging to the first octave interval [1,2). For example, the third fifth, (3/2)^3, falls into the second octave. This means it lies in the interval [2^1,2^2)=[2,4). Hence ((3/2)^3)/2^1 belongs to the first octave, the interval [1,2).
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LINKS
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Pythagorean Scale.
Eric Weisstein's World of Music, Pythagorean Scale
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FORMULA
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a(n)= A0982949(n)-1, n>=1.
a(n)= ceiling(tau*n)-1 with tau:=ln(3)/ln(2)-1 =.584962501... n>=1.
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EXAMPLE
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(3/2)^12 lies in the eighth octave [2^7,2^8) and
((3/2)^12)/2^a(12)= ((3/2)^12)/2^7 = 3^12/2^19 = 531441/524288 = 1.01363...
belongs to the first octave [1,2). This ratio is called the pythagorean comma.
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CROSSREFS
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This sequence differs from A074840 for the first time at entry a(41)=23: A074840(41)= 24.
Sequence in context: A163464 A139327 A076905 this_sequence A074840 A064542 A076935
Adjacent sequences: A098292 A098293 A098294 this_sequence A098296 A098297 A098298
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004
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