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A254531 a(n) is the position of the piano key whose frequency is closest to n Hz, start with A0 = the 1st key.

%I A254531 #17 Oct 14 2019 11:51:51
%S A254531 1,1,2,3,3,4,4,5,5,6,6,7,7,7,8,8,9,9,10,10,10,11,11,11,12,12,12,13,13,
%T A254531 13,14,14,14,15,15,15,15,16,16,16,16,17,17,17,17,18,18,18,18,19,19,19,
%U A254531 19,19,20,20,20,20,21,21,21,21,21,22,22,22,22,22,22
%N A254531 a(n) is the position of the piano key whose frequency is closest to n Hz, start with A0 = the 1st key.
%H A254531 Reinhard Zumkeller, <a href="/A254531/b254531.txt">Table of n, a(n) for n = 27..4308</a>
%H A254531 Wikipedia, <a href="http://en.wikipedia.org/wiki/Piano_key_frequencies">Piano Key Frequencies</a>
%H A254531 Wikipedia, <a href="http://en.wikipedia.org/wiki/Twelfth_root_of_two">Twelfth root of two</a>
%H A254531 <a href="/index/Mu#music">Index entries for sequences based on music</a>
%F A254531 a(n) = round(12*log_2(n/440)) + 49, 27 <= n <= 4308.
%F A254531 a(A214832(k)) = k for k = 1..88.
%e A254531 .     | Frequency [Hz] | Piano key | Pitch
%e A254531 .   i | f = A079731(i) |      a(f) |
%e A254531 .  ---+----------------+-----------+------
%e A254531 .   0 |             28 |         1 |  A0
%e A254531 .   1 |             55 |        13 |  A1
%e A254531 .   2 |            110 |        25 |  A2
%e A254531 .   3 |            220 |        37 |  A3
%e A254531 .   4 |            440 |        49 |  A4    A440
%e A254531 .   5 |            880 |        61 |  A5
%e A254531 .   6 |           1760 |        73 |  A6
%e A254531 .   7 |           3520 |        85 |  A7 .
%o A254531 (Haskell)
%o A254531 a254531 = (+ 49) . round . (* 12) . logBase 2 . (/ 440) . fromIntegral
%o A254531 (PARI) a(n) = round(12*log(n/440)/log(2))+49 \\ _Jianing Song_, Oct 14 2019
%Y A254531 Cf. A214832, A079731, A010774.
%K A254531 nonn,fini,full
%O A254531 27,3
%A A254531 _Reinhard Zumkeller_, Feb 01 2015
%E A254531 Corrected by _Jianing Song_, Oct 14 2019