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A071831
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Frequency ratios for notes of C-major scale starting at c = 1 (numerators).
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7
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1, 9, 5, 4, 3, 5, 15, 2, 9, 5, 8, 3, 10, 15, 4, 9, 5, 16, 6, 20, 15, 8, 9, 10, 32, 12, 40, 15, 16, 18, 20, 64, 24, 80, 30, 32, 36, 40, 128, 48, 160, 60, 64, 72, 80, 256, 96, 320, 120, 128, 144, 160, 512, 192, 640, 240, 256, 288, 320, 1024, 384, 1280, 480, 512, 576, 640, 2048
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listen;
history;
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (15*x^27 + 9*x^22 + 15*x^20 + 5*x^16 + 9*x^15 + 15*x^13 + 3*x^11 + 5*x^9 + 9*x^8 - 15*x^6 - 5*x^5 - 3*x^4 - 4*x^3 - 5*x^2 - 9*x - 1) / (2*x^7 - 1). - Colin Barker, Feb 14 2014
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EXAMPLE
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The ratios are 1 (c), 9/8 (d), 5/4 (e), 4/3 (f), 3/2 (g), 5/3 (a), 15/8 (b); followed by these 7 numbers multiplied by successive powers of 2.
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MATHEMATICA
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Numerator[2^Floor[#/7]Rationalize[2^((-1+Floor[12(1+Mod[#, 7])/7])/12), 2^-6]]&/@Range[0, 70] (* Federico Provvedi, Feb 14 2014 *)
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PROG
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(PARI) r=[1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8]; for(n=0, 10, a=2^n*r; for(m=1, 7, print1(numerator(a[m]), ", "))) - Rick L. Shepherd, Apr 06 2006
(PARI) A071831(n)=numerator([1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8][n%7+1]*2^(n\7)) \\ M. F. Hasler, Jun 13 2012
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CROSSREFS
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KEYWORD
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nonn,frac,easy,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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